Let me understand the task: 1. I need to implement a custom CUDA kernel for `torch.logsumexp(x, dim=0)` 2. Input shape is (R, B, D) = (4, 10, 32) 3. Output shape should be (B, D) 4. The operation is `logsumexp(x, dim=0)` which is equivalent to `log(sum(exp(x), dim=0))` but computed in a numerically stable way For logsumexp over dimension 0, I need to: 1. Find the maximum value along dim=0 for numerical stability 2. Compute `max + log(sum(exp(x - max), dim=0))` Let me start by getting GPU specs and then implement a kernel. The key insight is: - logsumexp(x, dim=0) = max(x, dim=0) + log(sum(exp(x - max(x, dim=0)), dim=0)) - This is computed for each (b, d) pair independently With R=4, B=10, D=32: - Each output element needs to process R=4 elements - Total output elements: B*D = 10*32 = 320 A simple approach: - Each thread processes one output element (b, d) - Thread reads R values, computes max, then computes logsumexp Let me write the kernel: ```python import torch from torch.utils.cpp_extension import load_inline cuda_source = """ #include <torch/extension.h> #include <cuda.h> #include <cuda_runtime.h> #include <cmath> __global__ void logsumexp_kernel( const float* __restrict__ input, float* __restrict__ output, const int R, const int B, const 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; // Find max along dim=0 float max_val = -INFINITY; for (int r = 0; r < R; r++) { float val = input[r * B * D + b * D + d]; if (val > max_val) max_val = val; } // Compute sum of exp(x - max) float sum_exp = 0.0f; for (int r = 0; r < R; r++) { float val = input[r * B * D + b * D + d]; sum_exp += expf(val - max_val); } output[b * D + d] = max_val + logf(sum_exp); } } torch::Tensor logsumexp_cuda(torch::Tensor x, int dim) { auto sizes = x.sizes(); int R = sizes[0]; int B = sizes[1]; int D = sizes[2]; auto output = torch::empty({B, D}, x.options()); int total = B * D; int threads = 256; int blocks = (total + threads - 1) / threads; logsumexp_kernel<<<blocks, threads>>>( x.data_ptr<float>(), output.data_ptr<float>(), R, B, D ); return output; } """ cpp_source = """ torch::Tensor logsumexp_cuda(torch::Tensor x, int dim); """ # Load the CUDA extension logsumexp_ext = load_inline( name='logsumexp_ext', cpp_sources=cpp_source, cuda_sources=cuda_source, functions=['logsumexp_cuda'], extra_cuda_cflags=['-O3'], verbose=True ) class ModelNew(nn.Module): def __init__(self): super().__init__() def forward(self, x: torch.Tensor) -> torch.Tensor: return logsumexp_ext.logsumexp_cuda(x, 0) ``` I'm implementing a logsumexp reduction along the first dimension. The kernel finds the maximum value first for numerical stability, then accumulates the exponentials of the differences, and finally takes the logarithm to complete the operation. Each thread handles one output element independently, reading R values from the input tensor positioned at the appropriate b and d indices.

Good, I have the GPU specs. Now let me write the initial kernel. The operation is: - Input: (R, B, D) = (4, 10, 32) - Output: (B, D) = (10, 32) - Compute: logsumexp along dim 0 For logsumexp, I need: 1. Find max across dim 0 for each (b, d) position 2. Compute sum of exp(x - max) across dim 0 3. Output = max + log(sum) Since R = 4 is small, each thread could compute the entire reduction. But let me think about how to parallelize this optimally. Total output elements: B * D = 10 * 32 = 320 One approach: each thread computes one output element. Each thread reads R=4 values, computes max, then sum. Let me write the kernel:

The kernel compiled successfully. Now let me check correctness.

The kernel is correct. Let me profile it to see performance:

Let me run correctness again to make sure the optimization still produces correct results.

Still correct. Let me profile this version to see if coalescing improved.

Let me check correctness and profile.

Let me check correctness and profile this version.

The kernel is correct. Let me profile this version to see if it's improved, and then decide whether to submit or try further optimizations.

The current kernel is correct and has reasonable performance (3.17μs GPU time). The profile shows it's latency-bound due to the small problem size (320 elements). The memory access pattern still shows 4.0x wasted bandwidth due to non-coalesced accesses, but given the small problem size, this is expected. Let me try one more optimization - using float4 loads for better memory coalescing, since we're reading 4 elements at stride BD apart for each position. Actually, wait - the issue is that each thread reads values at positions tid, tid+BD, tid+BD*2, tid+BD*3. These are NOT contiguous in memory for the same thread, but across a warp (32 threads), threads 0-31 read from positions 0-31, 320-351, 640-671, 960-991. These are NOT contiguous either, hence the poor coalescing. To improve coalescing, I could try: 1. Vectorized loads (float4) if the memory layout allows 2. Shared memory to cache input data Let me try a float4 approach - restructure to load contiguous data. But wait, the input is (R, B, D) = (4, 10, 32), so the memory layout is: - Position 0: x[0,0,0] - Position 1: x[0,0,1] - ... - Position 31: x[0,0,31] - Position 32: x[0,1,0] - ... - Position 319: x[0,9,31] - Position 320: x[1,0,0] - ... So for thread tid processing position tid in the output, the R values are at positions tid, tid+320, tid+640, tid+960. These are NOT contiguous, so float4 loads won't help directly. Actually, I think the kernel is reasonably optimized for this small problem. Let me check static analysis and submit.

The kernel is correct and passes static checks. Let me submit it now.