example_linear_attn_bwd.py

import torch
import tilelang
import tilelang.language as T
from tilelang.profiler import do_bench
import argparse
from fla.ops.linear_attn import fused_chunk_linear_attn  # We compare with FLA
from fla.modules.l2norm import l2norm_fwd
from einops import rearrange
from typing import Optional, Tuple


@tilelang.jit(
    pass_configs={
        tilelang.PassConfigKey.TL_DISABLE_TMA_LOWER: True,
        tilelang.PassConfigKey.TL_DISABLE_WARP_SPECIALIZED: True,
    })
def tl_fused_chunk_bwd_kernel(
    B,
    S,
    H,
    DK,
    DV,
    dtype: str = 'float16',
    scale: float = None,
) -> torch.Tensor:

    if scale is None:
        scale = DK**-0.5
    accum_dtype = 'float'

    chunk_size = 64
    BK = BV = 64  # Set to 128 can be faster, but has some numerical differences with FLA
    assert S % chunk_size == 0 and DK % BK == 0 and DV % BV == 0
    NK = tilelang.cdiv(DK, BK)
    NV = tilelang.cdiv(DV, BV)
    NT = tilelang.cdiv(S, chunk_size)

    @T.prim_func
    def fused_chunk_linear_attn_bwd(
            Q: T.Tensor([B, S, H, DK], dtype),  # type: ignore
            K: T.Tensor([B, S, H, DK], dtype),  # type: ignore
            V: T.Tensor([B, S, H, DV], dtype),  # type: ignore
            dO: T.Tensor([B, S, H, DV], dtype),  # type: ignore
            dQ: T.Tensor([B, S, H, DK], accum_dtype),  # type: ignore
            dK: T.Tensor([B, S, H, DK], accum_dtype),  # type: ignore
            dV: T.Tensor([B, S, H, DV], accum_dtype),  # type: ignore
    ):
        with T.Kernel(NV, NK, B * H) as (i_v, i_k, i_bh):
            i_b = i_bh // H
            i_h = i_bh % H

            ds = T.alloc_fragment([chunk_size, chunk_size], accum_dtype)
            ds_shared = T.alloc_shared([chunk_size, chunk_size], dtype)
            dq = T.alloc_fragment([chunk_size, BK], accum_dtype)
            dq_shared = T.alloc_shared([chunk_size, BK], accum_dtype)
            dk = T.alloc_fragment([chunk_size, BK], accum_dtype)
            dk_shared = T.alloc_shared([chunk_size, BK], accum_dtype)
            dv = T.alloc_fragment([chunk_size, BV], accum_dtype)
            dv_shared = T.alloc_shared([chunk_size, BV], accum_dtype)
            q = T.alloc_shared([chunk_size, BK], dtype)
            k = T.alloc_shared([chunk_size, BK], dtype)
            v = T.alloc_shared([chunk_size, BV], dtype)
            do = T.alloc_shared([chunk_size, BV], dtype)
            h = T.alloc_fragment([BV, BK], accum_dtype)
            h_shared = T.alloc_shared([BV, BK], dtype)
            dh = T.alloc_fragment([BK, BV], accum_dtype)
            dh_shared = T.alloc_shared([BK, BV], dtype)

            T.annotate_layout({
                dq_shared: tilelang.layout.make_swizzled_layout(dq_shared),
                dk_shared: tilelang.layout.make_swizzled_layout(dk_shared),
                dv_shared: tilelang.layout.make_swizzled_layout(dv_shared)
            })
            T.use_swizzle(10)

            T.clear(h)
            T.clear(dh)

            # Calculate dQ
            for i in T.Pipelined(0, NT):
                T.copy(K[i_b, i * chunk_size:(i + 1) * chunk_size, i_h, i_k * BK:(i_k + 1) * BK], k)
                T.copy(V[i_b, i * chunk_size:(i + 1) * chunk_size, i_h, i_v * BV:(i_v + 1) * BV], v)
                T.copy(dO[i_b, i * chunk_size:(i + 1) * chunk_size, i_h, i_v * BV:(i_v + 1) * BV],
                       do)

                T.gemm(do, v, ds, transpose_B=True, clear_accum=True)
                for row, col in T.Parallel(chunk_size, chunk_size):
                    ds_shared[row, col] = T.if_then_else(row >= col, ds[row, col], 0)

                T.gemm(ds_shared, k, dq, clear_accum=True)
                T.copy(h, h_shared)
                T.gemm(do, h_shared, dq)
                T.gemm(v, k, h, transpose_A=True)
                for row, col in T.Parallel(chunk_size, BK):
                    dq[row, col] *= scale
                T.copy(dq, dq_shared)
                T.atomic_add(
                    dQ[i_b, i * chunk_size:(i + 1) * chunk_size, i_h, i_k * BK:(i_k + 1) * BK],
                    dq_shared)

            # Calculate dK, dV (reversely)
            for i in T.Pipelined(1, NT + 1):
                start = NT - i
                for row, col in T.Parallel(chunk_size, BK):
                    q[row, col] = Q[i_b, start * chunk_size + row, i_h, i_k * BK + col] * scale
                T.copy(
                    K[i_b, start * chunk_size:(start + 1) * chunk_size, i_h,
                      i_k * BK:(i_k + 1) * BK], k)
                T.copy(
                    V[i_b, start * chunk_size:(start + 1) * chunk_size, i_h,
                      i_v * BV:(i_v + 1) * BV], v)
                T.copy(
                    dO[i_b, start * chunk_size:(start + 1) * chunk_size, i_h,
                       i_v * BV:(i_v + 1) * BV], do)

                # Calculate dk
                T.gemm(
                    v, do, ds, transpose_B=True, clear_accum=True
                )  # ds here actually means `s`, but we simply reuse the buffer `ds`
                for row, col in T.Parallel(chunk_size, chunk_size):
                    ds_shared[row, col] = T.if_then_else(row <= col, ds[row, col], 0)
                T.gemm(ds_shared, q, dk, clear_accum=True)
                T.copy(dh, dh_shared)
                T.gemm(v, dh_shared, dk, transpose_B=True)

                # Calculate dv
                T.gemm(k, q, ds, transpose_B=True, clear_accum=True)
                for row, col in T.Parallel(chunk_size, chunk_size):
                    ds_shared[row, col] = T.if_then_else(row <= col, ds[row, col], 0)
                T.gemm(ds_shared, do, dv, clear_accum=True)
                T.gemm(k, dh_shared, dv)

                # Update dh
                T.gemm(q, do, dh, transpose_A=True)

                T.copy(dk, dk_shared)
                T.atomic_add(
                    dK[i_b, start * chunk_size:(start + 1) * chunk_size, i_h,
                       i_k * BK:(i_k + 1) * BK], dk_shared)
                T.copy(dv, dv_shared)
                T.atomic_add(
                    dV[i_b, start * chunk_size:(start + 1) * chunk_size, i_h,
                       i_v * BV:(i_v + 1) * BV], dv_shared)

    return fused_chunk_linear_attn_bwd


def tl_fused_chunk_bwd(Q, K, V, dO):
    B, S, H, D = Q.shape
    kernel = tl_fused_chunk_bwd_kernel(B, S, H, D, D)
    dQ = torch.zeros_like(Q, dtype=torch.float32)
    dK = torch.zeros_like(K, dtype=torch.float32)
    dV = torch.zeros_like(V, dtype=torch.float32)
    kernel(Q, K, V, dO, dQ, dK, dV)
    return dQ.to(torch.float16), dK.to(torch.float16), dV.to(torch.float16)


def ref_program(q: torch.Tensor,
                k: torch.Tensor,
                v: torch.Tensor,
                scale: Optional[float] = None) -> Tuple[torch.Tensor, torch.Tensor]:
    q, k, v = q.float(), k.float(), v.float()
    if scale is None:
        scale = q.shape[-1]**-0.5
    chunk_size = 64
    q = rearrange(q, 'b (n c) h d -> b h n c d', c=chunk_size) * scale
    k = rearrange(k, 'b (n c) h d -> b h n c d', c=chunk_size)
    v = rearrange(v, 'b (n c) h d -> b h n c d', c=chunk_size)
    kv = k.transpose(-1, -2) @ v
    kv = kv.cumsum(2)
    h = kv[:, :, -1, :, :]
    kv = torch.cat([torch.zeros_like(kv[:, :, :1]), kv[:, :, :-1]], dim=2)
    inter = q @ kv
    intra = ((q @ k.transpose(-1, -2)).masked_fill_(
        torch.triu(torch.ones(chunk_size, chunk_size, dtype=bool, device=q.device), diagonal=1),
        0)) @ v
    o = inter + intra
    return rearrange(o, 'b h n c d -> b (n c) h d'), h


def main(B=1, S=1024, H=16, D=128):
    q = torch.randn((B, S, H, D), device='cuda', dtype=torch.float16, requires_grad=True)
    k = torch.randn((B, S, H, D), device='cuda', dtype=torch.float16, requires_grad=True)
    v = torch.randn((B, S, H, D), device='cuda', dtype=torch.float16, requires_grad=True)
    do = torch.randn((B, S, H, D), device='cuda', dtype=torch.float16)

    # qk norm is necessary for linear attn
    q = l2norm_fwd(q)[0].requires_grad_(True)
    k = l2norm_fwd(k)[0].requires_grad_(True)

    dq, dk, dv = tl_fused_chunk_bwd(q, k, v, do)
    q.grad = k.grad = v.grad = None
    o_ref, _ = ref_program(q, k, v)
    o_ref.backward(do, retain_graph=True)

    assert torch.allclose(
        dq, q.grad, atol=1e-2, rtol=1e-2), f'dq max err: {(dq - q.grad).abs().max()}'
    assert torch.allclose(
        dk, k.grad, atol=1e-2, rtol=1e-2), f'dk max err: {(dk - k.grad).abs().max()}'
    assert torch.allclose(
        dv, v.grad, atol=1e-2, rtol=1e-2), f'dv max err: {(dv - v.grad).abs().max()}'
    print('Passed all tests!✅')

    # Benchmark
    q.grad = k.grad = v.grad = None
    o_ref, _ = fused_chunk_linear_attn(q, k, v, output_final_state=True, normalize=False)
    t1 = do_bench(lambda: o_ref.backward(do, retain_graph=True), backend='cupti')
    t2 = do_bench(lambda: tl_fused_chunk_bwd(q, k, v, do), backend='cupti')
    print(f'Triton latency: {t1:.3f} ms')
    print(f'TileLang latency: {t2:.3f} ms')
    print(f'Speedup: {t1/t2:.3f}x')


if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument('--B', type=int, default=8, help='Batch size')
    parser.add_argument('--S', type=int, default=1024, help='Seq len')
    parser.add_argument('--H', type=int, default=32, help='Num heads')
    parser.add_argument('--D', type=int, default=128, help='Head dim')
    args = parser.parse_args()

    main(args.B, args.S, args.H, args.D)