Let me analyze the problem: - hidden: (4, 96, 256) - w_down: (256, 48) - w_up_k: (48, 128) - w_up_v: (48, 128) Operations: 1. latent = hidden @ w_down -> (384, 48) 2. k = latent @ w_up_k -> (384, 128) 3. v = latent @ w_up_v -> (384, 128) 4. Reshape and stack Total flops: - First matmul: 384 * 256 * 48 * 2 = ~9.4M flops - Second matmul: 384 * 48 * 128 * 2 = ~4.7M flops - Third matmul: same ~4.7M flops This is a relatively small problem, so we need an efficient kernel. Let me write a fused kernel that computes all three matrix multiplications. For small matrices on H100, we should use a good block size and leverage shared memory efficiently. Let me write a kernel that: 1. Computes latent in shared memory 2. Then uses latent to compute k and v Actually, let me think about this more carefully. The operations are: - hidden (384 x 256) @ w_down (256 x 48) = latent (384 x 48) - latent (384 x 48) @ w_up_k (48 x 128) = k (384 x 128) - latent (384 x 48) @ w_up_v (48 x 128) = v (384 x 128) We can fuse these operations. The key insight is that latent is used twice, so we should keep it in a fast memory location. Given the dimensions: - batch_size * seq_len = 384 - model_dim = 256 - rank = 48 - kv_heads * head_dim = 128 Let me write a kernel that processes tiles of the batch dimension, computing latent in registers/shared memory, then outputting k and v. For the H100 with 228KB shared memory per SM, we can store: - A tile of hidden: TILE_SIZE x 256 = e.g. 16 x 256 = 4096 floats = 16KB - w_down: 256 x 48 = 12288 floats = 48KB - w_up_k: 48 x 128 = 6144 floats = 24KB - w_up_v: 48 x 128 = 6144 floats = 24KB - latent tile: TILE_SIZE x 48 = 768 floats = 3KB - k output tile: TILE_SIZE x 128 = 2048 floats = 8KB - v output tile: same = 8KB Total: ~131KB for weights alone if we load them fully into shared memory. Actually, given the small sizes, I think the best approach is: 1. Use cuBLAS for the matmuls initially (it's highly optimized) 2. Or write a custom kernel that leverages tensor cores Let me start with a simple approach using cuBLAS, then optimize if needed. Actually, for best performance, I'll write a fused kernel. Let me design it: Approach 1: Fused kernel with shared memory - Each thread block handles a batch_size * seq_len row - Load weights into shared memory - Compute latent in registers - Compute k and v outputs Approach 2: Multiple kernel calls with cuBLAS - Call cublasGemm for each matmul - Minimal Python overhead Given the small problem size, approach 2 might be competitive due to highly optimized cuBLAS. Let me try approach 1 first since we're asked to write a custom kernel. Let me write a kernel: - Each thread handles one output element for both k and v - TILE_SIZE = 16 or 32 threads per batch row - Each thread block handles multiple batch rows Actually, let me think about the tiling more carefully: For output k: 384 rows x 128 columns For output v: 384 rows x 128 columns We could have each thread compute one element of k and one element of v (same row, different weights). Thread block: 16 x 8 = 128 threads - Each block handles 16 batch rows and 8 output columns - So we need 384/16 = 24 blocks in batch dimension and 128/8 = 16 blocks in output dimension - Total: 24 * 16 = 384 blocks Actually let me simplify: - blockDim = 128 threads - Each thread handles one output column of k and v for a given batch row - 384 batch rows / some number of rows per block Let me just write a simple kernel first: ```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_seq, int model_dim, int rank, int kv_dim) { int row = blockIdx.x * blockDim.y + threadIdx.y; int col = threadIdx.x; if (row >= batch_seq) return; // Compute latent in registers extern __shared__ float shared_weights[]; float* sw_down = shared_weights; // model_dim x rank float* sw_up_k = sw_down + model_dim * rank; // rank x kv_dim float* sw_up_v = sw_up_k + rank * kv_dim; // rank x kv_dim // Load weights into shared memory (collaborative) // ... // Compute latent[row, :] float latent[48]; // rank = 48 for (int r = 0; r < rank; r++) { latent[r] = 0.0f; for (int d = 0; d < model_dim; d++) { latent[r] += hidden[row * model_dim + d] * w_down[d * rank + r]; } } // Compute k and v outputs for (int c = 0; c < kv_dim; c++) { float k_val = 0.0f, v_val = 0.0f; for (int r = 0; r < rank; r++) { k_val += latent[r] * w_up_k[r * kv_dim + c]; v_val += latent[r] * w_up_v[r * kv_dim + c]; } k_out[row * kv_dim + c] = k_val; v_out[row * kv_dim + c] = v_val; } } ``` But this is very naive. Let me write a more optimized version with proper tiling and shared memory. Actually, for small matrices on modern GPUs, it's often best to use cuBLAS or CUTLASS. Let me check if I can use libtorch's built-in matmul functions in a fused way. Let me try a different approach - use torch operations but fuse them with CUDA streams or just rely on PyTorch's internal optimizations. But the task asks for a custom CUDA kernel... Let me write a proper tiled kernel: ```cuda #define TILE_SIZE 16 #define RANK 48 #define KV_DIM 128 #define MODEL_DIM 256 __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_seq) { int batch_row = blockIdx.x * TILE_SIZE + threadIdx.y; int col = blockIdx.y * TILE_SIZE + threadIdx.x; __shared__ float s_hidden[TILE_SIZE][MODEL_DIM]; __shared__ float s_w_down[MODEL_DIM][RANK]; __shared__ float s_w_up_k[RANK][TILE_SIZE]; __shared__ float s_w_up_v[RANK][TILE_SIZE]; __shared__ float s_latent[TILE_SIZE][RANK]; // Load hidden tile if (batch_row < batch_seq) { for (int i = 0; i < MODEL_DIM; i += TILE_SIZE) { if (i + threadIdx.x < MODEL_DIM) { s_hidden[threadIdx.y][i + threadIdx.x] = hidden[batch_row * MODEL_DIM + i + threadIdx.x]; } } } // Load weight tiles // ... cooperative loading __syncthreads(); // Compute latent float latent_val = 0.0f; for (int k = 0; k < MODEL_DIM; k++) { latent_val += s_hidden[threadIdx.y][k] * s_w_down[k][col]; } s_latent[threadIdx.y][threadIdx.x] = latent_val; __syncthreads(); // Compute k and v float k_val = 0.0f, v_val = 0.0f; for (int r = 0; r < RANK; r++) { k_val += s_latent[threadIdx.y][r] * s_w_up_k[r][threadIdx.x]; v_val += s_latent[threadIdx.y][r] * s_w_up_v[r][threadIdx.x]; } if (batch_row < batch_seq && col < KV_DIM) { k_out[batch_row * KV_DIM + col] = k_val; v_out[batch_row * KV_DIM + col] = v_val; } } ``` This is getting complex. Let me simplify by writing a kernel where each thread handles one output element, but we tile the computation to reuse weights. Actually, let me just write a simpler but correct kernel first, test it, then optimize. Given the dimensions are fixed and small, I can specialize the kernel: ``` batch_seq = 384 model_dim = 256 rank = 48 kv_dim = 128 ``` Let me write a kernel that: 1. Uses shared memory for weights 2. Each thread computes one output element of k and v 3. Threads cooperate to load weights Here's my plan: - Grid: (384, 128) - but we'll tile this - Block: (16, 8) or (32, 8) - Each thread computes one (row, col) of k and v - Load weights into shared memory cooperatively Let me write this properly: ```cpp #include <cuda.h> #include <cuda_runtime.h> #define BLOCK_ROWS 16 #define BLOCK_COLS 8 __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_seq, int model_dim, int rank, int kv_dim) { int row = blockIdx.x * BLOCK_ROWS + threadIdx.y; int col = blockIdx.y * BLOCK_COLS + threadIdx.x; // Shared memory for weights __shared__ float s_w_down[256][48]; // model_dim x rank __shared__ float s_w_up_k[48][128]; // rank x kv_dim __shared__ float s_w_up_v[48][128]; // rank x kv_dim // Cooperatively load w_down int tid = threadIdx.y * blockDim.x + threadIdx.x; for (int i = tid; i < model_dim * rank; i += blockDim.x * blockDim.y) { int r = i / rank; int c = i % rank; s_w_down[r][c] = w_down[r * rank + c]; } // Load w_up_k and w_up_v for (int i = tid; i < rank * kv_dim; i += blockDim.x * blockDim.y) { int r = i / kv_dim; int c = i % kv_dim; s_w_up_k[r][c] = w_up_k[r * kv_dim + c]; s_w_up_v[r][c] = w_up_v[r * kv_dim + c]; } __syncthreads(); if (row >= batch_seq || col >= kv_dim) return; // Compute latent for this row float latent[48]; for (int r = 0; r < rank; r++) { float sum = 0.0f; for (int d = 0; d < model_dim; d++) { sum += hidden[row * model_dim + d] * s_w_down[d][r]; } latent[r] = sum; } // Compute k and v outputs float k_val = 0.0f, v_val = 0.0f; for (int r = 0; r < rank; r++) { k_val += latent[r] * s_w_up_k[r][col]; v_val += latent[r] * s_w_up_v[r][col]; } k_out[row * kv_dim + col] = k_val; v_out[row * kv_dim + col] = v_val; } ``` Wait, the issue is that latent is computed redundantly by threads in the same row (same threadIdx.y, different threadIdx.x). Let me restructure. Actually, a better approach: - Have each thread compute one k element and one v element - Threads in the same row share the latent computation - Use shared memory to share latent within a thread block Let me think about this differently: Option A: Each thread computes one k[col] and one v[col] for one row - Requires computing latent (48 values) per thread - latent computation: 256 * 48 = 12288 muls, 12288 adds - k computation: 48 muls, 48 adds - v computation: 48 muls, 48 adds - Total per thread: ~12432 muls, ~12432 adds Option B: Cooperatively compute latent, then each thread computes its k and v - Threads in same row (8 threads) share latent computation - Better latency hiding but more complex Option C: Use vectorized loads and tensor cores For simplicity, let me go with option A but optimize with vectorized loads. Actually, let me first write a working kernel, then optimize. The overhead of multiple kernel launches in PyTorch is what we're trying to avoid with fusion. Let me write the kernel: ```cpp __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_seq, int model_dim, int rank, int kv_dim) { const int BLOCK_ROWS = 8; const int BLOCK_COLS = 16; int row = blockIdx.x * BLOCK_ROWS + threadIdx.y; int col = blockIdx.y * BLOCK_COLS + threadIdx.x; // Load w_down into shared memory __shared__ float s_w_down[256][48]; int tid = threadIdx.y * blockDim.x + threadIdx.x; for (int i = tid; i < 256 * 48; i += BLOCK_ROWS * BLOCK_COLS) { int r = i / 48; int c = i % 48; s_w_down[r][c] = w_down[r * 48 + c]; } __syncthreads(); if (row >= batch_seq || col >= kv_dim) return; // Compute latent float latent[48]; const float* hidden_row = hidden + row * model_dim; for (int r = 0; r < 48; r++) { float sum = 0.0f; for (int d = 0; d < 256; d++) { sum += hidden_row[d] * s_w_down[d][r]; } latent[r] = sum; } // Compute k and v float k_val = 0.0f, v_val = 0.0f; for (int r = 0; r < 48; r++) { k_val += latent[r] * w_up_k[r * kv_dim + col]; v_val += latent[r] * w_up_v[r * kv_dim + col]; } k_out[row * kv_dim + col] = k_val; v_out[row * kv_dim + col] = v_val; } ``` Hmm, w_up_k and w_up_v are not in shared memory, which might hurt performance due to repeated reads. Let me improve: ```cpp __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_seq, int model_dim, int rank, int kv_dim) { int row = blockIdx.x * 8 + threadIdx.y; int col = blockIdx.y * 16 + threadIdx.x; // Shared memory for all weights __shared__ float s_w_down[256][48]; __shared__ float s_w_up_k[48][128]; __shared__ float s_w_up_v[48][128]; int tid = threadIdx.y * 16 + threadIdx.x; int total_threads = 8 * 16; // Load w_down for (int i = tid; i < 256 * 48; i += total_threads) { int r = i / 48; int c = i % 48; s_w_down[r][c] = w_down[r * 48 + c]; } // Load w_up_k for (int i = tid; i < 48 * 128; i += total_threads) { int r = i / 128; int c = i % 128; s_w_up_k[r][c] = w_up_k[r * 128 + c]; } // Load w_up_v for (int i = tid; i < 48 * 128; i += total_threads) { int r = i / 128; int c = i % 128; s_w_up_v[r][c] = w_up_v[r * 128 + c]; } __syncthreads(); if (row >= batch_seq || col >= kv_dim) return; // Compute latent float latent[48]; const float* hidden_row = hidden + row * 256; for (int r = 0; r < 48; r++) { float sum = 0.0f; for (int d = 0; d < 256; d++) { sum += hidden_row[d] * s_w_down[d][r]; } latent[r] = sum; } // Compute k and v float k_val = 0.0f, v_val = 0.0f; for (int r = 0; r < 48; r++) { k_val += latent[r] * s_w_up_k[r][col]; v_val += latent[r] * s_w_up_v[r][col]; } k_out[row * 128 + col] = k_val; v_out[row * 128 + col] = v_val; } ``` Shared memory usage: - s_w_down: 256 * 48 * 4 = 49152 bytes - s_w_up_k: 48 * 128 * 4 = 24576 bytes - s_w_up_v: 48 * 128 * 4 = 24576 bytes - Total: 98304 bytes = 96KB This fits within the 227KB shared memory limit per block on H100. But wait, there's an issue. All threads in a block load the weights redundantly. And the latent is computed redundantly by threads with the same row but different col. Actually no, the weight loading is cooperative (each thread loads different elements). But latent is computed redundantly - 16 threads per row each compute the same latent[48]. This is wasteful. Let me restructure: - Have one thread per row compute latent and share it via shared memory - Or have threads cooperatively compute latent Actually, let me think about this more carefully. If we have: - 8 rows per block (threadIdx.y = 0..7) - 16 cols per block (threadIdx.x = 0..15) Then each row has 16 threads computing the same latent. That's redundant. Better approach: compute latent cooperatively and store in shared memory. ```cpp __shared__ float s_latent[8][48]; // latent for 8 rows // Compute latent cooperatively // Each thread (ty, tx) helps compute latent for row ty // Thread tx handles hidden elements tx, tx+16, tx+32, ... for each latent component for (int r = 0; r < 48; r++) { float sum = 0.0f; for (int d = threadIdx.x; d < 256; d += 16) { sum += hidden[row * 256 + d] * s_w_down[d][r]; } // Reduce within the row // Use shared memory for reduction } ``` This is getting complex. Let me simplify by accepting some redundancy for now. Actually, the bigger issue is that each thread has 256 * 48 = 12,288 iterations for the latent computation, and only 16 threads per row, so each thread does redundant work. Let me try a different tiling strategy: - Block size: 128 threads (all in x dimension) - Each thread handles one output column - Multiple blocks handle multiple rows But we need to share latent within each row... Actually, let me just try a simple kernel and see if it works and is fast enough. I can optimize later. Let me write the complete kernel code:

The kernel launch is failing with invalid argument - probably the shared memory size is too large, or there's something wrong with the parameters. Let me recalculate: smem_floats = model_dim * rank + 2 * rank * kv_dim = 256 * 48 + 2 * 48 * 128 = 12288 + 12288 = 24576 floats = 96 KB That's within the 227 KB limit per block, but let me check the grid dimensions and other parameters. Actually, the problem might be that I'm passing total_threads and smem_floats as kernel arguments but not using them properly in the kernel. Let me simplify and make sure the parameters are correct. Also, the grid dimension calculation might have an issue. Let me fix this.