code/flash-linear-attention/fla/ops/nsa/compression.py

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


import torch
import triton
import triton.language as tl

from fla.ops.attn.parallel import parallel_attn_bwd_preprocess
from fla.ops.utils import prepare_chunk_indices, prepare_chunk_offsets, prepare_token_indices
from fla.ops.utils.op import exp, log
from fla.utils import autocast_custom_bwd, autocast_custom_fwd, autotune_cache_kwargs, check_shared_mem, contiguous


@triton.heuristics({
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in [1, 2, 4]
    ],
    key=['BS', 'BK', 'BV'],
    **autotune_cache_kwargs,
)
@triton.jit
def parallel_nsa_compression_fwd_kernel(
    q,
    k,
    v,
    o,
    lse,
    scale,
    cu_seqlens,
    token_indices,
    chunk_offsets,
    T,
    H: tl.constexpr,
    HQ: tl.constexpr,
    G: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BC: tl.constexpr,
    BS: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    IS_VARLEN: tl.constexpr,
):
    i_t, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    i_b, i_h = i_bh // H, i_bh % H

    if IS_VARLEN:
        i_n, i_t = tl.load(token_indices + i_t * 2).to(tl.int32), tl.load(token_indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
        T = eos - bos
        boc = tl.load(chunk_offsets + i_n).to(tl.int32)
    else:
        bos, eos = i_b * T, i_b * T + T
        boc = i_b * tl.cdiv(T, BS)

    p_q = tl.make_block_ptr(q + (bos + i_t) * HQ*K, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))

    # the Q block is kept in the shared memory throughout the whole kernel
    # [G, BK]
    b_q = tl.load(p_q, boundary_check=(0, 1))
    b_q = (b_q * scale).to(b_q.dtype)

    # the number of compression representations in total
    TC = tl.cdiv(T, BS)
    # the number of compression representations required to iterate over
    # incomplete compression blocks are not included
    NC = (i_t + 1) // BS

    p_o = tl.make_block_ptr(o + (bos + i_t) * HQ*V, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV), (1, 0))
    # [G, BV]
    b_o = tl.zeros([G, BV], dtype=tl.float32)
    # max scores for the current block
    b_m = tl.full([G], float('-inf'), dtype=tl.float32)
    # lse = log(acc) + m
    b_acc = tl.zeros([G], dtype=tl.float32)

    for i_c in range(0, NC, BC):
        o_c = i_c + tl.arange(0, BC)

        p_k = tl.make_block_ptr(k + (boc * H + i_h) * K, (K, TC), (1, H*K), (0, i_c), (BK, BC), (0, 1))
        p_v = tl.make_block_ptr(v + (boc * H + i_h) * V, (TC, V), (H*V, 1), (i_c, i_v * BV), (BC, BV), (1, 0))
        # [BK, BC]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BC, BV]
        b_v = tl.load(p_v, boundary_check=(0, 1))
        # [G, BC]
        b_s = tl.dot(b_q, b_k)
        b_s = tl.where((o_c < NC)[None, :], b_s, float('-inf'))

        # [G]
        b_m, b_mp = tl.maximum(b_m, tl.max(b_s, 1)), b_m
        b_r = exp(b_mp - b_m)
        # [G, BC]
        b_p = exp(b_s - b_m[:, None])
        # [G]
        b_acc = b_acc * b_r + tl.sum(b_p, 1)

        # [G, BV]
        b_o = b_o * b_r[:, None] + tl.dot(b_p.to(b_q.dtype), b_v)

        b_mp = b_m
    if NC == 0:
        b_lse = tl.zeros([G], dtype=tl.float32)
    else:
        b_o = b_o / b_acc[:, None]
        b_lse = b_m + log(b_acc)

    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
    if i_v == 0:
        tl.store(lse + (bos + i_t) * HQ + i_h * G + tl.arange(0, G), b_lse.to(lse.dtype.element_ty))


@triton.heuristics({
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in [1, 2, 4]
    ],
    key=['BS', 'BK', 'BV'],
    **autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def parallel_nsa_compression_bwd_kernel_dq(
    q,
    k,
    v,
    lse,
    delta,
    do,
    dq,
    scale,
    cu_seqlens,
    token_indices,
    chunk_offsets,
    T,
    B: tl.constexpr,
    H: tl.constexpr,
    HQ: tl.constexpr,
    G: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BC: tl.constexpr,
    BS: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    IS_VARLEN: tl.constexpr,
):
    i_t, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    i_b, i_h = i_bh // H, i_bh % H

    all = B * T
    if IS_VARLEN:
        i_n, i_t = tl.load(token_indices + i_t * 2).to(tl.int32), tl.load(token_indices + i_t * 2 + 1).to(tl.int32)
        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
        T = eos - bos
        boc = tl.load(chunk_offsets + i_n).to(tl.int32)
    else:
        bos, eos = i_b * T, i_b * T + T
        boc = i_b * tl.cdiv(T, BS)

    q += (bos + i_t) * HQ*K
    do += (bos + i_t) * HQ*V
    lse += (bos + i_t) * HQ
    delta += (bos + i_t) * HQ
    dq += (i_v * all + bos + i_t) * HQ*K

    p_q = tl.make_block_ptr(q, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))
    p_dq = tl.make_block_ptr(dq, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))

    # [G, BK]
    b_q = tl.load(p_q, boundary_check=(0, 1))
    b_q = (b_q * scale).to(b_q.dtype)

    p_do = tl.make_block_ptr(do, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV), (1, 0))
    p_lse = lse + i_h * G + tl.arange(0, G)
    p_delta = delta + i_h * G + tl.arange(0, G)

    # the number of compression representations in total
    TC = tl.cdiv(T, BS)
    # the number of compression representations required to iterate over
    # incomplete compression blocks are not included
    NC = (i_t + 1) // BS

    # [G, BV]
    b_do = tl.load(p_do, boundary_check=(0, 1))
    # [G]
    b_lse = tl.load(p_lse)
    b_delta = tl.load(p_delta)

    # [G, BK]
    b_dq = tl.zeros([G, BK], dtype=tl.float32)
    for i_c in range(0, NC, BC):
        o_c = i_c + tl.arange(0, BC)
        p_k = tl.make_block_ptr(k + (boc * H + i_h) * K, (K, TC), (1, H*K), (0, i_c), (BK, BC), (0, 1))
        p_v = tl.make_block_ptr(v + (boc * H + i_h) * V, (V, TC), (1, H*V), (i_v * BV, i_c), (BV, BC), (0, 1))
        # [BK, BC]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BV, BC]
        b_v = tl.load(p_v, boundary_check=(0, 1))

        # [G, BC]
        b_s = tl.dot(b_q, b_k)
        b_p = exp(b_s - b_lse[:, None])
        b_p = tl.where((o_c < NC)[None, :], b_p, 0)

        # [G, BV] @ [BV, BC] -> [G, BC]
        b_dp = tl.dot(b_do, b_v)
        b_ds = b_p * (b_dp.to(tl.float32) - b_delta[:, None])
        # [G, BC] @ [BC, BK] -> [G, BK]
        b_dq += tl.dot(b_ds.to(b_k.dtype), tl.trans(b_k))
    b_dq *= scale
    tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))


@triton.heuristics({
    'IS_VARLEN': lambda args: args['cu_seqlens'] is not None,
})
@triton.autotune(
    configs=[
        triton.Config({}, num_warps=num_warps)
        for num_warps in [1, 2, 4]
    ],
    key=['BS', 'BK', 'BV'],
    **autotune_cache_kwargs,
)
@triton.jit(do_not_specialize=['T'])
def parallel_nsa_compression_bwd_kernel_dkv(
    q,
    k,
    v,
    lse,
    delta,
    do,
    dk,
    dv,
    cu_seqlens,
    chunk_indices,
    chunk_offsets,
    scale,
    T,
    B: tl.constexpr,
    H: tl.constexpr,
    HQ: tl.constexpr,
    G: tl.constexpr,
    K: tl.constexpr,
    V: tl.constexpr,
    BC: tl.constexpr,
    BS: tl.constexpr,
    BK: tl.constexpr,
    BV: tl.constexpr,
    IS_VARLEN: tl.constexpr,
):
    i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    i_b, i_h = i_bh // H, i_bh % H

    all = B * T
    if IS_VARLEN:
        i_n, i_c = tl.load(chunk_indices + i_c * 2).to(tl.int32), tl.load(chunk_indices + i_c * 2 + 1).to(tl.int32)
        bos, eos = tl.load(cu_seqlens + i_n).to(tl.int32), tl.load(cu_seqlens + i_n + 1).to(tl.int32)
        T = eos - bos
        boc = tl.load(chunk_offsets + i_n).to(tl.int32)
    else:
        bos, eos = i_b * T, i_b * T + T
        boc = i_b * tl.cdiv(T, BS)

    # the number of compression representations in total
    TC = tl.cdiv(T, BS)

    p_k = tl.make_block_ptr(k + (boc * H + i_h) * K, (TC, K), (H*K, 1), (i_c * BC, 0), (BC, BK), (1, 0))
    p_v = tl.make_block_ptr(v + (boc * H + i_h) * V, (TC, V), (H*V, 1), (i_c * BC, i_v * BV), (BC, BV), (1, 0))
    p_dk = tl.make_block_ptr(dk + (i_v * all*H + boc * H + i_h) * K, (TC, K), (H*K, 1), (i_c * BC, 0), (BC, BK), (1, 0))
    p_dv = tl.make_block_ptr(dv + (i_v * all*H + boc * H + i_h) * V, (TC, V), (H*V, 1), (i_c * BC, i_v * BV), (BC, BV), (1, 0))

    # [BC, BK]
    b_k = tl.load(p_k, boundary_check=(0, 1))
    b_dk = tl.zeros([BC, BK], dtype=tl.float32)
    # [BC, BV]
    b_v = tl.load(p_v, boundary_check=(0, 1))
    b_dv = tl.zeros([BC, BV], dtype=tl.float32)

    for i in range(i_c * BC * BS, T):
        o_c = i_c * BC + tl.arange(0, BC)

        p_q = tl.make_block_ptr(q + (bos + i) * HQ*K, (HQ, K), (K, 1), (i_h * G, 0), (G, BK), (1, 0))
        # [G, BK]
        b_q = tl.load(p_q, boundary_check=(0, 1))
        b_q = (b_q * scale).to(b_q.dtype)

        p_do = tl.make_block_ptr(do + (bos + i) * HQ*V, (HQ, V), (V, 1), (i_h * G, i_v * BV), (G, BV), (1, 0))
        p_lse = lse + (bos + i) * HQ + i_h * G + tl.arange(0, G)
        p_delta = delta + (bos + i) * HQ + i_h * G + tl.arange(0, G)
        # [G, BV]
        b_do = tl.load(p_do, boundary_check=(0, 1))
        # [G]
        b_lse = tl.load(p_lse)
        b_delta = tl.load(p_delta)
        # [BC, G]
        b_s = tl.dot(b_k, tl.trans(b_q))
        b_p = exp(b_s - b_lse[None, :])
        b_p = tl.where((i >= max(0, (o_c + 1) * BS - 1))[:, None], b_p, 0)
        # [BC, G] @ [G, BV] -> [BC, BV]
        b_dv += tl.dot(b_p.to(b_do.dtype), b_do)
        # [BC, BV] @ [BV, G] -> [BC, G]
        b_dp = tl.dot(b_v, tl.trans(b_do))
        # [BC, G]
        b_ds = b_p * (b_dp - b_delta[None, :])
        # [BC, G] @ [G, BK] -> [BC, BK]
        b_dk += tl.dot(b_ds.to(b_q.dtype), b_q)

    tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
    tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))


def parallel_nsa_compression_fwd(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    block_size: int,
    scale: float,
    cu_seqlens: torch.LongTensor | None = None,
    token_indices: torch.LongTensor | None = None,
):
    B, T, HQ, K, V = *q.shape, v.shape[-1]
    H = k.shape[2]
    G = HQ // H
    BC = BS = block_size
    if check_shared_mem('hopper', q.device.index):
        BK = min(256, triton.next_power_of_2(K))
        BV = min(256, triton.next_power_of_2(V))
    else:
        BK = min(128, triton.next_power_of_2(K))
        BV = min(128, triton.next_power_of_2(V))
    NK = triton.cdiv(K, BK)
    NV = triton.cdiv(V, BV)
    assert NK == 1, "The key dimension can not be larger than 256"

    chunk_offsets = prepare_chunk_offsets(cu_seqlens, BS) if cu_seqlens is not None else None

    grid = (T, NV, B * H)
    o = torch.empty(B, T, HQ, V, dtype=v.dtype, device=q.device)
    lse = torch.empty(B, T, HQ, dtype=torch.float, device=q.device)

    parallel_nsa_compression_fwd_kernel[grid](
        q=q,
        k=k,
        v=v,
        o=o,
        lse=lse,
        scale=scale,
        cu_seqlens=cu_seqlens,
        token_indices=token_indices,
        chunk_offsets=chunk_offsets,
        T=T,
        H=H,
        HQ=HQ,
        G=G,
        K=K,
        V=V,
        BC=BC,
        BS=BS,
        BK=BK,
        BV=BV,
    )
    return o, lse


def parallel_nsa_compression_bwd(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    o: torch.Tensor,
    lse: torch.Tensor,
    do: torch.Tensor,
    block_size: int = 64,
    scale: float = None,
    cu_seqlens: torch.LongTensor | None = None,
    token_indices: torch.LongTensor | None = None,
):
    B, T, HQ, K, V = *q.shape, v.shape[-1]
    H = k.shape[2]
    G = HQ // H
    BC = BS = block_size
    BK = max(triton.next_power_of_2(K), 16)
    BV = min(128, max(triton.next_power_of_2(v.shape[-1]), 16))
    NV = triton.cdiv(V, BV)
    if cu_seqlens is not None:
        chunk_indices, chunk_offsets = prepare_chunk_indices(cu_seqlens, BS), prepare_chunk_offsets(cu_seqlens, BS)
        NC = len(chunk_indices)
    else:
        chunk_indices, chunk_offsets = None, None
        NC = triton.cdiv(triton.cdiv(T, BS), BC)

    delta = parallel_attn_bwd_preprocess(o, do)

    dq = torch.empty(NV, *q.shape, dtype=q.dtype if NV == 1 else torch.float, device=q.device)
    grid = (T, NV, B * H)
    parallel_nsa_compression_bwd_kernel_dq[grid](
        q=q,
        k=k,
        v=v,
        lse=lse,
        delta=delta,
        do=do,
        dq=dq,
        scale=scale,
        cu_seqlens=cu_seqlens,
        token_indices=token_indices,
        chunk_offsets=chunk_offsets,
        T=T,
        B=B,
        H=H,
        HQ=HQ,
        G=G,
        K=K,
        V=V,
        BC=BC,
        BS=BS,
        BK=BK,
        BV=BV,
    )
    dq = dq.sum(0)

    dk = torch.empty(NV, *k.shape, dtype=k.dtype if NV == 1 else torch.float, device=q.device)
    dv = torch.empty(v.shape, dtype=v.dtype, device=q.device)

    grid = (NV, NC, B * H)
    parallel_nsa_compression_bwd_kernel_dkv[grid](
        q=q,
        k=k,
        v=v,
        lse=lse,
        delta=delta,
        do=do,
        dk=dk,
        dv=dv,
        cu_seqlens=cu_seqlens,
        chunk_indices=chunk_indices,
        chunk_offsets=chunk_offsets,
        scale=scale,
        T=T,
        B=B,
        H=H,
        HQ=HQ,
        G=G,
        K=K,
        V=V,
        BC=BC,
        BS=BS,
        BK=BK,
        BV=BV,
    )
    dk = dk.sum(0)
    return dq, dk, dv


class ParallelNSACompressionFunction(torch.autograd.Function):

    @staticmethod
    @contiguous
    @autocast_custom_fwd
    def forward(
        ctx,
        q,
        k,
        v,
        block_size,
        scale,
        cu_seqlens,
    ):
        ctx.dtype = q.dtype

        # 2-d sequence indices denoting the cu_seqlens of tokens in each sequence
        # for example, if the passed `cu_seqlens` is [0, 2, 6],
        # then there are 2 and 4 tokens in the 1st and 2nd sequences respectively, and `token_indices` will be
        # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]]
        token_indices = prepare_token_indices(cu_seqlens) if cu_seqlens is not None else None

        o, lse = parallel_nsa_compression_fwd(
            q=q,
            k=k,
            v=v,
            block_size=block_size,
            scale=scale,
            cu_seqlens=cu_seqlens,
            token_indices=token_indices,
        )
        ctx.save_for_backward(q, k, v, o, lse)
        ctx.cu_seqlens = cu_seqlens
        ctx.token_indices = token_indices
        ctx.block_size = block_size
        ctx.scale = scale
        return o.to(q.dtype), lse

    @staticmethod
    @contiguous
    @autocast_custom_bwd
    def backward(ctx, do, *args):
        q, k, v, o, lse = ctx.saved_tensors
        dq, dk, dv = parallel_nsa_compression_bwd(
            q=q,
            k=k,
            v=v,
            o=o,
            lse=lse,
            do=do,
            block_size=ctx.block_size,
            scale=ctx.scale,
            cu_seqlens=ctx.cu_seqlens,
            token_indices=ctx.token_indices,
        )
        return dq.to(q), dk.to(k), dv.to(v), None, None, None


def parallel_nsa_compression(
    q: torch.Tensor,
    k: torch.Tensor,
    v: torch.Tensor,
    block_size: int = 64,
    scale: float = None,
    cu_seqlens: torch.LongTensor | None = None,
):
    if scale is None:
        scale = k.shape[-1] ** -0.5
    return ParallelNSACompressionFunction.apply(
        q,
        k,
        v,
        block_size,
        scale,
        cu_seqlens,
    )