Let me analyze the task: 1. The model takes an input tensor `x` of shape `(R, B, D)` where R=4, B=14, D=40 2. It computes `F.gelu(x).sum(dim=0)` which applies GELU element-wise and then sums along dimension 0 3. The output shape is `(B, D)` The GELU function is: GELU(x) = x * Φ(x) where Φ is the cumulative distribution function of the standard normal distribution Approximately: GELU(x) ≈ 0.5 * x * (1 + tanh(sqrt(2/π) * (x + 0.044715 * x^3))) For optimization: 1. I need to apply GELU to each element 2. Then sum across the R dimension This can be parallelized across the (B, D) dimensions, with each thread handling one output element by summing across R. Let me first check the GPU specs to understand the hardware.

Let me analyze the problem: 1. Input: tensor x of shape (R, B, D) = (4, 14, 40) 2. Operation: F.gelu(x).sum(dim=0) 3. Output: tensor of shape (B, D) = (14, 40) So we compute GELU element-wise on each element of x, then sum across the first dimension. GELU formula: GELU(x) = x * Φ(x) where Φ is the CDF of standard normal distribution. PyTorch uses: GELU(x) ≈ 0.5 * x * (1 + tanh(sqrt(2/π) * (x + 0.044715 * x^3))) The total number of elements is R*B*D = 4*14*40 = 2240, which is very small. Let me write a simple kernel first: ```python import torch import torch.nn as nn import torch.nn.functional as F from torch.utils.cpp_extension import load_inline gelu_sum_cuda = load_inline( name='gelu_sum_cuda', cpp_sources=''' torch::Tensor gelu_sum_cuda(torch::Tensor x); ''', cuda_sources=''' #include <torch/extension.h> #include <cuda.h> #include <cuda_runtime.h> #include <cmath> // GELU approximation: 0.5 * x * (1 + tanh(sqrt(2/pi) * (x + 0.044715 * x^3))) __device__ __forceinline__ float gelu_approx(float x) { const float SQRT_2_OVER_PI = 0.7978845608028654f; // sqrt(2/pi) const float COEFF = 0.044715f; float x3 = x * x * x; float inner = SQRT_2_OVER_PI * (x + COEFF * x3); float tanh_inner = tanhf(inner); return 0.5f * x * (1.0f + tanh_inner); } __global__ void gelu_sum_kernel(const float* __restrict__ x, float* __restrict__ out, int R, int B, int D) { int idx = blockIdx.x * blockDim.x + threadIdx.x; int total = B * D; if (idx < total) { int b = idx / D; int d = idx % D; float sum = 0.0f; for (int r = 0; r < R; r++) { float val = x[r * B * D + b * D + d]; sum += gelu_approx(val); } out[idx] = sum; } } torch::Tensor gelu_sum_cuda(torch::Tensor x) { int R = x.size(0); int B = x.size(1); int D = x.size(2); auto out = torch::empty({B, D}, x.options()); int total = B * D; int threads = 256; int blocks = (total + threads - 1) / threads; gelu_sum_kernel<<<blocks, threads>>>( x.data_ptr<float>(), out.data_ptr<float>(), R, B, D ); return out; } ''', functions=['gelu_sum_cuda'], verbose=True ) class ModelNew(nn.Module): def __init__(self): super().__init__() def forward(self, x: torch.Tensor) -> torch.Tensor: return gelu_sum_cuda.gelu_sum_cuda(x) ``` Let me compile this first.

Good, the kernel compiled. Now let me check correctness against the reference.

The GELU approximation isn't close enough to PyTorch's GELU implementation. PyTorch's GELU uses the exact formula: `x * 0.5 * (1.0 + erf(x / sqrt(2)))`. Let me use this instead for better precision.

Let me test correctness again.

Correctness passes. Now let me check the static analysis and then submit.

The warning about torch.nn compute layer is probably from the F import, but it doesn't seem to be a blocking issue. The kernel is correct and passes the static check. Let me submit it.