reasoning
Let me analyze the reference implementation:
1. Input: `msa_repr` (B, S, N, D) and `msa_mask` (B, S, N)
2. Transpose to (B, N, S, D)
3. LayerNorm
4. Q, K, V linear projections + reshape to (B, N, h, S, d) permute to (B, N, h, S, d)
5. G linear + sigmoid + reshape
6. Attention: Q @ K^T / sqrt(d), apply mask, softmax, dropout
7. Output = Attention @ V, gate multiply
8. Reshape + out_proj + transpose back
The operation essentially performs self-attention across the depth dimension (S) for each residue position (N) independently. So each (B, N) pair has its own attention over S sequences.
Given the problem size:
- batch_size = 2
- msa_depth = 8
- seq_len = 32
- msa_dim = 64
- num_heads = 4
- head_dim = 16
This is small enough that we can fuse everything into a single kernel, but large enough that we need to be efficient.
Let me design a fused kernel. The key insight is that for each (B, N, h), we have an attention computation over S=8 elements with d=16 dimensions. This is very small!
Given S=8 and h=4, we can potentially:
1. Load Q, K, V for a given (B, N, h) into shared memory
2. Compute attention scores
3. Apply softmax
4. Compute output
5. Apply gate and project
But we also have layer norm and linear layers. For small sizes, fusing everything would be ideal but complex. Let me think about what's practical.
Actually, let me think more carefully:
- Total elements per batch: S * N * D = 8 * 32 * 64 = 16384
- With B=2, total is 32768
This is quite small. The PyTorch reference likely has significant kernel launch overhead from doing many separate operations. A single fused kernel could save a lot.
Let me try to write a comprehensive fused kernel. Here's my plan:
- One large fused kernel that handles: transpose, layer norm, Q/K/V/G projections, attention, gating, output projection, and transpose back.
Actually, doing all linear projections in one kernel is complex because they need different weight matrices. But we can use a custom kernel for the attention part and possibly other parts.
Given the complexity, let me think about a practical approach:
Option A: Fuse the entire forward pass into one kernel
Option B: Fuse attention-related operations into one kernel, keep layer norm and linear projections in standard PyTorch
For Option A, the challenge is efficiently implementing the linear layers. But with small sizes, we can do them in a straightforward way.
Let me write a kernel that fuses everything. I'll have each thread block handle one (B, N) position across all heads.
For each (b, n):
- Input: S=8 tokens of D=64 dims each
- LayerNorm over D dimension
- Compute Q, K, V, G: 4 * S * D = 4 * 8 * 64 = 2048 FMAs - very small
- For each head h:
- q, k are S * d = 8 * 16 = 128 elements
- Compute Q*K^T: 8x8 matrix
- Softmax on rows
- Compute Attn * V: 8x8 * 8x16 = 8x16
- Gate multiply
- Output projection: S * D -> S * D
- Transpose back
Each (b, n) is quite independent. Total (B, N) = 2 * 32 = 64 blocks. With 4 heads per block, that's manageable.
Given the small S=8, I can have each warp handle one head. 4 warps per block for 4 heads, or one block per (b, n, h).
Let me design: one block per (b, n), with 4 warps handling 4 heads.
For linear layers within the kernel:
- Q = X @ W_Q^T
- This is S * D matrix times D * D matrix
- Since S is small (8), we can have threads each compute a few output elements
Actually, to keep things manageable and correct, let me first try fusing attention + gate + output projection, and keep layer norm and input/output linears in PyTorch but transposed. But the reference does permute, then layer norm, then Q/K/V on the permuted tensor. So if we want to fuse, we need to handle the permute in the kernel too.
Let me think about this differently. The PyTorch reference does:
1. permute(0, 2, 1, 3) -> (B, N, S, D)
2. layer_norm over D
3. Q, K, V, G linears (each D->D)
4. reshape to heads
5. attention
6. gate
7. reshape
8. out_proj
9. permute back
For maximum fusion, I want one kernel that takes (B, S, N, D) and produces (B, S, N, D).
But each linear layer needs its own weight matrix. We can pass them all as arguments.
Let me try a fused kernel where:
- Each block handles one (B, N) pair
- Block has enough threads to compute all linears and attention
- We use shared memory for intermediate results
For (B, N) = (2, 32), we have 64 blocks. Each block handles S=8, h=4, d=16, D=64.
Shared memory needs:
- Input X: 8 * 64 * 4B = 2KB
- Q/K/V/G: 4 * 8 * 64 * 4B = 8KB
- Attention scores: 8 * 8 * 4B = 256B per head = 1KB total
- Various buffers
Total shared memory: ~16KB, well within limits.
Let me write a kernel with 256 threads per block (8 warps). With 64 blocks, that's 16384 threads total. The GPU can handle many more, but this is fine for a first attempt.
Actually, I want to be more careful about the linear layers. Computing Q = X @ W_Q^T where X is (S, D) and W_Q is (D, D):
- Each output element is dot product of a row of X with a column of W_Q (which is a row of W_Q^T)
- We have 256 threads computing 8 * 64 = 512 output elements for Q
- Each thread computes 2 elements, with each element being a dot product of 64 floats
- This can be parallelized as: each thread loads some elements of X to shared mem, then each thread computes some output elements
For such small matrices, we can use a simple approach: each thread computes one output element of Q (or a small tile). 256 threads, 512 outputs -> 2 outputs per thread. For each output, we read the corresponding row of X from shared mem and iterate over the 64 columns of W_Q.
Wait, W_Q is stored in global memory (or we can load it to shared mem). W_Q is 64*64 = 4096 floats = 16KB. For 4 different weights (WQ, WK, WV, WG), that's 64KB. Plus out_proj is another 16KB. Total 80KB. That's a lot for shared memory but manageable if we reuse it.
Actually, on H100, shared memory is 228KB per SM, and with 64 blocks, each SM might get 1 block (132 SMs on H100? Actually no, 64 blocks on an H100 with many SMs means some SMs are idle or get 1 block). With 64KB of weights + 16KB for intermediates, we need ~80KB shared memory per block. This might reduce occupancy but could still be okay.
Let me reconsider. Actually H100 has 132 SMs, so 64 blocks means about half the SMs get one block. With 80KB shared memory per block, we'd use ~5MB of shared memory total (which is fine since it's distributed across SMs). The shared memory per SM is 228KB, so 80KB per block is okay.
But wait - occupancy might be limited if we use too much shared memory. On H100, each SM can have up to 32 thread blocks. With 80KB per block, max blocks per SM = 228KB/80KB = 2 blocks. That's fine.
Let me design the kernel more carefully:
```cuda
__global__ void fused_attention(
const float* __restrict__ msa_repr,
const float* __restrict__ msa_mask,
const float* __restrict__ weight_q,
const float* __restrict__ weight_k,
const float* __restrict__ weight_v,
const float* __restrict__ weight_g,
const float* __restrict__ weight_out,
const float* __restrict__ bias_g,
const float* __restrict__ bias_out,
const float* __restrict__ ln_weight,
const float* __restrict__ ln_bias,
float* __restrict__ out,
int B, int S, int N, int D, int H, int d)
```
Wait, the reference has:
- `gate = nn.Linear(msa_dim, msa_dim)` - has bias
- `out_proj = nn.Linear(msa_dim, msa_dim)` - has bias
- `layer_norm = nn.LayerNorm(msa_dim)` - has weight and bias
- `query, key, value = nn.Linear(msa_dim, msa_dim, bias=False)` - no bias
I need to extract these weights and pass them to the kernel.
Actually, `nn.Linear` stores weights as (out_features, in_features) and they're accessible as `module.weight.data` and `module.bias.data`.
Wait, let me re-examine the problem. The evaluation system creates a `ModelNew` with the same constructor args, then runs it with the same inputs. I need to initialize my weights the same way and use them.
But I can't easily use custom CUDA kernels with nn.Linear weights because of the RowMajor vs ColMajor issue. PyTorch stores linear weights as (out_features, in_features) in row-major order, so `weight[o, i]` gives the weight from input i to output o.
In CUDA, when I do `output[s, o] = sum_i X[s, i] * W[o, i]`, that's correct for PyTorch's weight layout.
Wait, for PyTorch nn.Linear: `y = x @ W^T + b` where W is (out, in).
So `y[i, o] = sum_j x[i, j] * W[o, j]`.
Yes, so in CUDA, for output position (s, o), I sum over j: `X[s, j] * W[o, j]`.
Alright, let me write a more practical kernel. Given the complexity of perfectly fusing everything, let me first try a simpler approach: do the permutation, layer norm, and input linears in PyTorch, but fuse the attention, gating, output projection, and final permutation in a custom kernel.
Actually, let me reconsider. Given the small sizes, each PyTorch operation might have high overhead. Fusing more is better. But let me start with a reasonable fusion and see if it's fast enough.
Strategy 1: Keep layer norm + 4 linears in PyTorch, fuse attention + gate + out_proj + final permute.
Strategy 2: Fuse everything into one kernel.
Let me try Strategy 2 because the problem sizes are tiny and kernel launch overhead dominates.
Actually, let me think about how to efficiently parallelize the linear layers. With D=64 and S=8:
- Computing Q from X: X is (8, 64), W_Q is (64, 64)
- Each of the 512 output elements needs a dot product of 64 elements
- With 256 threads, each thread does 2 dot products of length 64
- That's very little work per thread
But attention is also small: Q*K^T is (8, 8) with d=16, so each element needs 16 multiplies and 15 adds.
Then softmax over 8 elements.
Then attn @ V is (8, 8) * (8, 16) = 8*16, each element needs 8 multiplies and 7 adds.
So per head:
- Linear Q, K, V, G: 4 * 8 * 64 * 64 = 131072 FLOPs
- Attention scores: 8 * 8 * 16 = 1024 FLOPs
- Softmax: negligible
- Attn * V: 8 * 8 * 16 = 1024 FLOPs
- Gate multiply: 8 * 64 = 512 FLOPs
- Out proj: 8 * 64 * 64 = 32768 FLOPs
Total per head: ~165K FLOPs, so ~660K FLOPs per (B, N)
For 64 (B, N) pairs: ~42M FLOPs total
At 67 TFLOPS, this would take less than 1 microsecond if compute bound. But we're very memory bound or overhead bound with such small sizes.
Actually, the PyTorch kernels each launch with some overhead and each reads/writes memory. Fusing into one kernel with one memory read and one memory write could be ~10-50x faster.
Let me design the kernel with one block per (b, n), which handles all 4 heads.
For the linear layers, let me use a simple but correct approach. Since S=8 and D=64 are small, I'll load X into shared memory, then have threads compute output elements.
```cuda
// Shared memory layout:
// smem[0:512] = X (8 x 64)
// smem[512:512+512] = Q (8 x 64)
// etc.
// But we can reuse shared memory more carefully.
// Step 1: Load X from global to shared mem
// Step 2: LayerNorm over D dimension
// Step 3: Compute Q, K, V, G using weights from global mem
// Step 4: For each head, compute attention
// Step 5: Gate multiply
// Step 6: Output projection
// Step 7: Write result
```
Actually, since we have 4 heads and head_dim=16, we can think of Q/K/V/G as (S, H, d) = (8, 4, 16) = same 512 elements.
For attention, I'll process one head at a time or all heads simultaneously depending on thread count.
With 256 threads and 4 heads, I can assign 64 threads per head.
For Q*K^T:
- Each head has Q: (8, 16), K: (8, 16)
- Need to compute (8, 8) attention scores
- With 64 threads per head, each thread can compute one row of 8 scores, or compute some scores collaboratively.
Actually, for such tiny matrices, it might be fastest to have all 64 threads collaboratively compute the 8x8 matrix.
Let me think about a simpler approach: use just 128 threads per block, or even 64.
With 64 threads per block (one warp per head!):
- 4 warps, 1 warp per head = 128 threads total... wait no, 4 warps = 128 threads.
- Actually, if we want one warp per head, that's 32 threads * 4 heads = 128 threads.
- But 32 threads computing an 8x8 attention might have some idle threads.
Actually, let me use 64 threads per block, where each thread handles one (s, h) across all heads? No, let me use a different organization.
Let me try a simpler organization at first and see if it works. I'll use 128 threads = 4 warps. Warp 0 handles head 0, warp 1 handles head 1, etc.
Within a warp handling one head:
- Q is (8, 16), but we can view it as 128 elements
- K is (8, 16), 128 elements
- V is (8, 16), 128 elements
- G is (8, 16), 128 elements
For computing attention scores (8x8):
- Each thread in the warp (32 threads) can compute a portion.
- 8x8 = 64 scores. 32 threads -> each thread computes 2 scores.
- A score at (i, j) = dot(Q[i], K[j]) / sqrt(d)
- Each thread loads Q[i] and K[j] from shared memory and computes dot product of 16 elements.
For softmax over 8 elements per row:
- Each thread in a warp can compute softmax for one row. 8 rows, but we have 32 threads. Let's have 8 threads each compute one row, with the rest idle. Or better, use warp-level primitives.
- Actually, with 32 threads per warp and 8 rows, we can have thread i compute row i % 8.
For attention @ V:
- Result is (8, 16) = 128 elements
- 32 threads -> 4 elements per thread
- Each element at (i, k) = sum_j attn[i, j] * V[j, k]
- 32 threads could compute one row at a time: for row i, compute 16 elements. 32 threads -> about 2 threads per element? Or just have 16 threads each do one element, 16 idle.
This seems messy. Let me think of a cleaner approach.
What if each block has just D=64 threads? Then for each head (d=16), we have 64 threads.
For attention scores: we need to compute 8x8 matrix. Maybe use a different thread organization.
Actually, here's a cleaner idea: use one thread per output element for most operations.
For Q computation: Q has S*D = 512 elements. With 512 threads, one thread per element. But 512 threads per block might be too many (we only have 64 blocks and 132 SMs). Actually 512 threads * 64 blocks = 32768 threads, and H100 can handle that easily.
But let me check: 512 threads per block, 64 blocks. With 2048 threads per SM, each SM could theoretically run 4 blocks (if shared memory allows). But 512 threads per block on H100 has 16 warps, which is fine.
Wait, let's see. With 512 threads, we have 16 warps per block, 64 blocks = 1024 warps total. H100 has 132 SMs, each can have 64 warps = 8448 warps. So we're well under the limit.
With 512 threads per block:
- Load X: 8*64 = 512 elements, each thread loads one element. Perfect.
- LayerNorm: each thread loads one element, we need warp-level reduce for mean and variance. With 512 threads over 8*64, actually we do per-row (over D). For each of the 8 rows, 64 threads compute the mean and variance of that row. Perfect! 64 threads per row.
- Compute Q: Q has 512 elements, each thread computes one. Each element is a dot product of length 64. We can have threads load X to shared mem, then each thread reads a row of X and a column of W_Q.
Actually, computing one element of Q requires reading one row of X (64 floats) and one column of W_Q (64 floats). If each thread does this independently, we'd read X 512 times. Better to load X to shared mem once.
If X is in shared mem and W_Q is in global mem, each thread reads one row of X from shared mem and one column of W_Q from global mem, then computes dot product.
The same pattern applies to K, V, G.
For attention: Now Q, K are in shared mem. For head h, Q_h is (8, 16).
We have 512 threads, 4 heads = 128 threads per head.
For head h, attention scores are (8, 8) = 64 elements.
We can have 64 of the 128 threads each compute one score, and the other 64 help with loading or are idle.
Actually, better: each score is dot(Q[i], K[j]) / sqrt(d), length 16.
With 64 threads each computing one score, we can compute all 64 scores in parallel. Then for softmax, we'd need to synchronize.
Hmm, but how are the threads organized within a head? Let me think...
128 threads per head:
- For attention scores (8, 8 = 64 scores): 64 threads active, 64 idle. Not great.
- For matmul attn @ V (8, 16 = 128 outputs): 128 threads active, one per output. Perfect!
Let me try a different idea: instead of 128 threads per head, use 32 threads per head (one warp).
- For attention scores (64 elements): each thread computes 2 scores.
- For softmax: can use warp shuffle to compute max and sum for each row.
- For attn @ V (128 elements): each thread computes 4 elements.
This seems much cleaner! 4 warps * 32 threads = 128 threads per block.
So: 128 threads per block, 4 warps, one warp per head, 64 blocks for (B, N).
Total: 8192 threads. H100 has ~16896 CUDA cores, so we're using about half. But with such small work, this might be fine.
Let me design with 128 threads per block, 4 warps where warp w handles head w.
Wait, but layer norm and linear layers need to operate across all 512 elements. With only 128 threads, each thread would do 4 elements. That's fine! Actually, it might be even better than 512 threads because we need fewer blocks.
Let me reconsider: 64 blocks with 128 threads = 8192 threads total. H100 has 132 SMs, so each SM gets on average ~62 threads, which is 2 warps. That's potentially low occupancy but might still be okay.
Actually, if each warp handles one head and there are 4 warps per block, and 64 blocks, that's 256 warps total. H100 can handle 8448 warps, so we're at ~3% occupancy. That's not ideal. But the work per warp is substantial enough that maybe it's okay.
Wait, let me reconsider the occupancy issue. H100 can have up to 2048 threads per SM (64 warps). With 128-thread blocks, each SM could run up to 16 blocks. But we only have 64 blocks total. So unless the kernel is heavily compute bound, we might not saturate the GPU.
However, given that each block does substantial work (several linear layers + attention), and the entire problem only needs ~40MFLOPs which is tiny, the kernel might still be faster than PyTorch simply due to avoiding intermediate memory traffic and kernel launches.
Let me try with 256 threads per block. That gives us 8 warps per block. We have 64 blocks, so 512 warps total. Still low but better. Each block is larger.
With 256 threads:
- We can assign 64 threads per head (2 warps per head)
- For linear layers, 256 threads divide 512 output elements evenly: 2 elements per thread
- For attention scores, 64 per head compute 64 scores: 1 score per thread
- For attn @ V, 64 per head compute 128 outputs: 2 outputs per thread
That seems good! Let me go with 256 threads per block.
Let me write out the kernel design:
Block dimensions: (256) - one-dimensional
Grid dimensions: (B, N) = (2, 32) -> 64 blocks
Shared memory:
- X_layernormed: 8 * 64 * 4 = 2048 bytes (or we can compute in place)
- QKVG: 4 * 8 * 64 * 4 = 8192 bytes, but we can reuse
- Attn scores: 8 * 8 * 4 = 256 bytes per head. We can compute and store in registers or shared.
- Actually, let's be careful about shared memory usage. We want to fit within 48KB or so to allow more blocks per SM if needed.
Let's use:
- smem_X: 8 * 64 floats = 2048 bytes (input after layer norm)
- For each head, we compute Q/K/V/G on the fly or reuse smem_QKVG
Actually, since D=64 and we're processing one head at a time in groups of threads, we might not need to store all Q/K/V/G simultaneously.
Let me think more carefully about the thread assignment with 256 threads and 4 heads.
I'll use a 2D thread mapping conceptually: threads are organized as (head, tid_in_head) where head is 0..3 and tid_in_head is 0..63.
For linear layers:
- Q has shape (8, 64) but really (8, 4, 16). For output Q[s, h, d], we need dot(X[s, :], W_Q[h*d + d, :]).
- With 256 threads = 4 heads * 64 threads per head.
- Each of the 64 threads per head computes 8 * 16 / 64 = 2 elements of Q per head.
- Specifically, thread (h, t) computes Q[s, h, d] for some (s, d) pairs.
Actually, let me map it explicitly:
- Flatten output as [h * 128 + s * 16 + d] where h in [0, 3], s in [0, 7], d in [0, 15]
- Total 512 elements. 256 threads -> each thread handles 2 output elements.
- Thread idx computes elements at positions 2*idx and 2*idx+1 in the flattened output.
- For each element, the thread loads the corresponding row of X from shared mem and does dot product with the corresponding row of W from global mem.
For PyTorch nn.Linear weights: W is (out, in). So W_Q[o, i] is the weight from input i to output o.
For Q output at position (s, o), we compute: sum_i X[s, i] * W_Q[o, i].
So if thread idx handles output positions o1 and o2, it needs to read X[s1, :] and X[s2, :] from shared mem, and W_Q[o1, :] and W_Q[o2, :] from global mem, then compute two dot products of length 64.
This is nice because each thread is independent for the linear layers!
Similarly for K, V, G.
For layer norm:
- 256 threads handling 8 rows. For each row, 32 threads can participate in the reduction.
- With 8 rows, we need 256 threads total. Perfect! 32 threads per row.
- Row r is handled by threads r*32 to (r+1)*32-1.
- Mean and variance computed using warp shuffle.
Alright, let me try to write this kernel.
For attention scores:
- For head h, we have Q_h (8, 16) and K_h (8, 16) in some form.
- With 64 threads per head, how do we compute the 8x8=64 scores?
- Thread t in head h can compute score[t] where t in [0, 63].
- Map t to (i, j) = (t / 8, t % 8).
- Score(i, j) = dot(Q_h[i, :], K_h[j, :]) / sqrt(d)
- Each thread loads Q_h[i, :] and K_h[j, :] and computes dot product of 16 elements.
- We can store Q_h and K_h in shared memory for the head.
But 8x16 = 128 elements per head. For 4 heads, that's 512 elements = 2048 bytes. Plus V (another 2048 bytes) and attn scores (8*8*4 = 256 bytes per head = 1024 bytes total). Total ~7KB. Fine.
Actually, we could store all Q/K/V/G in the same smem_X space if we don't need X anymore after computing them. But let's use separate buffers for clarity.
Wait, we do need X for all 4 linear layers. So X stays in shared mem. Q/K/V/G can be computed and stored, or we can reuse space.
Let me use 5 separate shared memory regions:
- smem_X: 8 * 64 floats
- smem_Q: 8 * 64 floats (but really Q for all heads)
- smem_K: 8 * 64 floats
- smem_V: 8 * 64 floats
- smem_G: 8 * 64 floats (for gate after sigmoid)
Total: 5 * 2048 = 10240 bytes = 10KB
Then for attention per head:
- smem_attn: 8 * 8 floats = 256 bytes per head
- We can compute head by head and reuse the same 256 bytes, or use 1024 bytes total.
- Then smem_out_attn: 8 * 16 floats = 512 bytes per head
- Or we can compute directly to registers.
Actually, since each head's threads are distinct, they can use registers for intermediate results. Let me think about what needs to be in shared memory vs registers.
Let me try a different approach: instead of trying to be clever with shared memory, let me do:
1. Load X from global to shared memory.
2. Layer norm in shared memory.
3. Each thread computes its assigned elements of Q, K, V, G and stores them in shared memory.
4. __syncthreads()
5. For attention: thread in head h computes its assigned attention scores using Q and K from shared memory. Stores in shared memory (or registers if only needed for one row).
6. __syncthreads()
7. Softmax: per row. This requires some care. With 64 threads per head and 8 rows, 8 threads per row can do the reduction.
8. __syncthreads()
9. Each thread computes its assigned outputs of attn @ V.
10. Multiply by gate.
11. __syncthreads()
12. Output projection: similar to step 3, but now input is the attention output (8 x 64) and weight is W_out (64 x 64).
13. Write to global memory (with proper transpose to get back to B, S, N, D).
For softmax, it might be easier to store attention scores in shared memory. Let's use smem_attn[4][8][8] or smem_attn[8][8] reused per head.
Wait, with 4 heads and 64 threads per head computing all 64 scores simultaneously, we need 4*64 = 256 threads. Perfect!
But then for softmax, each head needs to normalize 8 rows of 8 elements. With 64 threads per head, we can assign 8 threads per row.
Actually, let me process one head at a time at the block level to simplify. No wait, we want parallelism across heads too.
OK here's my revised plan:
**Block**: 256 threads
**Mapping**: thread_idx -> (head_id = idx / 64, local_tid = idx % 64)
For attention, all 256 threads are active simultaneously computing scores for their respective heads.
For softmax within a head, head_id uses local_tid in [0, 63]. There are 8 rows and each row has 8 elements. We can do a reduction over the 8 elements of each row.
Option A: Use warp shuffle. Assign local_tid to row = local_tid / 8. Then threads with the same row work together. But 64 / 8 = 8 threads per row. That's not a full warp. We could use local_tid % 8 to pick the column, with 8 threads cooperating per row. With 8 threads, we can do a cooperative reduction.
Actually, 8 threads per row might be a bit synchrony-heavy but should work. Let me think about how to do softmax with 8 threads:
For each row i:
- thread j (j in 0..7) loads score[i, j]
- Compute max using shared memory or warp shuffle
- Compute exp(score - max) for each element
- Compute sum using shared memory or warp shuffle
- Divide by sum
With only 8 threads, warp shuffle over the first warp (threads 0-31) would include threads from multiple rows. But since 8 threads per row, 4 rows fit in one warp. That's messy.
Alternative: Have each thread compute softmax for an entire row independently. 8 threads per head compute 8 rows. The other 56 threads are idle during softmax. That's simple and the cost is tiny (only 8 rows of 8 elements each).
Yes, let's do that! For softmax, 8 threads per head each compute one full row of 8 elements. The remaining 56 threads per head are idle. Since this is a tiny amount of work, the divergence cost is negligible.
Then for attn @ V, all 64 threads per head are active again.
Great, let me write this kernel!
Actually, I realize we might want to do the softmax in registers to avoid extra shared memory. Let me just have each thread store 8 scores in registers, compute softmax, and then use those for attn @ V.
But wait - if each thread only computed one row of scores, then for attn @ V at (i, k) = sum_j attn[i, j] * V[j, k], we'd need the full row of scores.
Let me reconsider the score computation.
Option 1: Each thread computes one or more complete rows of scores.
- 8 rows, 64 threads per head -> 8 threads per row. Not clean.
Option 2: Each thread computes one score (as I originally thought).
- 64 threads, 64 scores. Then for softmax, 8 threads each need a full row.
- Problem: thread 0 has score(0,0), thread 1 has score(0,1), etc. To compute softmax of row 0, these 8 threads need to share their values.
With warp shuffle, threads in the same warp can share. If we arrange it so that row 0's scores are in threads 0-7 of a warp, then thread 0 could do the softmax for row 0 using shuffles... but we'd need to broadcast the max and sum to threads 0-7.
Actually, with 64 threads per head, and we have 4 heads, that's 256 threads = 8 warps. Warp 0 and 1 handle head 0, warp 2 and 3 handle head 1, etc. (2 warps per head = 64 threads).
Within a head's 2 warps (64 threads), if we map:
- local_tid 0..7: row 0
- local_tid 8..15: row 1
- etc.
- local_tid 56..63: row 7
Then each row's 8 threads are in the same warp (since 32 threads per warp, rows 0-3 are in warp 0 and rows 4-7 are in warp 1).
For row 0 in warp 0:
- Threads 0-7 have score[0][0..7].
- Thread 0 can compute the max using warp shuffle across threads 0-7 (or actually, since divergent threads in a warp are fine for reductions, we can have thread 0 compute the max of all 8 elements using shuffles, then broadcast).
- Actually, this is getting complicated.
Simplest approach: store the full 8x8 attention matrix in shared memory per head. Then any thread can read any element.
smem_attn: 8 * 8 floats per head. If we process heads sequentially at some level, we just need one 8x8 buffer. But 64 blocks * 8 * 8 * 4B = 16KB total if all blocks run concurrently, which is fine. Or we can have 4 separate 8x8 buffers = 1KB per block.
Let me use a small shared memory buffer for attn scores and do everything in a straightforward way.
Actually, for maximum simplicity: I'll have each head's 64 threads compute all 64 scores and write to shared memory. Then __syncthreads(). Then 8 threads per head read a row, compute softmax in registers, and write back. Then __syncthreads(). Then 64 threads each compute 2 elements of attn @ V.
Wait, 8 x 16 = 128 elements in attn @ V output. With 64 threads, that's 2 elements per thread. Nice!
Let me map:
- Score computation: thread t computes score[t] where t = i*8 + j.
- Store in smem_attn[i][j].
- __syncthreads()
- Softmax: thread r (r in 0..7) reads row r of smem_attn into registers, computes softmax, writes back.
- __syncthreads()
- Attn @ V: thread t computes output[t] where t in 0..127. Map t = i*16 + k.
- For output[i][k] = sum_j smem_attn[i][j] * V[j][k]
- Each thread does 8 multiplies and 7 adds.
- Perfect!
So per head, we need:
- smem_attn: 8x8 floats
- smem_V_head: 8x16 floats (but V for all heads is 8x64 = 512 floats = 2KB)
With 4 heads running simultaneously and sharing the same smem_attn? No, each head needs its own softmax. So we'd need 4 * 8x8 = 256 floats = 1KB. Or we can reuse one 8x8 buffer across heads if we process heads sequentially.
Since we have 64 threads per head and want all 4 heads active, we need separate buffers. 4 * 64 * 4 = 1024 bytes. That's fine.
Total shared memory:
- smem_X: 8 * 64 * 4 = 2KB
- smem_Q: 8 * 64 * 4 = 2KB (can reuse as needed)
- smem_K: 8 * 64 * 4 = 2KB
- smem_V: 8 * 64 * 4 = 2KB
- smem_G: 8 * 64 * 4 = 2KB
- smem_attn: 4 * 8 * 8 * 4 = 1KB
- smem_out_proj_input: 8 * 64 * 4 = 2KB (before output projection)
- smem_out: 8 * 64 * 4 = 2KB
Total: ~15KB. That's very reasonable!
Actually, let me reuse buffers more aggressively:
- smem_X: 2KB (kept throughout for linear layers, or we can overwrite after computing Q/K/V/G)
- We can compute Q, K, V, G into their own buffers, but Q and K are only needed for attention, V and G are needed later.
- After computing attention, Q and K buffers can be reused.
- So: smem_Q + smem_K + smem_V + smem_G = 8KB.
- After attention, smem_Q and smem_K can be freed. smem_V and smem_G still needed.
- smem_attn = 1KB.
- After attn @ V + gate, the result goes into say smem_Q (8x64). Then we do out_proj: input is smem_Q, output is smem_out.
- So we need: 2KB (X) + 8KB (QKVG) + 1KB (attn) + 2KB (out) = 13KB.
Actually, I'm overcomplicating this. Let me just lay out all the buffers and not worry about 13KB being too much.
Now let me write the actual CUDA kernel code.
Oh wait, I also need to handle the mask! In the reference:
```python
col_mask = msa_mask.permute(0, 2, 1) # (B, N, S)
mask = col_mask.view(B, N, 1, 1, S).expand_as(attn)
attn = attn.masked_fill(mask == 0, float("-inf"))
```
So mask is applied per (B, N, S). The mask tells us which sequences in the MSA are present. mask[b, n, s] = 0 or 1.
If mask == 0, we set attn to -inf before softmax. This means that in the softmax, those positions get 0 attention weight.
We can incorporate this into the attention score computation: if mask[s'] == 0 for key position s', then score[i, s'] = -inf.
Actually, the mask is applied to the key dimension. For each query position i, we look at mask[j] for key position j. If mask[j] == 0, set score[i, j] = -inf.
Wait, but the mask is (B, S, N). After permute, it's (B, N, S). So for a given (b, n), we have mask_s[s] for each s in 0..S-1.
So in the kernel, for (b, n), we need to read the mask values. If mask_s[s] == 0, then all key positions with that s get -inf attention.
Let me load the mask into shared memory or registers as well. It's only 8 floats per (b, n).
Now, for dropout - the reference uses nn.Dropout but the task says we need numerical equivalence. Actually, dropout is stochastic. But in evaluation for correctness, I think they might use dropout=0.0 or set a fixed seed? Let me check the constructor.
Looking at the get_init_inputs: `return [msa_dim, num_heads]`. So `dropout=0.0` by default.
In the forward pass, the reference does `attn = self.dropout(attn)`. With dropout=0.0, this should be a no-op (or identity). PyTorch Dropout with p=0 returns input unchanged.
So I can ignore dropout. Great!
Actually wait, I should double check. If dropout=0.0, nn.Dropout(0.0) returns identity. In the reference, `self.dropout = nn.Dropout(dropout)`, and since default dropout is 0.0, it's a no-op. I'll assume this is the case.
Now let me also consider: the reference initializes weights randomly (from default PyTorch init). My ModelNew needs to use the same weights if it reuses the reference layers, or I need to initialize my own weights and do custom matmuls.
The simplest and most reliable approach is:
1. In ModelNew.__init__, create the same nn.Modules as Model
2. In ModelNew.forward, call the custom kernel with the module weights
This way, I don't need to worry about weight initialization - PyTorch handles it the same way.
So in ModelNew:
```python
self.layer_norm = nn.LayerNorm(msa_dim)
self.query = nn.Linear(msa_dim, msa_dim, bias=False)
self.key = nn.Linear(msa_dim, msa_dim, bias=False)
self.value = nn.Linear(msa_dim, msa_dim, bias=False)
self.gate = nn.Linear(msa_dim, msa_dim)
self.out_proj = nn.Linear(msa_dim, msa_dim)
# No dropout (or identity dropout)
```
In forward, I extract the weights and call the kernel.
Wait, but I also need to match the same random initialization. Since PyTorch's init for nn.Linear and nn.LayerNorm is deterministic given the same seed, and the evaluation framework probably creates Model and ModelNew separately, they might have different initializations unless I copy weights or rely on the same seed.
Hmm, wait. The evaluation procedure says "Replace the forward computation". It probably compares ModelNew against Model by running both. But it doesn't explicitly say the weights must be initialized identically.
Actually, it says "Accept the same constructor arguments as Model." and "Implement forward() with the same signature." and "Produce numerically equivalent outputs."
For numerical equivalence, the weights need to be the same. I think the evaluation must somehow ensure this, or it initializes both models with the same state (or doesn't care about init and tests with zero weights or something).
Actually, the typical setup is: the evaluation creates ModelNew with get_init_inputs, then runs get_inputs through it. The weights are whatever PyTorch initializes them to. For comparison, they probably also create a Model with the same args, or they use a fixed seed, or they verify correctness by checking the implementation matches in some controlled way.
Let me not worry about this too much. If I use the same nn.Module constructors, the weights will be initialized the same way given the same RNG state. But different model instantiations have different RNG state unless we set the seed.
I think the standard approach in these tasks is to just use the same nn.Modules in ModelNew and trust that the evaluation handles this correctly (maybe by zeroing weights or using a fixed seed, or maybe by just comparing structure and then testing with specific weight values).
Actually, a safer approach is just to inherit from Model or replicate it exactly, then add the custom kernel. But the task says "Replace the forward computation".
You know what, let me just use the same nn.Module initialization as the reference and assume the evaluation handles weight matching appropriately. If it doesn't, I can adjust.
Actually, looking at similar tasks, the evaluation usually checks that ModelNew.forward produces exactly the same output as Model.forward given the same weights. So they probably copy weights or test in a way that ensures matching weights.
To be safe, in my .forward() I can pass self.layer_norm.weight, self.query.weight, etc. to the kernel, regardless of their actual values. This means my kernel just needs to perform the same mathematical operations.
Let me now write the full kernel.
Key parameters:
- B = batch_size (2)
- S = msa_depth (8) - sequences
- N = seq_len (32) - positions
- D = msa_dim (64) - dimension
- H = num_heads (4)
- d = head_dim (16)
Memory layout:
- Input msa_repr: (B, S, N, D) in row-major. Index: msa_repr[b*S*N*D + s*N*D + n*D + d]
- Output: same layout
- msa_mask: (B, S, N). Index: msa_mask[b*S*N + s*N + n]
Inside kernel for block (b, n):
- Read X[s, d] = msa_repr[b, s, n, d] for s in [0, S-1], d in [0, D-1]
- Read mask_s[s] = msa_mask[b, s, n] for s in [0, S-1]
Wait, I need to be careful about the mask. In the reference:
```python
col_mask = msa_mask.permute(0, 2, 1) # (B, N, S)
mask = col_mask.view(B, N, 1, 1, S).expand_as(attn)
```
So mask[b, n, s] corresponds to sequence s at position n. In the attention, mask is applied to the key dimension. If mask[b, n, j] == 0, then all query positions i have attention score to key j set to -inf.
In the kernel, for block (b, n), I load mask_per_seq[s] = msa_mask[b, s, n]. Wait, msa_mask is (B, S, N), so msa_mask[b, s, n] gives the mask for batch b, sequence s, position n.
After permute(0, 2, 1), it becomes (B, N, S), so col_mask[b, n, s] = msa_mask[b, s, n]. Yes.
So in the kernel, mask_s[s] = msa_mask[b * S * N + s * N + n].
For the attention mask logic: if mask_s[j] == 0, then attn[i, j] = -inf for all i.
For softmax: if all mask_s[j] for j in a row are 0, then softmax gives NaN. But typically there should be at least one non-zero mask value.
Let me also think about LayerNorm. Standard PyTorch LayerNorm:
```python
y = (x - mean) / sqrt(var + eps) * weight + bias
```
Where mean and var are computed over the last dimension (D=64).
- eps is 1e-5 by default.
OK let me write the kernel. I'll use a template/constexpr approach for the sizes since they're fixed for this specific model, but actually I should make it work for any sizes. But given the small fixed sizes in the problem, I can either hardcode or use runtime values. I'll use runtime values with the understanding that it should work for any valid sizes.
Actually, for simplicity and performance, let me hardcode the known sizes where it helps, but still accept general sizes. Or I can just write it generally and trust the compiler to optimize.
Let me write the code:
```cuda
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <math.h>
__global__ void fused_msa_attention_kernel(
const float* __restrict__ msa_repr,
const float* __restrict__ msa_mask,
const float* __restrict__ q_weight,
const float* __restrict__ k_weight,
const float* __restrict__ v_weight,
const float* __restrict__ g_weight,
const float* __restrict__ out_weight,
const float* __restrict__ g_bias,
const float* __restrict__ out_bias,
const float* __restrict__ ln_weight,
const float* __restrict__ ln_bias,
float* __restrict__ output,
int B, int S, int N, int D, int H)
{
// Each block handles one (b, n) pair
int b = blockIdx.x;
int n = blockIdx.y;
if (b >= B || n >= N) return;
int tid = threadIdx.x;
int num_threads = blockDim.x;
// We assume D is a multiple of H and other expected properties
int d = D / H;
float scale = 1.0f / sqrtf((float)d);
// Shared memory declarations
extern __shared__ float shared_mem[];
// Layout:
// smem_X: S * D
// smem_Q: S * D
// smem_K: S * D
// smem_V: S * D
// smem_G: S * D
// smem_attn: H * S * S (not really needed if we process sequentially, but let's say H * S * S)
// Actually, let me simplify and use smaller buffers
float* smem_X = shared_mem;
float* smem_Q = smem_X + S * D;
float* smem_K = smem_Q + S * D;
float* smem_V = smem_K + S * D;
float* smem_G = smem_V + S * D;
float* smem_attn = smem_G + S * D; // H * S * S
float* smem_out = smem_attn + H * S * S;
// Load X and mask from global memory
const float* x_ptr = msa_repr + b * S * N * D + n * D;
// Note: msa_repr[b, s, n, d] = msa_repr[b * S * N * D + s * N * D + n * D + d]
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int d_idx = idx % D;
// x_ptr points to msa_repr[b, 0, n, 0], so offset is s * N * D + d_idx
smem_X[idx] = x_ptr[s * N * D + d_idx];
}
// Load mask: S elements
float mask_s[8]; // S is small, can load into registers
if (tid < S) {
mask_s[tid] = msa_mask[b * S * N + tid * N + n];
}
__syncthreads();
// LayerNorm over D dimension for each of S rows
// Each row handled by D threads? No, we have num_threads threads.
// Let's do it simply: each thread handles some rows.
for (int s = tid; s < S; s += num_threads) {
float* row = smem_X + s * D;
// Compute mean
float sum = 0.0f;
for (int i = 0; i < D; i++) {
sum += row[i];
}
float mean = sum / D;
// Compute variance
float var_sum = 0.0f;
for (int i = 0; i < D; i++) {
float diff = row[i] - mean;
var_sum += diff * diff;
}
float var = var_sum / D;
float inv_std = 1.0f / sqrtf(var + 1e-5f);
// Normalize
for (int i = 0; i < D; i++) {
row[i] = (row[i] - mean) * inv_std * ln_weight[i] + ln_bias[i];
}
}
__syncthreads();
// Compute Q, K, V, G
// Q[o] = sum_i X[i] * W_Q[o, i]
// W_Q shape: (D, D). W_Q[o, i] is at q_weight[o * D + i]
// Output shape: S * D
auto compute_linear = [&](float* out, const float* weight, const float* bias, bool use_bias, bool use_sigmoid) {
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float* x_row = smem_X + s * D;
float sum = 0.0f;
for (int i = 0; i < D; i++) {
sum += x_row[i] * weight[o * D + i];
}
if (use_bias) {
sum += bias[o];
}
if (use_sigmoid) {
sum = 1.0f / (1.0f + expf(-sum));
}
out[idx] = sum;
}
};
compute_linear(smem_Q, q_weight, nullptr, false, false);
__syncthreads();
compute_linear(smem_K, k_weight, nullptr, false, false);
__syncthreads();
compute_linear(smem_V, v_weight, nullptr, false, false);
__syncthreads();
compute_linear(smem_G, g_weight, g_bias, true, true);
__syncthreads();
// Attention computation
// For each head
for (int h = 0; h < H; h++) {
float* q_h = smem_Q + h * d; // Actually Q is stored as (S, H, d)
float* k_h = smem_K + h * d;
float* v_h = smem_V + h * d;
float* g_h = smem_G + h * d;
float* attn_h = smem_attn + h * S * S;
// Compute Q*K^T / sqrt(d)
for (int idx = tid; idx < S * S; idx += num_threads) {
int i = idx / S;
int j = idx % S;
// If mask for key j is 0, set to -inf
if (mask_s[j] == 0.0f) {
attn_h[idx] = -INFINITY;
} else {
float sum = 0.0f;
float* q_i = q_h + i * D; // Wait, Q shape is (S, D), so q_h + i * D gives start of row i, but within head h it's q_h + i * D + ... ?
// No. If Q is (S, D) = (S, H, d), then Q[s, h, d] is at smem_Q[s * D + h * d + dd]
// So for head h, row i starts at smem_Q + i * D + h * d
float* q_row = smem_Q + i * D + h * d;
float* k_row = smem_K + j * D + h * d;
for (int dd = 0; dd < d; dd++) {
sum += q_row[dd] * k_row[dd];
}
attn_h[idx] = sum * scale;
}
}
__syncthreads();
// Softmax over rows (dim -1 in the reference)
for (int i = tid; i < S; i += num_threads) {
// Find max for numerical stability
float max_val = -INFINITY;
for (int j = 0; j < S; j++) {
max_val = fmaxf(max_val, attn_h[i * S + j]);
}
// Compute exp and sum
float exp_sum = 0.0f;
for (int j = 0; j < S; j++) {
float val = expf(attn_h[i * S + j] - max_val);
attn_h[i * S + j] = val;
exp_sum += val;
}
// Normalize
for (int j = 0; j < S; j++) {
attn_h[i * S + j] /= exp_sum;
}
}
__syncthreads();
// Compute attn @ V
for (int idx = tid; idx < S * d; idx += num_threads) {
int i = idx / d;
int k = idx % d;
float sum = 0.0f;
for (int j = 0; j < S; j++) {
sum += attn_h[i * S + j] * smem_V[j * D + h * d + k];
}
// Multiply by gate
sum *= smem_G[i * D + h * d + k];
smem_out[i * D + h * d + k] = sum;
}
__syncthreads();
}
// Out projection: smem_out (S, D) @ W_out^T -> output (S, D)
// W_out shape: (D, D)
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float* in_row = smem_out + s * D;
float sum = 0.0f;
for (int i = 0; i < D; i++) {
sum += in_row[i] * out_weight[o * D + i];
}
sum += out_bias[o];
// Write to global memory with transpose: back to (B, S, N, D)
// output[b, s, n, o] = sum
output[b * S * N * D + s * N * D + n * D + o] = sum;
}
}
```
Wait, there are some issues:
1. `smem_out` isn't defined in my shared memory layout. Let me fix that.
2. The attention output should not overwrite itself incorrectly across heads. Currently I have `smem_out` as a buffer, but the gate multiply writes to it for each head. If each head writes to different parts (h * d offset), and S * d threads handle all heads simultaneously... wait no, the loop processes heads sequentially. For head h, we write to `smem_out[i * D + h * d + k]`. If all heads are in the same loop, then for h=0 we write some values, then for h=1 we write different positions, etc. That should be fine as long as we don't have a __syncthreads() issue.
Actually, looking at my code: the gate multiply writes to `smem_out[i * D + h * d + k]` inside the head loop. Since each iteration of h writes to non-overlapping sections, and there's a __syncthreads() at the end of each iteration, this is correct.
But wait, if `num_threads` is 256 and we have a loop over H=4 heads, then only the first S*S=64 threads might be active in the attention score computation, and only S=8 threads in softmax, then S*d=128 threads in attn @ V. With 256 threads, half are idle in the attention score and softmax steps. That's fine.
Actually, a bigger issue: `smem_out` needs to be allocated! Let me recalculate shared memory sizes:
- smem_X: S * D
- smem_Q: S * D
- smem_K: S * D
- smem_V: S * D
- smem_G: S * D
- smem_attn: H * S * S
- smem_out: S * D
Total shared memory elements: 6 * S * D + H * S * S
For S=8, D=64, H=4:
6 * 512 + 4 * 64 = 3072 + 256 = 3328 floats = ~13KB
That's well within limits.
But there's a problem with how I defined smem_out in the attention loop. Let me redefine it:
```cuda
float* smem_attn = smem_G + S * D;
float* smem_out = smem_attn + H * S * S;
```
OK, but we need to make sure `smem_out` is used correctly. The attention result for each head is written into different parts of smem_out, which is fine.
Actually, there's another issue: `for (int idx = tid; idx < S * S; idx += num_threads)` with num_threads=256 means only the first 64 threads participate in computing attention scores for a given head. But since the head loop is sequential, threads 0..63 compute head 0, then head 1, etc. Threads 64..255 are idle during this part. That's fine for correctness, but a bit wasteful.
We could parallelize across heads as well. But since H=4 is small and S*S=64, it's hard to use all 256 threads effectively. We could have each head use 64 threads, and all 4 heads simultaneously use 256 threads. Let me restructure:
Instead of `for (int h = 0; h < H; h++)`, we can have `int h = tid / (S * S)` for score computation, but then we'd need separate thread mappings for different parts.
Actually, let me keep it simple. With 64 blocks and 256 threads each, we're launching 16384 threads. The overhead and memory savings from fusion will likely dominate. Let me start with this simpler version and see if it's fast enough.
Wait, looking more carefully at my code, there's a correctness issue with the mask. I declared `float mask_s[8];` inside the kernel as a per-thread array, but then I only load it if `tid < S`. Other threads will have uninitialized values. And when we check `mask_s[j] == 0.0f`, only threads with tid < S have valid masks.
For the score computation, all threads check `mask_s[j]`, but only threads with valid mask_s should do this. Actually, I should load mask_s into shared memory!
Let me fix that. Add a small shared memory buffer or just load it once per block.
Actually, the simplest fix: put mask in shared memory.
```cuda
float* smem_mask = smem_out + S * D; // S elements
```
But then my total shared memory increases by S=8 floats. Still fine.
Or even simpler: after __syncthreads() post-X-load, have thread 0 load all mask values:
```cuda
if (tid == 0) {
for (int s = 0; s < S; s++) {
mask_s_shared[s] = msa_mask[b * S * N + s * N + n];
}
}
__syncthreads();
```
But really, the simplest is to just have all threads load mask values when needed from global memory directly, since it's cached:
```cuda
float mask_j = msa_mask[b * S * N + j * N + n];
if (mask_j == 0.0f) {
attn_h[idx] = -INFINITY;
}
```
Since we're reading mask sequentially and it's small, global memory load should be cached. Let me do this.
Actually, let me simplify my kernel a lot by handling the mask directly in global memory.
Another issue: I'm not handling the case where a row of attention is all -inf (all masked out). In that case, softmax would give NaN. But this probably doesn't happen in normal inputs, and the reference would do the same.
Let me also reconsider the structure. A cleaner approach might be to use one block per head per (b, n), giving us B * N * H = 2 * 32 * 4 = 256 blocks. Then each block has S*d = 128 threads (or fewer). But then we'd need to sync across blocks for the output projection, which isn't possible.
Alternatively, one block per (b, n) with threads per head = 64 is reasonable.
Let me try a cleaner version of the kernel with explicit shared memory size calculation.
Actually, I realize my kernel might be able to be much simpler if I don't try to optimize the linear layers too much. Since D=64 and S=8, even a naive dot product loop should be fine.
Let me now write the actual complete Python module.
```python
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
from torch.utils.cpp_extension import load_inline
cuda_source = """
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <math.h>
__global__ void fused_msa_attention_kernel(
const float* __restrict__ msa_repr,
const float* __restrict__ msa_mask,
const float* __restrict__ q_weight,
const float* __restrict__ k_weight,
const float* __restrict__ v_weight,
const float* __restrict__ g_weight,
const float* __restrict__ out_weight,
const float* __restrict__ g_bias,
const float* __restrict__ out_bias,
const float* __restrict__ ln_weight,
const float* __restrict__ ln_bias,
float* __restrict__ output,
int B, int S, int N, int D, int H)
{
int b = blockIdx.x;
int n = blockIdx.y;
if (b >= B || n >= N) return;
int tid = threadIdx.x;
int num_threads = blockDim.x;
int d = D / H;
float scale = 1.0f / sqrtf((float)d);
extern __shared__ float shared_mem[];
float* smem_X = shared_mem;
float* smem_Q = smem_X + S * D;
float* smem_K = smem_Q + S * D;
float* smem_V = smem_K + S * D;
float* smem_G = smem_V + S * D;
float* smem_attn = smem_G + S * D;
float* smem_out = smem_attn + H * S * S;
// Load X
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int d_idx = idx % D;
smem_X[idx] = msa_repr[b * S * N * D + s * N * D + n * D + d_idx];
}
__syncthreads();
// LayerNorm
for (int s = tid; s < S; s += num_threads) {
float* row = smem_X + s * D;
float sum = 0.0f;
for (int i = 0; i < D; i++) sum += row[i];
float mean = sum / D;
float var_sum = 0.0f;
for (int i = 0; i < D; i++) {
float diff = row[i] - mean;
var_sum += diff * diff;
}
float inv_std = 1.0f / sqrtf(var_sum / D + 1e-5f);
for (int i = 0; i < D; i++) {
row[i] = (row[i] - mean) * inv_std * ln_weight[i] + ln_bias[i];
}
}
__syncthreads();
// Helper lambda doesn't work in CUDA C easily, just inline
// Compute Q
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
for (int i = 0; i < D; i++) {
sum += x_row[i] * q_weight[o * D + i];
}
smem_Q[idx] = sum;
}
__syncthreads();
// Compute K
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
for (int i = 0; i < D; i++) {
sum += x_row[i] * k_weight[o * D + i];
}
smem_K[idx] = sum;
}
__syncthreads();
// Compute V
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
for (int i = 0; i < D; i++) {
sum += x_row[i] * v_weight[o * D + i];
}
smem_V[idx] = sum;
}
__syncthreads();
// Compute G with sigmoid
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
for (int i = 0; i < D; i++) {
sum += x_row[i] * g_weight[o * D + i];
}
sum += g_bias[o];
smem_G[idx] = 1.0f / (1.0f + expf(-sum));
}
__syncthreads();
// Attention for each head
for (int h = 0; h < H; h++) {
// Compute scores
for (int idx = tid; idx < S * S; idx += num_threads) {
int i = idx / S;
int j = idx % S;
float mask_j = msa_mask[b * S * N + j * N + n];
if (mask_j == 0.0f) {
smem_attn[h * S * S + idx] = -INFINITY;
} else {
float sum = 0.0f;
for (int dd = 0; dd < d; dd++) {
sum += smem_Q[i * D + h * d + dd] * smem_K[j * D + h * d + dd];
}
smem_attn[h * S * S + idx] = sum * scale;
}
}
__syncthreads();
// Softmax
for (int i = tid; i < S; i += num_threads) {
float max_val = -INFINITY;
for (int j = 0; j < S; j++) {
max_val = fmaxf(max_val, smem_attn[h * S * S + i * S + j]);
}
float exp_sum = 0.0f;
for (int j = 0; j < S; j++) {
float val = expf(smem_attn[h * S * S + i * S + j] - max_val);
smem_attn[h * S * S + i * S + j] = val;
exp_sum += val;
}
for (int j = 0; j < S; j++) {
smem_attn[h * S * S + i * S + j] /= exp_sum;
}
}
__syncthreads();
// Attn @ V and gate
for (int idx = tid; idx < S * d; idx += num_threads) {
int i = idx / d;
int k = idx % d;
float sum = 0.0f;
for (int j = 0; j < S; j++) {
sum += smem_attn[h * S * S + i * S + j] * smem_V[j * D + h * d + k];
}
sum *= smem_G[i * D + h * d + k];
smem_out[i * D + h * d + k] = sum;
}
__syncthreads();
}
// Output projection
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* in_row = smem_out + s * D;
for (int i = 0; i < D; i++) {
sum += in_row[i] * out_weight[o * D + i];
}
sum += out_bias[o];
output[b * S * N * D + s * N * D + n * D + o] = sum;
}
}
"""
# Wait, I need to define a wrapper function for pybind
```
Actually, I need to be more careful about the wrapper function and how load_inline works.
For load_inline, I provide:
- `cuda_sources`: Contains the CUDA kernel(s)
- `cpp_sources`: Contains C++ wrapper functions using ATen tensors
The wrapper function name gets added to the `functions=[...]` list, and load_inline auto-generates a pybind11 module.
Let me write the complete code properly.
```python
import torch
import torch.nn as nn
import math
from torch.utils.cpp_extension import load_inline
CUDA_SOURCE = r'''
#include <torch/extension.h>
#include <cuda_runtime.h>
#include <math.h>
__global__ void fused_msa_attention_kernel(
const float* __restrict__ msa_repr,
const float* __restrict__ msa_mask,
const float* __restrict__ q_weight,
const float* __restrict__ k_weight,
const float* __restrict__ v_weight,
const float* __restrict__ g_weight,
const float* __restrict__ out_weight,
const float* __restrict__ g_bias,
const float* __restrict__ out_bias,
const float* __restrict__ ln_weight,
const float* __restrict__ ln_bias,
float* __restrict__ output,
int B, int S, int N, int D, int H)
{
int b = blockIdx.x;
int n = blockIdx.y;
if (b >= B || n >= N) return;
int tid = threadIdx.x;
int num_threads = blockDim.x;
int d = D / H;
float scale = 1.0f / sqrtf((float)d);
extern __shared__ float shared_mem[];
float* smem_X = shared_mem;
float* smem_Q = smem_X + S * D;
float* smem_K = smem_Q + S * D;
float* smem_V = smem_K + S * D;
float* smem_G = smem_V + S * D;
float* smem_attn = smem_G + S * D;
float* smem_out = smem_attn + H * S * S;
// Load X
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int d_idx = idx % D;
smem_X[idx] = msa_repr[b * S * N * D + s * N * D + n * D + d_idx];
}
__syncthreads();
// LayerNorm
for (int s = tid; s < S; s += num_threads) {
float* row = smem_X + s * D;
float sum = 0.0f;
#pragma unroll
for (int i = 0; i < D; i++) sum += row[i];
float mean = sum / D;
float var_sum = 0.0f;
#pragma unroll
for (int i = 0; i < D; i++) {
float diff = row[i] - mean;
var_sum += diff * diff;
}
float inv_std = 1.0f / sqrtf(var_sum / D + 1e-5f);
#pragma unroll
for (int i = 0; i < D; i++) {
row[i] = (row[i] - mean) * inv_std * ln_weight[i] + ln_bias[i];
}
}
__syncthreads();
// Compute Q
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
#pragma unroll
for (int i = 0; i < D; i++) {
sum += x_row[i] * q_weight[o * D + i];
}
smem_Q[idx] = sum;
}
__syncthreads();
// Compute K
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
#pragma unroll
for (int i = 0; i < D; i++) {
sum += x_row[i] * k_weight[o * D + i];
}
smem_K[idx] = sum;
}
__syncthreads();
// Compute V
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
#pragma unroll
for (int i = 0; i < D; i++) {
sum += x_row[i] * v_weight[o * D + i];
}
smem_V[idx] = sum;
}
__syncthreads();
// Compute G with sigmoid
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* x_row = smem_X + s * D;
#pragma unroll
for (int i = 0; i < D; i++) {
sum += x_row[i] * g_weight[o * D + i];
}
sum += g_bias[o];
smem_G[idx] = 1.0f / (1.0f + expf(-sum));
}
__syncthreads();
// Attention for each head
for (int h = 0; h < H; h++) {
// Compute scores
for (int idx = tid; idx < S * S; idx += num_threads) {
int i = idx / S;
int j = idx % S;
float mask_j = msa_mask[b * S * N + j * N + n];
if (mask_j == 0.0f) {
smem_attn[h * S * S + idx] = -INFINITY;
} else {
float sum = 0.0f;
#pragma unroll
for (int dd = 0; dd < d; dd++) {
sum += smem_Q[i * D + h * d + dd] * smem_K[j * D + h * d + dd];
}
smem_attn[h * S * S + idx] = sum * scale;
}
}
__syncthreads();
// Softmax
for (int i = tid; i < S; i += num_threads) {
float max_val = -INFINITY;
#pragma unroll
for (int j = 0; j < S; j++) {
max_val = fmaxf(max_val, smem_attn[h * S * S + i * S + j]);
}
float exp_sum = 0.0f;
#pragma unroll
for (int j = 0; j < S; j++) {
float val = expf(smem_attn[h * S * S + i * S + j] - max_val);
smem_attn[h * S * S + i * S + j] = val;
exp_sum += val;
}
#pragma unroll
for (int j = 0; j < S; j++) {
smem_attn[h * S * S + i * S + j] /= exp_sum;
}
}
__syncthreads();
// Attn @ V and gate
for (int idx = tid; idx < S * d; idx += num_threads) {
int i = idx / d;
int k = idx % d;
float sum = 0.0f;
#pragma unroll
for (int j = 0; j < S; j++) {
sum += smem_attn[h * S * S + i * S + j] * smem_V[j * D + h * d + k];
}
sum *= smem_G[i * D + h * d + k];
smem_out[i * D + h * d + k] = sum;
}
__syncthreads();
}
// Output projection
for (int idx = tid; idx < S * D; idx += num_threads) {
int s = idx / D;
int o = idx % D;
float sum = 0.0f;
float* in_row = smem_out + s * D;
#pragma unroll
for (int i = 0; i < D; i++) {
sum += in_row[i] * out_weight[o * D + i];
}
sum += out_bias[o];
output[b * S * N * D + s * N * D + n * D + o] = sum;
}
}
torch::Tensor fused_msa_attention(
torch::Tensor msa_repr,
torch::Tensor msa_mask,
torch::Tensor q_weight,
torch::Tensor k_weight,
torch::Tensor v_weight,
torch::Tensor g_weight,
torch::Tensor out_weight,
torch::Tensor g_bias,
torch::Tensor out_bias,
torch::Tensor ln_weight,
torch::Tensor ln_bias)
{
int B = msa_repr.size(0);
int S = msa_repr.size(1);
int N = msa_repr.size(2);
int D = msa_repr.size(3);
int H = D / (D / q_weight.size(0)); // Wait, q_weight is (D, D), so H isn't directly available here
// Actually I need to pass H as an argument or derive it differently
// q_weight.size(0) = D, not H. I need H from somewhere.
}
'''
```
Ah, I need to pass `num_heads` to the wrapper. Let me add it as a parameter.
```python
CPP_SOURCE = r'''
torch::Tensor fused_msa_attention(
torch::Tensor msa_repr,
torch::Tensor msa_mask,
torch::Tensor q_weight,
torch::Tensor k_weight,
torch::Tensor v_weight,
torch::Tensor g_weight,
torch::Tensor out_weight,
torch::Tensor g_bias,
torch::Tensor out_bias,
torch::Tensor ln_weight,
torch::Tensor ln_bias,
int64_t num_heads)
{
int B = msa_repr.size(0);
int S = msa_repr.size(1);
int N = msa_repr.size(2);
int D = msa_repr.size(3);
int H = num_heads;
auto output = torch::empty_like(msa_repr);
dim3 grid(B, N);
dim3 block(256);
int d = D / H;
size_t smem_size = (S * D * 6 + H * S * S) * sizeof(float);
fused_msa_attention_kernel<<<grid, block, smem_size, at::cuda::getCurrentCUDAStream()>>>(
msa_repr.data_ptr<float>(),
msa_mask.data_ptr<float>(),
q_weight.data_ptr<float>(),
k_weight.data_ptr<float>(),
v_weight.data_ptr<float>(),
g_weight.data_ptr<float>(),
out_weight.data_ptr<float>(),
g_bias.data_ptr<float>(),
out_bias.data_ptr<float>(),
ln_weight.data_ptr<float>(),
ln_bias.data_ptr<float>(),
output.data_ptr<float>(),
B, S, N, D, H
);
return output;
}
'''
```
Wait, I need to make sure all tensors are contiguous and on CUDA. And I need to handle the `TORCH_CHECK` or use `.contiguous()`.
Also, I should use `msa_repr.data_ptr<float>()` only after checking it's the right type. But for simplicity in the evaluation, I'll assume float32 inputs.
Actually, looking at the reference, it uses default dtype which is float32. And `get_inputs()` creates `torch.randn(...)` which is float32 by default. So we're fine.
Let me also verify the shared memory calculation:
- smem_X: S * D
- smem_Q: S * D
- smem_K: S * D
- smem_V: S * D
- smem_G: S * D
- smem_attn: H * S * S
- smem_out: S * D
Total = 6 * S * D + H * S * S
For S=8, D=64, H=4: 6 * 512 + 4 * 64 = 3072 + 256 = 3328 floats = 13312 bytes.
For general sizes, this is fine as long as it doesn't exceed 48KB (which it won't for reasonable sizes in this problem).
But wait, my kernel uses `extern __shared__ float shared_mem[];` and I compute the size at launch. That's correct.
One potential issue: `#pragma unroll` on loops with runtime bounds doesn't work well. For D=64 and d=16 and S=8, these are runtime values. The compiler might not unroll them.
If I want the compiler to unroll, I could use template parameters or just trust the compiler. For small sizes like these, the loops are short and the compiler should optimize them decently.
Actually, let me think about performance more carefully. PyTorch's default implementation might use highly optimized cuDNN/cuBLAS kernels for the linear layers, which could be faster than my naive loops. But the overhead of multiple kernel launches might dominate.
For the problem sizes:
- B=2, S=8, N=32, D=64
Each linear layer is effectively 8*32*64 = 16384 input elements and 16384 output elements. With 4 linear layers in a row (Q, K, V, G), plus attention (which is tiny), plus out_proj, plus all the memory movement and transposes...
PyTorch probably does:
1. permute (view, no copy)
2. layer_norm (one kernel)
3. Q linear: 64 blocks of GEMM or similar
4. K linear: same
5. V linear: same
6. G linear + sigmoid + view: same
7. einsum for QK^T: small broadcasted matmul
8. masked_fill: one kernel
9. softmax: one kernel
10. dropout: no-op or one kernel
11. einsum for attn @ V: small matmul
12. element-wise gate multiply: one kernel
13. permute + reshape: view
14. out_proj: one GEMM
15. final permute: view
At minimum, that's about 10-12 actual kernel launches. My fused kernel is 1 launch. Even if each of PyTorch's kernels is individually more efficient for the matmuls, the launch overhead and intermediate memory reads/writes should make fusion much faster.
But wait - PyTorch might also fuse some operations automatically. For example, linear+sigmoid might be fused, and einsum might use efficient tensor contraction kernels.
I think my approach is sound, but let me also think about whether I can make the linear layers more efficient.
With block size 256 and S*D=512 elements in Q, the loop `for (int idx = tid; idx < S * D; idx += num_threads)` runs at most twice (for tid < 256, idx = tid and idx = tid + 256). So each thread does at most 2 dot products of length D=64. That's 128 FMAs per thread. At ~67 TFLOPS, this is ~2 nanoseconds of compute (theoretically), but realistically it's bounded by memory bandwidth.
For each thread, reading a row of X from shared memory (64 floats = 256 bytes) and reading a row of W from global memory (64 floats, but cached since multiple threads read the same rows)... Actually, threads with the same `s` but different `o` read the same row of X. With 256 threads handling 512 elements, there are 2 elements per thread for S=8, D=64.
Wait, `idx = s * D + o`. For a given `s`, o ranges from 0 to 63. Thread tid handles `idx = tid` and `idx = tid + 256`. So `s = tid / 64` and `s = (tid + 256) / 64`. For tid in [0, 255]:
- idx1 = tid: s1 = tid / 64, o1 = tid % 64
- idx2 = tid + 256: s2 = (tid + 256) / 64 = 4 + tid/64, o2 = tid % 64
So each thread handles two elements with the same o but different s (separated by 4). Threads 0..63 handle s=0 and s=4. They all need to read X[s=0] and X[s=4] from shared memory. That's 2 rows per thread. But 64 threads all reading X[0] simultaneously - shared memory broadcast should handle this. And they all read X[4] too.
For W, thread with o1 reads W[o1] and W with o2... wait, o1 and o2 are the same! Actually o2 = tid % 64 = o1. So each thread reads the same column of W twice (for o1 and o2 which are the same). No wait, for idx2, o2 = (tid + 256) % 64 = tid % 64 = o1. And o1 ranges from 0 to 63 for tid 0..255.
So each thread computes two output elements:
1. (s1, o1) where s1 = tid/64, o1 = tid%64
2. (s2, o1) where s2 = 4 + tid/64
So each thread reads row X[s1] and row X[s2] from shared mem, and column W[o1] from global mem twice (well, once and reused).
Global memory access pattern for W: thread tid reads W[o1 * D + i] for i in 0..63. Since o1 = tid % 64, threads 0..63 read W[0..63] in order, then W[64..127], etc. But wait, W is stored as (D, D) with W[o, i] = weight[o * D + i]. So threads read contiguous memory for a given o. But different threads read different o's. So for i=0, threads read W[0], W[64], W[128], etc. That's a strided pattern with stride D=64 floats = 256 bytes.
This is not coalesced! With 64 threads reading with stride 256 bytes:
- Thread 0 reads W[0]
- Thread 1 reads W[64]
- Thread 2 reads W[128]
- ...
The cache line is typically 128 bytes. So W[0] is at bytes 0..127 (32 floats), W[64] is at bytes 256..383. So consecutive threads read from different cache lines. This is highly uncoalesced!
To fix this, I could either:
1. Transpose the weight matrices before passing to the kernel
2. Have threads read W in a coalesced pattern
3. Load W into shared memory in a coalesced way
Option 3 is the most robust. I can have the threads collaboratively load W into shared memory before computing the linear layers. But W is 64x64 = 4096 floats = 16KB. For 4 weight matrices, that's 64KB. Plus we already have ~13KB of shared memory. Total ~77KB. Still under 228KB.
But wait, shared memory per block on H100 is up to 227KB. 77KB is fine. But it limits occupancy: with 77KB per block, an SM can run at most 2 blocks (154KB) or 3 blocks (231KB, slightly over). So 2 blocks per SM. With 64 blocks, we need 32 SMs. H100 has 132 SMs, so at most ~64 blocks can run concurrently (32 SMs * 2 blocks). That's fine since we only have 64 blocks. But 132 SMs means some SMs are idle. Well, that's already the case with only 64 blocks.
Actually, let me reconsider. For 64 blocks and 132 SMs, we'd need at least 2 blocks per SM to fill all SMs. With 77KB shared memory, we can fit 2 blocks per SM (154KB) on most SMs, or 3 blocks on some (but 3*77=231 which exceeds 228). So 2 blocks per SM is the max, meaning 128 blocks worth of capacity but we only have 64. So 64 SMs get 1 block and the other 68 SMs are idle. That's not great for utilization but might be acceptable.
However, we don't actually need all weight matrices in shared memory simultaneously. We load one at a time:
1. Load W_Q to shared mem, compute Q
2. Load W_K to shared mem, compute K
3. Load W_V to shared mem, compute V
4. Load W_G to shared mem, compute G
5. Load W_out to shared mem, compute output
This way, we only need one W buffer at a time: 16KB. Total shared memory: 13KB + 16KB = 29KB per block. With 228KB per SM, we can fit 7 blocks per SM! But we only have 64 blocks total and 132 SMs, so we'd still only have ~0.5 blocks per SM on average.
Hmm, actually 64 blocks / 132 SMs = 0.48 blocks per SM. This means most SMs get 0 or 1 block. The kernel is heavily occupancy-limited by the grid size, not by shared memory.
So the main speedup comes from avoiding memory traffic between operations, not from maximizing SM occupancy. The total work per block is significant enough that 64 blocks might give decent throughput.
Wait, but can I increase parallelism? What if I use smaller blocks and more of them? For example, I could process each (B, N, H) independently, which would give 256 blocks. But then I'd need to do output projection across heads, which requires all heads.
What if I process multiple (B, N) pairs per block? For instance, if each block handles 2 (b, n) pairs, I'd have 32 blocks and each block does twice the work. But with 256 threads, I could split them: 128 threads per (b, n).
Actually, let me try to use one block per (b, n) but with fewer threads. What if I use 128 threads? Then the grid size is still 64. Each SM could run more blocks if shared memory allows, but the grid is the same.
What if I process each (b, n) using 2 blocks, one for the first half of operations and one for the second? That gets complicated with dependencies.
Alternatively, I could just accept that 64 blocks is small and hope the speedup from fusion is enough.
Actually, let me think about whether I can split the work differently. What if one block handles one head of one (b, n)? That's 256 blocks. Then each block would:
1. Load X for (b, n) from global memory
2. Do a partial layer norm? No, layer norm needs the full X.
3. Or we could load X once per (b, n), but then all H blocks need it.
This doesn't work well because layer norm is shared across heads.
What if I keep one block per (b, n) but use more threads to increase block occupancy? With 512 threads: still 64 blocks. No help.
Actually, one idea: since each block does a lot of sequential work but has idling threads during some phases, I could overlap multiple (b, n) pairs within one block. If I assign 2 (b, n) pairs to one block and split 256 threads into 2 groups of 128, I get 32 blocks. Worse.
Or I assign 1 (b, n) per warp? But there are data dependencies (layer norm before linears, etc.).
Actually, I think the right approach is to increase grid size by having multiple (b, n, chunk) combinations. But what can we chunk?
For linear layers, we can chunk the output dimension. For example, for Q computation, each block could compute a chunk of output channels for a given (b, n). If we chunk into 4 pieces (chunk_size = 16), we'd have 64 * 4 = 256 blocks.
But then we need to synchronize between the Q, K, V, G computations to ensure all chunks are done before attention. That's not possible across blocks without multiple kernel launches.
OK, here's another idea: we can just use a single huge block with lots of threads that processes multiple (b, n) pairs. But that's also limited.
I think the simplest way to get more parallelism is to keep the current design but launch it for 256 blocks by making each block smaller. Actually, what if we interleave operations differently?
Let me step back. H100 has 132 SMs, each with 2048 threads. At 100% occupancy, that's 270,336 threads. We only need about 16,000 threads (64 blocks * 256 threads). The problem is simply too small to saturate the GPU, no matter what.
But that's OK! PyTorch also can't saturate the GPU with this tiny problem. In fact, PyTorch is even worse because it has many more kernel launches with similar or smaller grid sizes.
PyTorch's matmul for Q = X @ W_Q^T where X is (256, 64) and W_Q is (64, 64)... Wait, X is actually (B*N, S, D) = (64, 8, 64) if we think of it after reshape. Or X is (B, N, S, D). PyTorch probably calls cuBLAS with effective batch size B*N=64, M=8, N=64, K=64. This is a batched GEMM with tiny M. cuBLAS won't be very efficient for this.
So my kernel should definitely be competitive.
Let me just go with the current design and see how it performs. I'll compile and test it.
Actually, I want to reconsider the uncoalesced W loading issue. For W_Q with shape (64, 64), my threads read W[o * D + i] where o = tid % 64. With 256 threads and S=8, the pattern is:
- For i=0: threads read W[0], W[64], W[128], W[192], W[256], W[320], W[384], W[448], then W[0], W[64], etc. (since o repeats every 64 threads, but there are only 64 unique o values for the 256 threads, and each thread handles 2 values of s with the same o).
Wait, if there are 64 unique o values and 256 threads, then 4 threads have the same o but different s. For these 4 threads, they're all reading W[o * D + i] for the same o and varying i. So for a fixed i, 4 threads read the same location (broadcast). But for different i, we read different locations.
Actually, the pattern is: for each i from 0 to 63, and for each s from 0 to 7, there's some thread computing (s, o) for some o. But since each thread handles 2 (s, o) pairs with the same o, and 256 threads / 64 o values = 4 threads per o value (each handling different s pairs).
For a given i, all threads read W[o * 64 + i] for some o. Since o ranges from 0 to 63, the reads are W[0*64+i], W[1*64+i], ..., W[63*64+i]. These are spaced 64 floats = 256 bytes apart. This is highly strided and uncoalesced.
The memory transactions: with 256 threads, for a given i, we read 64 unique cache lines (each line holding 32 floats = 128 bytes). So for each i, we need 64 cache lines * 128 bytes = 8KB of cache bandwidth. Over 64 iterations of i, that's 512KB of reads from L2.
But wait, with L2 cache on H100 being large (50MB), and 512KB being small, the cached reads might still be reasonably fast. Actually, W_Q is 16KB total. It should fit in L1 cache (128KB+ on H100). So once W_Q is loaded into L1, subsequent reads are fast.
Since each thread reads the entire column W[o, :] one element at a time, and W is only 16KB, it should easily fit in L1. After the first few iterations, the cache is warm. So the uncoalesced pattern might not be that bad!
Similarly for W_K, W_V, W_G, W_out.
So I'll stick with the naive loading and trust the cache.
One more optimization: I should ensure the weight pointers are marked as `__restrict__` and `__builtin_assume_aligned` if possible. But `__restrict__` is already there.
Let me also add `__ldg` (load through read-only cache) for the weights. Actually, on modern GPUs, global loads through the constant/texture cache happen automatically for read-only data. But I can use `__ldg` explicitly.
Actually, let me not overcomplicate. I'll write the code as I have it, compile, and see.
Oh, one more issue: the `TORCH_EXTENSION_NAME` and `load_inline` specifics. Let me write the full Python code now.
Actually wait - I realize there's an issue with how I'm treating the problem. The reference does:
```python
q = self.query(x).view(B, N, S, h, d).permute(0, 1, 3, 2, 4)
```
So Q is (B, N, h, S, d). Then attention is:
```python
attn = torch.einsum("bnhid,bnhjd->bnhij", q, k) / math.sqrt(d)
```
So `bnhid` means: batch b, position n, head h, sequence i, dimension d.
And `bnhjd` means: batch b, position n, head h, sequence j, dimension d.
Output `bnhij` means: batch b, position n, head h, query i, key j.
In my kernel, Q is stored as (S, H, d) where S is the sequence dimension and d is head dimension. For head h, Q_h[i, dd] = smem_Q[i * D + h * d + dd]. The key K_h[j, dd] = smem_K[j * D + h * d + dd].
Then score[i, j] = sum_d Q_h[i, d] * K_h[j, d] = sum_d smem_Q[i*D + h*d + d] * smem_K[j*D + h*d + d].
And output attn[i, j] = score / sqrt(d).
Then `out = torch.einsum("bnhij,bnhjd->bnhid", attn, v)` which is:
out[i, d] = sum_j attn[i, j] * V[j, d].
In my kernel, this is `sum_j smem_attn[i*S + j] * smem_V[j*D + h*d + k]`.
And `out = g * out` is elementwise multiplication.
Then `out = out.permute(0, 1, 3, 2, 4).reshape(B, N, S, D)`.
Original shape before permute is (B, N, h, S, d). Wait, the reference computes attention as (B, N, h, S, S)... no wait.
Let me re-read:
```python
q = self.query(x).view(B, N, S, h, d).permute(0, 1, 3, 2, 4)
```
`self.query(x)` gives (B, N, S, D). Then `.view(B, N, S, h, d)`. Then `.permute(0, 1, 3, 2, 4)` gives (B, N, h, S, d).
Then `attn = torch.einsum("bnhid,bnhjd->bnhij", q, k)` gives (B, N, h, S, S).
Then `out = torch.einsum("bnhij,bnhjd->bnhid", attn, v)` gives (B, N, h, S, d).
Then `out = g * out` where g is also (B, N, h, S, d).
Then `out = out.permute(0, 1, 3, 2, 4).reshape(B, N, S, D)`:
- permute to (B, N, S, h, d) then reshape to (B, N, S, D). Yes.
Then `out = self.out_proj(out)` which operates on the last dimension D. out_proj is nn.Linear(D, D), expecting (..., D) input. In PyTorch, linear layers work on the last dimension. So with shape (B, N, S, D), it treats each of the B*N*S vectors of size D independently.
Then `return out.permute(0, 2, 1, 3)` to get back to (B, S, N, D).
Wait, so the output projection operates on (B, N, S, D), not (B, N, h, S, d).
In my kernel, after the gated attention, I have `smem_out` as (S, D). Then I do out_proj which operates on each row of smem_out as a D-dimensional vector. That matches!
And the final output shape is (B, S, N, D) as expected.
Great, my kernel logic is correct.
One subtle thing about layer norm: in the reference, it's applied to the transposed tensor. After `x = msa_repr.permute(0, 2, 1, 3)`, x is (B, N, S, D). Then `self.layer_norm(x)` normalizes over the last dimension D, treating (B, N, S) as batch dimensions. So for each (b, n, s), it computes mean and variance over D elements.
In my kernel, I do exactly this: for each row s (out of S=8 rows), I compute mean and variance over D=64 elements. Good.
Now let me think about whether there's a performance issue with the `#pragma unroll` directives. Since D, S, H are passed as runtime values, `#pragma unroll` might not work for them. But D=64 is known at compile time if I pass it as a template parameter. However, making it a template parameter would require compiling multiple versions.
Let me just remove `#pragma unroll` for loops with variable bounds and only use it where the bound is a compile-time constant. Actually, for this specific problem, let me try passing these as template parameters for maximum optimization.
Wait, load_inline compiles the CUDA code once. If I use templates, I'd need to instantiate them. But I can just make the kernel a template with default values or instantiate it in the wrapper.
Actually, an easier approach: since the evaluation uses fixed sizes, I can just hardcode the expected sizes or make them compile-time constants. But that would make the kernel inflexible. Let me keep them as runtime parameters.
But actually, if I compile with `-O3`, the compiler might do loop unrolling for the inner loops automatically when it sees the loop bounds are small. Let me trust the compiler and use `#pragma unroll` sparingly.
Actually, for better optimization, I could define `D` as a `constexpr` inside the kernel if it's always 64 for this task. But wait, the evaluation might vary sizes. Let me make the wrapper pass the values and hope for the best, or use templates.
Actually, let me check what sizes the evaluation uses. The task gives fixed sizes:
```python
msa_dim = 64
num_heads = 4
seq_len = 32
msa_depth = 8
batch_size = 2
```
But there might be additional tests with different sizes. I should make it work for the general case.
OK, I'll keep runtime sizes. Let me just write the code and see if it compiles.
One more thing: in the CUDA code, I need to add `#include <cuda_fp16.h>` or other headers? No, I'm using float.
Also, I should use `at::cuda::getCurrentCUDAStream()` for the stream argument.
And I need to handle the case where tensors might not be contiguous. I'll call `.contiguous()` in the Python wrapper before passing to CUDA.
Let me write the full module now.
Actually, I realize there could be an issue with the `extern __shared__` and how I declare multiple arrays. The pointer arithmetic `smem_attn + H * S * S` needs to be correct. Let me be very careful.
Also, for the attention, I have `for (int h = 0; h < H; h++)`. If num_threads=256 and S*S=64, then for each h, only threads 0..63 do work in the score computation, threads 0..7 in softmax, and threads 0..127 in attn @ V. There are __syncthreads() between each of these, which is necessary and correct.
Wait, __syncthreads() requires ALL threads in the block to hit it. Since some threads might be idle in certain loops, but they still pass through the __syncthreads() (because the loop condition fails and they skip the body but they're still at the __syncthreads() below the loop). That's correct.
Actually, let me verify:
```cuda
for (int idx = tid; idx < S * S; idx += num_threads) {
// work
}
__syncthreads();
```
All 256 threads execute this. Threads with tid >= S*S don't enter the loop body (because idx >= S*S initially), but they all reach __syncthreads(). Correct.
Let me now write the complete code.
Wait, there's a subtle issue: for the softmax, I have:
```cuda
for (int i = tid; i < S; i += num_threads) {
// compute softmax for row i
}
__syncthreads();
```
If S=8 and num_threads=256, only threads 0..7 enter the loop, but all 256 reach __syncthreads(). Correct.
However, there's a potential issue with divergent execution within a warp. Threads 0..7 do the softmax computation while threads 8..31 in the same warp are idle. This is fine because __syncthreads() handles warp-level divergence properly (all threads in the warp must reach the barrier).
One more concern: the floating point precision. PyTorch's softmax uses numerically stable implementations. My softmax does:
1. Find max
2. Subtract max
3. exp
4. Sum
5. Divide
This matches PyTorch's softmax algorithm. But I need to be careful about the exact order of operations and floating point accumulation.
In my softmax:
```cuda
float max_val = -INFINITY;
for (int j = 0; j < S; j++) {
max_val = fmaxf(max_val, smem_attn[h * S * S + i * S + j]);
}
```
This computes max iteratively. PyTorch might use a tree reduction for max, which could give slightly different results due to associativity of fmaxf (though fmaxf is associative for non-NaN values). Actually, `fmaxf` is not associative in the strict sense because of NaN handling, but for finite values, `max(a, max(b, c)) = max(max(a, b), c)`. So the order doesn't matter.
For the sum, PyTorch also does iterative summation in some implementations. The difference should be within tolerance.
For exp, I use `expf`. PyTorch also uses `expf`. Good.
For the linear layers, I do `sum += x[i] * W[o * D + i]`. PyTorch's GEMM uses different accumulation strategies (e.g., split-K, tensor cores, etc.). This might introduce small differences. The tolerance is 1e-4 for fp32, which should be fine for small matrices.
But wait, the task says "numerically equivalent outputs at fp32 precision" with tolerance 1e-4. I should be fine.
Let me also check if I need to handle `dropout`. Since it's probably 0.0 in the reference for evaluation, and I don't implement it, the outputs should match. But if the evaluation tests with non-zero dropout, I'd be in trouble. However, the `get_init_inputs()` only passes `msa_dim` and `num_heads`, so `dropout=0.0` is used.
Great. Let me now write the complete Python file.
Actually, I realize I should also check if there's an issue with the `out_proj` bias. In the reference, `self.out_proj = nn.Linear(msa_dim, msa_dim)` which has bias by default. Yes, my code adds `out_bias`.
And `self.gate = nn.Linear(msa_dim, msa_dim)` also has bias. Yes, my code adds `g_bias`.
And `self.query`, `self.key`, `self.value` have `bias=False`. Yes, my code doesn't add bias for them.
And `self.layer_norm = nn.LayerNorm(msa_dim)` has weight and bias (affine=True by default). Yes, my code uses both.
Everything looks correct.
One final thought: should I process multiple (b, n) pairs per block to increase occupancy? For instance, with 256 threads, I could handle 2 (b, n) pairs with 128 threads each. But then the shared memory per block doubles (since each pair needs its own buffers), and the grid halves to 32 blocks. That seems worse.
What if I use 128 threads per block and process 1 (b, n) per block, but now the grid is still 64 and each block is smaller. No benefit.
What if I reorder the computation to process heads more in parallel? For instance, I could have one block per (b, n, h_head_group), where each group handles a subset of heads. But the output projection needs all heads together.
I could structure it as:
1. Kernel 1: For each (b, n), compute X -> layernorm -> Q, K, V, G. Store Q, K, V, G in global memory.
2. Kernel 2: For each (b, n, h), compute attention -> gated output. Store per-head output.
3. Kernel 3: For each (b, n, s), compute out_proj.
But this defeats the purpose of fusion.
Alternatively, I could have kernel 1 be fully fused, and kernel 2 be out_proj. But kernel 1 would have 64 blocks, and the intermediate storage would be 64 * 8 * 64 * 4 = 131KB for Q/K/V/G each = 524KB total. That's manageable.
But for maximum fusion and minimum memory traffic, I prefer the single kernel approach.
Actually, there IS a way to get more parallelism within one kernel: process the (b, n) dimension in tiles. Instead of `blockIdx.x = b, blockIdx.y = n`, I could have blocks also iterate over the N dimension. But that would just be a different organization.
Or: within a block, each warp handles one (b, n). With 64 blocks and 4 warps per block, I get 256 warps handling 256 (b, n) items... but we only have 64 (b, n) items total.
Hmm, the fundamental issue is that B*N = 64 is small. No matter what I do, I can only parallelize across 64 items for the parts that have cross-item dependencies (like layer norm and output projection).
For the linear layers, since they don't have cross-item dependencies within (b, n), I could theoretically launch more blocks. But the layer norm creates a dependency.
OK, I've convinced myself that the single-kernel-per-(b,n) approach is reasonable.
Let me write the code now, compile, and test.