code/flash-linear-attention/fla/ops/kda/chunk.py

# Copyright (c) 2023-2025, Songlin Yang, Yu Zhang


import torch

from fla.modules.l2norm import l2norm_bwd, l2norm_fwd
from fla.ops.common.chunk_delta_h import chunk_gated_delta_rule_bwd_dhu, chunk_gated_delta_rule_fwd_h
from fla.ops.common.chunk_o import chunk_bwd_dv_local
from fla.ops.gla.chunk import chunk_gla_bwd_dA, chunk_gla_fwd_o_gk
from fla.ops.kda.chunk_inter import chunk_kda_bwd_dqkwg
from fla.ops.kda.chunk_intra import chunk_kda_bwd_intra, chunk_kda_fwd_intra
from fla.ops.kda.wy_fast import prepare_wy_repr_bwd, recompute_w_u_fwd
from fla.ops.utils import chunk_local_cumsum
from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard


def chunk_kda_fwd(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    g: torch.Tensor,
    beta: torch.Tensor,
    scale: float,
    initial_state: torch.Tensor,
    output_final_state: bool,
    cu_seqlens: torch.LongTensor | None = None,
):
    chunk_size = 64
    g = chunk_local_cumsum(g, chunk_size=chunk_size, cu_seqlens=cu_seqlens)
    # the intra Aqk is kept in fp32
    # the computation has very marginal effect on the entire throughput
    Aqk, Akk = chunk_kda_fwd_intra(
        q=q,
        k=k,
        gk=g,
        beta=beta,
        scale=scale,
        cu_seqlens=cu_seqlens,
        output_dtype=torch.float32,
    )
    w, u, _, kg = recompute_w_u_fwd(
        k=k,
        v=v,
        beta=beta,
        A=Akk,
        gk=g,
        cu_seqlens=cu_seqlens,
    )
    h, v_new, final_state = chunk_gated_delta_rule_fwd_h(
        k=kg,
        w=w,
        u=u,
        gk=g,
        initial_state=initial_state,
        output_final_state=output_final_state,
        cu_seqlens=cu_seqlens,
    )

    o = chunk_gla_fwd_o_gk(
        q=q,
        v=v_new,
        g=g,
        A=Aqk,
        h=h,
        scale=scale,
        cu_seqlens=cu_seqlens,
        chunk_size=chunk_size,
    )
    return g, o, Aqk, Akk, final_state


def chunk_kda_bwd(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    g: torch.Tensor,
    beta: torch.Tensor,
    Aqk: torch.Tensor,
    Akk: torch.Tensor,
    scale: float,
    initial_state: torch.Tensor,
    do: torch.Tensor,
    dht: torch.Tensor,
    cu_seqlens: torch.LongTensor | None = None,
):
    chunk_size = 64
    w, u, qg, kg = recompute_w_u_fwd(
        q=q,
        k=k,
        v=v,
        beta=beta,
        A=Akk,
        gk=g,
        cu_seqlens=cu_seqlens,
    )
    h, v_new, _ = chunk_gated_delta_rule_fwd_h(
        k=kg,
        w=w,
        u=u,
        gk=g,
        initial_state=initial_state,
        output_final_state=False,
        cu_seqlens=cu_seqlens,
    )
    dv = chunk_bwd_dv_local(
        q=q,
        k=k,
        do=do,
        A=Aqk,
        scale=scale,
        cu_seqlens=cu_seqlens,
        chunk_size=chunk_size,
    )

    dh, dh0, dv = chunk_gated_delta_rule_bwd_dhu(
        q=qg,
        k=kg,
        w=w,
        gk=g,
        h0=initial_state,
        dht=dht,
        do=do,
        dv=dv,
        scale=scale,
        cu_seqlens=cu_seqlens,
    )

    # dq dk in fp32
    dAqk = chunk_gla_bwd_dA(
        v=v_new,
        do=do,
        scale=scale,
        cu_seqlens=cu_seqlens,
        chunk_size=chunk_size,
    )
    dq, dk, dw, dg = chunk_kda_bwd_dqkwg(
        q=q,
        k=k,
        v=v_new,
        w=w,
        g=g,
        h=h,
        dv=dv,
        do=do,
        dh=dh,
        scale=scale,
        cu_seqlens=cu_seqlens,
        chunk_size=chunk_size,
    )
    dk2, dv, db, dg2, dAkk = prepare_wy_repr_bwd(
        k=k,
        v=v,
        beta=beta,
        gk=g,
        A=Akk,
        dw=dw,
        du=dv,
        cu_seqlens=cu_seqlens,
    )
    dq, dk2, db, dg2 = chunk_kda_bwd_intra(
        q=q,
        k=k,
        g=g,
        beta=beta,
        dAqk=dAqk,
        dAkk=dAkk,
        dq=dq,
        dk=dk2,
        db=db,
        dg=dg2,
        cu_seqlens=cu_seqlens,
        chunk_size=chunk_size,
    )
    dk.add_(dk2)
    dg.add_(dg2)
    return dq, dk, dv, db, dg, dh0


class ChunkKDAFunction(torch.autograd.Function):

    @staticmethod
    @input_guard
    @autocast_custom_fwd
    def forward(
        ctx,
        q: torch.Tensor,
        k: torch.Tensor,
        v: torch.Tensor,
        g: torch.Tensor,
        beta: torch.Tensor,
        scale: float,
        initial_state: torch.Tensor,
        output_final_state: bool = False,
        use_qk_l2norm_in_kernel: bool = False,
        cu_seqlens: torch.LongTensor | None = None,
    ):
        q_rstd, k_rstd = None, None
        if use_qk_l2norm_in_kernel:
            q, q_rstd = l2norm_fwd(q)
            k, k_rstd = l2norm_fwd(k)

        g, o, Aqk, Akk, final_state = chunk_kda_fwd(
            q=q,
            k=k,
            v=v,
            g=g,
            beta=beta,
            scale=scale,
            initial_state=initial_state,
            output_final_state=output_final_state,
            cu_seqlens=cu_seqlens,
        )
        ctx.save_for_backward(q, q_rstd, k, k_rstd, v, g, beta, Aqk, Akk, initial_state, cu_seqlens)
        ctx.scale = scale
        ctx.use_qk_l2norm_in_kernel = use_qk_l2norm_in_kernel
        return o.to(q.dtype), final_state

    @staticmethod
    @input_guard
    @autocast_custom_bwd
    def backward(
        ctx,
        do: torch.Tensor,
        dht: torch.Tensor,
    ):
        q, q_rstd, k, k_rstd, v, g, beta, Aqk, Akk, initial_state, cu_seqlens = ctx.saved_tensors
        dq, dk, dv, db, dg, dh0 = chunk_kda_bwd(
            q=q,
            k=k,
            v=v,
            g=g,
            beta=beta,
            Aqk=Aqk,
            Akk=Akk,
            scale=ctx.scale,
            initial_state=initial_state,
            do=do,
            dht=dht,
            cu_seqlens=cu_seqlens,
        )
        if ctx.use_qk_l2norm_in_kernel:
            dq = l2norm_bwd(q, q_rstd, dq)
            dk = l2norm_bwd(k, k_rstd, dk)
        return dq.to(q), dk.to(k), dv.to(v), dg.to(g), db.to(beta), None, dh0, None, None, None


@torch.compiler.disable
def chunk_kda(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    g: torch.Tensor,
    beta: torch.Tensor,
    scale: float = None,
    initial_state: torch.Tensor = None,
    output_final_state: bool = False,
    use_qk_l2norm_in_kernel: bool = False,
    cu_seqlens: torch.LongTensor | None = None,
    **kwargs,
):
    r"""
    Args:
        q (torch.Tensor):
            queries of shape `[B, T, H, K]`.
        k (torch.Tensor):
            keys of shape `[B, T, H, K]`.
        v (torch.Tensor):
            values of shape `[B, T, H, V]`.
        g (torch.Tensor):
            (forget) gating tensor (in log space!) of shape `[B, T, H, K]`.
        beta (torch.Tensor):
            betas of shape `[B, T, H]`.
        scale (Optional[float]):
            Scale factor for the RetNet attention scores.
            If not provided, it will default to `1 / sqrt(K)`. Default: `None`.
        initial_state (Optional[torch.Tensor]):
            Initial state of shape `[N, H, K, V]` for `N` input sequences.
            For equal-length input sequences, `N` equals the batch size `B`.
            Default: `None`.
        output_final_state (Optional[bool]):
            Whether to output the final state of shape `[N, H, K, V]`. Default: `False`.
        use_qk_l2norm_in_kernel (bool):
            Whether to apply L2norm to the q,k tensor internally. Default: `False`.
        cu_seqlens (torch.LongTensor):
            Cumulative sequence lengths of shape `[N+1]` used for variable-length training,
            consistent with the FlashAttention API.

    Returns:
        o (torch.Tensor):
            Outputs of shape `[B, T, H, V]`.
        final_state (torch.Tensor):
            Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`.

    Examples::
        >>> import torch
        >>> import torch.nn.functional as F
        >>> from einops import rearrange
        >>> from fla.ops.kda import chunk_kda
        # inputs with equal lengths
        >>> B, T, H, K, V = 4, 2048, 4, 512, 512
        >>> q = torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda')
        >>> k = torch.randn(B, T, H, K, dtype=torch.bfloat16, device='cuda')
        >>> v = torch.randn(B, T, H, V, dtype=torch.bfloat16, device='cuda')
        >>> beta = torch.rand(B, T, H, dtype=torch.bfloat16, device='cuda').sigmoid()
        >>> g = F.logsigmoid(torch.rand(B, T, H, dtype=torch.bfloat16, device='cuda'))
        >>> h0 = torch.randn(B, H, K, V, dtype=torch.bfloat16, device='cuda')
        >>> o, ht = chunk_kda(
            q, k, v, g, beta,
            use_qk_l2norm_in_kernel=True,
            initial_state=h0,
            output_final_state=True
        )
        # for variable-length inputs, the batch size `B` is expected to be 1 and `cu_seqlens` is required
        >>> q, k, v, beta, g = map(lambda x: rearrange(x, 'b t ... -> 1 (b t) ...'), (q, k, v, beta, g))
        # for a batch with 4 sequences, `cu_seqlens` with 5 start/end positions are expected
        >>> cu_seqlens = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long)
        >>> o, ht = chunk_kda(
            q, k, v, g, beta,
            use_qk_l2norm_in_kernel=True,
            initial_state=h0,
            output_final_state=True,
            cu_seqlens=cu_seqlens
        )
    """

    if cu_seqlens is not None:
        if q.shape[0] != 1:
            raise ValueError(
                f"The batch size is expected to be 1 rather than {q.shape[0]} when using `cu_seqlens`."
                f"Please flatten variable-length inputs before processing.",
            )
        if initial_state is not None and initial_state.shape[0] != len(cu_seqlens) - 1:
            raise ValueError(
                f"The number of initial states is expected to be equal to the number of input sequences, "
                f"i.e., {len(cu_seqlens) - 1} rather than {initial_state.shape[0]}.",
            )
    if scale is None:
        scale = k.shape[-1] ** -0.5
    o, final_state = ChunkKDAFunction.apply(
        q,
        k,
        v,
        g,
        beta,
        scale,
        initial_state,
        output_final_state,
        use_qk_l2norm_in_kernel,
        cu_seqlens,
    )
    return o, final_state