reasoning (truncated 10781 chars): Let me analyze the task: 1. The model performs: - Reshape hidden from (batch, seq, model_dim) to (batch*seq, model_dim) - MatMul with w_down: (batch*seq, model_dim) @ (model_dim, rank) -> (batch*seq, rank) - MatMul with w_up_k: (batch*seq, rank) @ (rank, kv_heads*head_dim) -> (batch*seq, 128) - MatMul with w_up_v: (batch*seq, rank) @ (rank, kv_heads*head_dim) -> (batch*seq, 128) - Reshape k and v to (batch, seq, kv_heads, head_dim) - Stack k and v along dim 2 to get (batch, seq, 2, kv_heads, head_dim) Dimensions: - batch_size = 4 - seq_len = 96 - model_dim = 256 - rank = 48 - kv_heads = 4 - head_dim = 32 So the matrices are: - hidden: (4, 96, 256) - w_down: (256, 48) - w_up_k: (48, 128) - w_up_v: (48, 128) This is essentially two fused GEMM operations: 1. hidden @ w_down -> latent (shared) 2. latent @ w_up_k -> k 3. latent @ w_up_v -> v The key optimization opportunity is to fuse these operations. Instead of computing latent first and then using it twice, we could potentially: 1. Fuse the entire computation into a single kernel 2. Use shared memory efficiently Actually, looking at this more carefully: - The first matmul is: (384, 256) @ (256, 48) -> (384, 48) - The second matmul is: (384, 48) @ (48, 128) -> (384, 128) - The third matmul is: (384, 48) @ (48, 128) -> (384, 128) The dimensions are quite small, so I should fuse the two GEMM operations where latent serves as the intermediate result for both k and v computations. This avoids materializing the intermediate latent tensor and keeps everything in shared memory. I'll write a custom CUDA kernel that computes both k and v simultaneously, avoiding the materialization of the full latent intermediate. The approach is to have each thread handle one output element, computing the necessary partial products from hidden through w_down and w_up. A better strategy is to first project hidden through w_down to get latent, then reuse this result for both w_up_k and w_up_v computations. Here's a fused kernel implementation that processes the entire computation in one pass: ```cuda __global__ void fused_mla_kernel( const float* __restrict__ hidden, const float* __restrict__ w_down, const float* __restrict__ w_up_k, const float* __restrict__ w_up_v, float* __restrict__ k_out, float* __restrict__ v_out, int batch_size, int seq_len, int model_dim, int rank, int kv_heads, int head_dim) { int batch_seq_idx = blockIdx.x; int head_idx = blockIdx.y; int dim_idx = threadIdx.x; int output_size = kv_heads * head_dim; if (batch_seq_idx < batch_size * seq_len && head_idx < kv_heads) { // Shared memory for latent vector extern __shared__ float latent[]; // Compute latent (one thread per element) if (dim_idx < rank) { float sum = 0.0f; for (int m = 0; m < model_dim; m++) { sum += hidden[batch_seq_idx * model_dim + m] * w_down[m * rank + dim_idx]; } latent[dim_idx] = sum; } __syncthreads(); // Compute k and v outputs int out_idx = batch_seq_idx * output_size + head_idx * head_dim + dim_idx; if (dim_idx < head_dim) { float k_sum = 0.0f; float v_sum = 0.0f; for (int r = 0; r < rank; r++) { k_sum += latent[r] * w_up_k[r * output_size + head_idx * head_dim + dim_idx]; v_sum += latent[r] * w_up_v[r * output_size + head_idx * head_dim + dim_idx]; } k_out[out_idx] = k_sum; v_out[out_idx] = v_sum; } } } ``` The kernel computes the latent vector in shared memory first, then each thread calculates both k and v components by multiplying the latent vector with the appropriate weight matrices. The thread and block indexing maps each output element to a specific thread, computing both k and v outputs simultaneously. However, with `blockIdx.y < kv_heads` (4 blocks in the y-dimension), the thread synchronization becomes problematic since threads from different y-blocks won't coordinate properly during the latent computation phase. The shared memory approach needs reconsideration to handle the block structure correctly. A better strategy separates the concerns: one kernel handles the latent computation while another processes the output generation. The first kernel (batch_size * seq_len blocks, rank threads per block) computes the latent vectors from hidden states. The second kernel (batch_size * seq_len blocks, kv_heads * head_dim threads per block) transforms the latent representations into k and v outputs. This separation allows proper synchronization within each kernel and avoids the coordination issues from the multi-dimensional block structure. d_dim; stride *= blockDim.x) { int idx = stride * blockDim.x + threadIdx.x; if (idx < kv_heads * head_dim) { for (int h = 0; h < kv_heads; h++) { for (int d = 0; d < head_dim; d++) { int out_idx = batch_seq_idx * kv_heads * head_dim + h * head_dim + d; // ... } } } } } } ``` I need to reconsider the output structure. The final tensor has shape (batch_size, seq_len, 2, kv_heads, head_dim), where the third dimension indexes k and v. When stacking along dimension 2, k and v each contribute to different slices of this dimension. The stack operation interleaves k at index 0 and v at index 1 along that axis. Looking at the memory layout, after stacking k and v—both shaped (batch_size, seq_len, kv_heads, head_dim)—I get (batch_size, seq_len, 2, kv_heads, head_dim). The resulting memory pattern interleaves k and v blocks sequentially. The first kv_heads * head_dim elements correspond to k, followed by v at the same offset. Tracing through the indexing: for a given batch_idx and seq_idx, the offset is (batch_idx * seq_len + seq_idx) * 2 * kv_heads * head_dim. Within this block, k values are accessible at offset + h * head_dim + d, while v values are at offset + kv_heads * head_dim + h * head_dim + d. This matches the stacked output shape of (batch, seq, 2, kv_heads, head_dim), so the kernel should write to this layout directly. I'm considering using cuBLAS for the GEMM operations rather than writing a custom kernel, since the problem sizes are relatively small. The computation involves three matrix multiplications: hidden (384 × 256) multiplied by w_down (256 × 48) produces latent (384 × 48), then latent is multiplied by both w_up_k and w_up_v (each 48 × 128) to generate k and v (384 × 128 each). PyTorch's built-in operations would handle this efficiently, but a fused kernel could reduce memory overhead by reusing the latent computation across both k and v calculations. However, for these matrix sizes, cuBLAS is highly optimized and difficult to outperform with a custom implementation. The real opportunity is avoiding intermediate memory allocation—instead of storing the latent matrix as a separate tensor, I can compute it once and immediately feed it into both downstream multiplications, keeping the values in cache or registers between the two operations. I could also explore `torch.baddbmm` or similar fused operations to chain the computations more efficiently, but the core strategy remains: minimize memory traffic by keeping intermediate results in fast storage. Let me design a kernel where each block processes one row of the output matrices, computing latent values on-the-fly and reusing them for both k and v calculations. ```python import torch from torch.utils.cpp_extension import load_inline cuda_source = """ #include <torch/extension.h> #include <cuda.h> #include <cuda_runtime.h> __global__ void fused_mla_kernel( const float* __restrict__ hidden, const float* __restrict__ w_down, const float* __restrict__ w_up_k, const float* __restrict__ w_up_v, ...[ omitted 10781 characters ]... sizeof(float); fused_mla_kernel<<<blocks, threads, shared_mem>>>( hidden.data_ptr<float>(), w_down.data_ptr<float>(), w_up_k.data_ptr<float>(), w_up_v.data_ptr<float>(), output.data_ptr<float>(), batch_seq_len, model_dim, rank, output_dim); return output; } """ module = load_inline( name='fused_mla', cpp_sources='', cuda_sources=cuda_source, functions=['fused_mla_cuda'], extra_cuda_cflags=['-O3'], verbose=False ) class ModelNew(nn.Module): def __init__(self): super().__init__() def forward(self, hidden, w_down, w_up_k, w_up_v): batch_size, seq_len, model_dim = hidden.shape rank = w_down.shape[1] kv_heads = 4 head_dim = w_up_k.shape[1] // kv_heads # Reshape hidden to (batch_size * seq_len, model_dim) hidden_flat = hidden.reshape(batch_size * seq_len, model_dim).contiguous() output = module.fused_mla_cuda(hidden_flat, w_down, w_up_k, w_up_v) return output ``` I need to handle the batch_size extraction more carefully in the CUDA kernel. Since seq_len can vary, I should pass it as a parameter rather than assuming a fixed value of 96. Looking at the reference implementation more carefully, the key and value projections both use the same latent representation computed from the down projection. The latent is computed once, then separately projected into k and v. The output stacks these as a tuple, so I need to compute both projections from the shared latent representation. The memory layout is critical here. After stacking k and v along dimension 2, the contiguous tensor interleaves the k and v blocks per batch-sequence position. Each position stores k's 128 values first, then v's 128 values, before moving to the next position. This means the stride pattern is: for each batch-sequence index, the first 128 elements are k, the next 128 are v, then repeat for subsequent positions. The kernel output indexing aligns with this layout—batch_seq_idx * 2 * output_dim gives the base offset for a position, and adding output_dim skips past k to reach v. I should pass batch_size and seq_len as kernel arguments to make the function more flexible, and ensure contiguous() calls are applied to all input tensors. Optimization opportunities include leveraging __ldg for read-only cache on weight matrices, using vectorized loads via float4, and enabling loop unrolling with #pragma. I'll implement these optimizations while keeping the core logic straightforward. The kernel performs a fused linear transformation: first projecting input through a down-sampling matrix into a latent representation stored in shared memory, then projecting that latent through separate matrices to produce key and value outputs. Each thread handles a portion of the computation cooperatively, with the latent vector computed collaboratively across the block before being used to generate the final outputs. _seq_len, int model_dim, int rank, int output_dim) { int batch_seq_len = hidden.size(0); int model_dim = hidden.size(1); int rank = w_down.size(1); int output_dim = w_up_k.size(1); TORCH_CHECK(hidden.size(0) == batch_size * seq_len, "Hidden size mismatch"); TORCH_CHECK(w_down.size(0) == model_dim, "w_down size mismatch"); TORCH_CHECK(w_up_k.size(0) == rank, "w_up_k size mismatch"); TORCH_CHECK(w_up_v.size(0) == rank, "w_up_v size mismatch"); TORCH_CHECK(w_up_k.size(1) == w_up_v.size(1), "w_up_k and w_up_v output dim mismatch"); int kv_heads = 4; int head_dim = output_dim / kv_heads; auto output = torch::zeros({batch_size, seq_len, 2, kv_heads, head_dim}, hidden.options()); int threads = 128; int blocks = batch_seq_len; int shared_mem = rank * sizeof(float); fused_mla_kernel<<<blocks, threads, shared_mem>>>( hidden.data_ptr<float>(), w_down.data_ptr<float>(), w_up_k.data_ptr<float>(), w_up_v.data_ptr<float>(), output.data_ptr<float>(), batch_seq_len, model_dim, rank, output_dim); return output; } The C++ wrapper extracts tensor dimensions, validates shapes, allocates output storage with the expected layout, and configures kernel launch parameters with 128 threads per block and one block per sequence position. ```python class ModelNew(nn.Module): def __init__(self): super().__init__() def forward(self, hidden, w_down, w_up_k, w_up_v): batch_size, seq_len, model_dim = hidden.shape rank = w_down.shape[1] kv_heads = 4 head_dim = w_up_k.shape[1] // kv_heads hidden_flat = hidden.reshape(batch_size * seq_len, model_dim).contiguous() output = module.fused_mla_cuda(hidden_flat, w_down, w_up_k, w_up_v, batch_size, seq_len) return output ``` The Python interface flattens the hidden tensor, passes it through the fused CUDA kernel, and returns the multi-head attention outputs. There's an issue with how the hidden tensor gets reshaped though. The CUDA kernel expects the hidden tensor already flattened to (batch_size * seq_len, model_dim), so I need to ensure the reshape happens before the kernel launch. The function signature should take the original batch and sequence dimensions as separate parameters to properly reconstruct the output tensor shape. I should add contiguity checks for all weight tensors since the kernel assumes they're stored contiguously in memory. Let me refactor the code to handle the reshape correctly and add those safety checks. _output_dim; for (int r = 0; r < rank; r++) { k_sum += latent[r] * __ldg(&w_up_k[r * output_dim + out_idx]); v_sum += latent[r] * __ldg(&w_up_v[r * output_dim + out_idx]); } output[k_offset] = k_sum; output[v_offset] = v_sum; } } torch::Tensor fused_mla_cuda( torch::Tensor hidden, torch::Tensor w_down, torch::Tensor w_up_k, torch::Tensor w_up_v, int batch_size, int seq_len) { int batch_seq_len = batch_size * seq_len; int model_dim = hidden.size(1); int rank = w_down.size(1); int output_dim = w_up_k.size(1); int kv_heads = 4; int head_dim = output_dim / kv_heads; auto output = torch::zeros({batch_size, seq_len, 2, kv_heads, head_dim}, hidden.options()); int threads = 128; int blocks = batch_seq_len; int shared_mem = rank * sizeof(float); fused_mla_kernel<<<blocks, threads, shared_mem>>>( hidden.data_ptr<float>(), w_down.data_ptr<float>(), w_up_k.data_ptr<float>(), w_up_v.data_ptr<float>(), output.data_ptr<float>(), batch_seq_len, model_dim, rank, output_dim); return output; } """ module = load_inline( name='fused_mla_v2', cpp_sources='', cuda_sources=cuda_source, functions=['fused_mla_cuda'], extra_cuda_cflags=['-O3'], verbose=False ) class ModelNew(nn.Module): def __init__(self): super().__init__() def forward(self, hidden, w_down, w_up_k, w_up_v): batch_size, seq_len, model_dim = hidden.shape # Ensure contiguous memory hidden_flat = hidden.reshape(batch_size * seq_len, model_dim).contiguous() w_down = w_down.contiguous() w_up_k = w_up_k.contiguous() w_up_v = w_up_v.contiguous() return module.fused_mla_cuda(hidden_flat, w_down, w_up_k, w_up_v, batch_size, seq_len) ``` The kernel computes key and value projections cooperatively across threads, using __ldg for read-only weight access to optimize memory bandwidth. Each thread processes multiple output elements when the output dimension exceeds the block size, accumulating partial sums before writing final results. The Python interface handles memory contiguity requirements before launching the kernel with batch and sequence dimensions.