fla/ops/retention/parallel.py

# -*- coding: utf-8 -*-
# Copyright (c) 2023, Yu Zhang, Songlin Yang

import torch
import triton
import triton.language as tl
from torch.cuda.amp import custom_bwd, custom_fwd

from fla.utils import contiguous


@triton.jit
def parallel_retention_fwd_kernel(
    # B: batch_size, H: n_heads, T: seq_len, D: d_head
    q,  # query [B, H, L, D_head_K]
    k,  # key [B, H, L, D_head_V]
    v,  # value [B, H, L, D_head_V]
    o,  # output [B, H, L, D_head_V]
    s_qk_h,  # stride size: L * D_head_K
    s_qk_t,  # stride size: D_head_K
    s_qk_d,  # stride size: 1
    s_vo_h,  # stride size: L * D_head_V
    s_vo_t,  # stride size: D_head_V
    s_vo_d,  # stride size: 1
    B,  # batch size
    H,  # n_heads
    T,  # seq_len
    scale,  # D_head_K ** -0.5
    BTL: tl.constexpr,  # BLOCK SIZE along the sequence dimension for Q
    BTS: tl.constexpr,  # BLOCK SIZE along the sequence dimension for K/V
    BK: tl.constexpr,  # BLOCK SIZE along the K dimension
    BV: tl.constexpr,  # BLOCK SIZE along the V dimension
    DK: tl.constexpr,  # D_head_K
    DV: tl.constexpr,  # D_head_V
):
    # i_c: chunk index. used for sequence parallelism
    i_kv, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    NV = tl.cdiv(DV, BV)
    i_k = i_kv // (NV)
    i_v = i_kv % (NV)
    i_h = i_bh % H
    # decay rate given the head index
    b_b = tl.math.log2(1 - tl.math.pow(2, -5 - i_h * 1.0))
    # cumulative decay from the end of the chunk
    o_k = tl.arange(0, BTS)
    d_h = tl.math.exp2((BTS - o_k) * b_b)

    p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (T, DK),
                            (s_qk_t, s_qk_d), (i_c * BTL, i_k * BK), (BTL, BK), (1, 0))
    p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (DK, T),
                            (s_qk_d, s_qk_t), (i_k * BK, 0), (BK, BTS), (0, 1))
    p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV),
                            (s_vo_t, s_vo_d), (0, i_v * BV), (BTS, BV), (1, 0))

    # [BQ, BD] block Q, in the shared memory throughout the whole kernel
    b_q = tl.load(p_q, boundary_check=(0, 1))
    b_q = (b_q * scale).to(b_q.dtype)
    b_o = tl.zeros([BTL, BV], dtype=tl.float32)

    # Q block and K block have no overlap
    # no need for mask, thereby saving flops
    for _ in range(0, i_c * BTL, BTS):
        # [BK, BTS]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BTS, BV]
        b_v = tl.load(p_v, boundary_check=(0, 1))
        # [BTL, BTS]
        b_s = tl.dot(b_q, (b_k), allow_tf32=False) * d_h[None, :]
        # [BQ, BD]
        b_o = b_o * tl.math.exp2(b_b * BTS)
        b_o = b_o + tl.dot(b_s.to(b_v.dtype), b_v, allow_tf32=False)
        p_k = tl.advance(p_k, (0, BTS))
        p_v = tl.advance(p_v, (BTS, 0))

    # # rescale interchunk output
    tl.debug_barrier()
    o_q = tl.arange(0, BTL)
    d_q = tl.math.exp2(tl.arange(0, BTL) * b_b)
    b_o *= d_q[:, None]
    # # sync threads, easy for compiler to optimize
    # tl.debug_barrier()

    o_k = tl.arange(0, BTS)
    p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (DK, T),
                            (s_qk_d, s_qk_t), (i_k * BK, i_c * BTL), (BK, BTS), (0, 1))
    p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV),
                            (s_vo_t, s_vo_d), (i_c * BTL, i_v * BV), (BTS, BV), (1, 0))
    # Q block and K block have overlap. masks required
    for _ in range(i_c * BTL, (i_c + 1) * BTL, BTS):
        # [BK, BTS]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BTS, BV]
        b_v = tl.load(p_v, boundary_check=(0, 1))
        # [BTL, BTS]
        m_s = o_q[:, None] >= o_k[None, :]
        d_s = tl.where(m_s, tl.math.exp2(
            (o_q[:, None] - o_k[None, :]) * b_b), 0)
        b_s = tl.dot(b_q, b_k, allow_tf32=False) * d_s
        # [BTL, BV]
        b_o += tl.dot(b_s.to(b_q.dtype), b_v, allow_tf32=False)

        p_k = tl.advance(p_k, (0, BTS))
        p_v = tl.advance(p_v, (BTS, 0))
        o_k += BTS

    p_o = tl.make_block_ptr(o + (i_bh + B * H * i_k) * s_vo_h, (T, DV),
                            (s_vo_t, s_vo_d), (i_c*BTL, i_v*BV), (BTL, BV), (1, 0))
    tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))


@triton.jit
def _parallel_retention_bwd_dq(
    i_bh, i_c, i_k, i_v, i_h,
    k, v, do, dq, s_qk_h, s_qk_t, s_qk_d, s_vo_h,
    s_vo_t, s_vo_d, B, H, T, scale,
    BTL: tl.constexpr, BTS: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr,
    DK: tl.constexpr,  DV: tl.constexpr,
):
    p_do = tl.make_block_ptr(do + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d),
                             (i_c * BTL, i_v * BV), (BTL, BV), (1, 0))
    b_do = tl.load(p_do, boundary_check=(0, 1))
    b_dq = tl.zeros([BTL, BK], dtype=tl.float32)
    p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK),
                            (s_qk_t, s_qk_d), (0, i_k * BK), (BTS, BK), (1, 0))
    p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (DV, T),
                            (s_vo_d, s_vo_t), (i_v * BV, 0), (BV, BTS), (0, 1))
    # decay rate given the head index
    b_b = tl.math.log2(1 - tl.math.pow(2, -5 - i_h * 1.0))
    # overall decay rate for an entire block
    d_b = tl.math.exp2(b_b * BTS)
    # cumulative decay from the end of the chunk
    d_h = tl.math.exp2((BTS - tl.arange(0, BTS)) * b_b)
    for _ in range(0, i_c * BTL, BTS):
        # [BTS, BK]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BV, BTS]
        b_v = tl.load(p_v, boundary_check=(0, 1))
        # [BTL, BTS]
        b_ds = tl.dot(b_do, b_v, allow_tf32=False) * d_h[None, :]
        # [BQ, BD]
        b_dq *= d_b
        b_dq += tl.dot(b_ds.to(b_v.dtype), b_k, allow_tf32=False)
        p_k = tl.advance(p_k, (BTS, 0))
        p_v = tl.advance(p_v, (0, BTS))
    b_dq *= tl.math.exp2(tl.arange(0, BTL) * b_b)[:, None] * scale
    o_q = tl.arange(0, BTL)
    o_k = tl.arange(0, BTS)
    p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK),
                            (s_qk_t, s_qk_d), (i_c * BTL, i_k * BK), (BTS, BK), (1, 0))
    p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (DV, T),
                            (s_vo_d, s_vo_t), (i_v * BV, i_c * BTL), (BV, BTS), (0, 1))
    # Q block and K block have overlap. masks required
    for _ in range(i_c * BTL, (i_c + 1) * BTL, BTS):
        # [BTS, BK]
        b_k = tl.load(p_k, boundary_check=(0, 1))
        # [BV, BTS]
        b_v = tl.load(p_v, boundary_check=(0, 1))
        # [BTL, BTS]
        m_s = o_q[:, None] >= o_k[None, :]
        d_s = tl.where(m_s, tl.math.exp2(
            (o_q[:, None] - o_k[None, :]) * b_b), 0)
        b_ds = tl.dot(b_do, b_v, allow_tf32=False) * d_s * scale
        # [BTL, BK]
        b_dq += tl.dot(b_ds.to(b_k.dtype), b_k, allow_tf32=False)
        p_k = tl.advance(p_k, (BTS, 0))
        p_v = tl.advance(p_v, (0, BTS))
        o_k += BTS
    p_dq = tl.make_block_ptr(dq + (i_bh + B * H * i_v) * s_qk_h, (T, DK),
                             (s_qk_t, s_qk_d), (i_c*BTL, i_k*BK), (BTL, BK), (1, 0))
    tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
    return


@triton.jit
def _parallel_retention_bwd_dkv(
    i_bh, i_c, i_k, i_v, i_h,
    q, k, v, do, dk, dv, s_qk_h, s_qk_t, s_qk_d, s_vo_h,
    s_vo_t, s_vo_d, B, H, T, scale,
    BTL: tl.constexpr, BTS: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr,
    DK: tl.constexpr,  DV: tl.constexpr,
):
    # no overlap. no need for mask.
    b_b = tl.math.log2(1 - tl.math.pow(2, -5 - i_h * 1.0))
    # overall decay rate for an entire block
    d_b = tl.math.exp2(b_b * BTS)
    # compute dk dv
    p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d),
                            (i_c * BTL, i_k * BK), (BTL, BK), (1, 0))
    p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d),
                            (i_c * BTL, i_v * BV), (BTL, BV), (1, 0))
    b_k, b_v = tl.load(p_k, boundary_check=(0, 1)), tl.load(
        p_v, boundary_check=(0, 1))
    b_dk, b_dv = tl.zeros([BTL, BK], dtype=tl.float32), tl.zeros(
        [BTL, BV], dtype=tl.float32)
    d_h = tl.math.exp2((BTL - tl.arange(0, BTL)) * b_b)
    b_kd = (b_k * d_h[:, None]).to(b_k.dtype)
    d_q = tl.math.exp2(tl.arange(0, BTS) * b_b)
    for i in range((tl.cdiv(T, BTS) * BTS)-BTS, (i_c + 1) * BTL - BTS, -BTS):
        p_q = tl.make_block_ptr(
            q + i_bh * s_qk_h, (DK, T), (s_qk_d, s_qk_t), (i_k * BK, i), (BK, BTS), (0, 1))
        p_do = tl.make_block_ptr(
            do + i_bh * s_vo_h, (DV, T), (s_vo_d, s_vo_t), (i_v * BV, i), (BV, BTS), (0, 1))
        b_q = tl.load(p_q, boundary_check=(0, 1))  # [BK, BTS]
        b_do = tl.load(p_do, boundary_check=(0, 1))  # [BV, BTS]
        b_do = (b_do * d_q[None, :]).to(b_do.dtype)

        b_dv *= d_b
        b_s = tl.dot(b_kd.to(b_q.dtype), b_q, allow_tf32=False)  # [BTL, BTS]
        b_dv += tl.dot(b_s.to(b_q.dtype), tl.trans(b_do), allow_tf32=False)

        b_dk *= d_b
        b_ds = tl.dot(b_v, b_do, allow_tf32=False)
        b_dk += tl.dot(b_ds.to(b_q.dtype), tl.trans(b_q), allow_tf32=False)
    b_dk *= d_h[:, None] * scale
    b_dv *= scale
    tl.debug_barrier()
    o_q, o_k = tl.arange(0, BTS), tl.arange(0, BTL)
    for i in range(i_c*BTL, (i_c+1)*BTL, BTS):
        p_q = tl.make_block_ptr(
            q + i_bh * s_qk_h, (DK, T), (s_qk_d, s_qk_t), (i_k * BK, i), (BK, BTS), (0, 1))
        p_do = tl.make_block_ptr(
            do + i_bh * s_vo_h, (DV, T), (s_vo_d, s_vo_t), (i_v * BV, i), (BV, BTS), (0, 1))
        b_q = tl.load(p_q, boundary_check=(0, 1))  # [BD, BQ]
        b_do = tl.load(p_do, boundary_check=(0, 1))
        # [BK, BQ]
        m_s = o_k[:, None] <= o_q[None, :]
        d_s = tl.where(m_s, tl.math.exp2(
            (-o_k[:, None] + o_q[None, :]) * b_b.to(tl.float32)), 0) * scale
        b_s = tl.dot(b_k, b_q, allow_tf32=False) * d_s
        b_ds = tl.dot(b_v, b_do, allow_tf32=False) * d_s
        # [BK, BD]
        b_dk += tl.dot(b_ds.to(b_q.dtype), tl.trans(b_q), allow_tf32=False)
        b_dv += tl.dot(b_s.to(b_q.dtype), tl.trans(b_do), allow_tf32=False)
        o_q += BTS
    p_dk = tl.make_block_ptr(dk + (i_bh + B * H * i_v) * s_qk_h,
                             (T, DK), (s_qk_t, s_qk_d), (i_c*BTL, i_k*BK), (BTL, BK), (1, 0))
    p_dv = tl.make_block_ptr(dv + (i_bh + B * H * i_k) * s_vo_h,
                             (T, DV), (s_vo_t, s_vo_d), (i_c*BTL, i_v*BV), (BTL, BV), (1, 0))
    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))
    return


@triton.jit
def parallel_retention_bwd_kernel(
    q, k, v, do, dq, dk, dv, s_qk_h, s_qk_t, s_qk_d, s_vo_h,
    s_vo_t, s_vo_d, B, H, T, scale,
    BTL: tl.constexpr, BTS: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr,
    DK: tl.constexpr,  DV: tl.constexpr,
):
    i_kv, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
    NV = tl.cdiv(DV, BV)
    i_k = i_kv // (NV)
    i_v = i_kv % (NV)
    i_h = i_bh % H
    _parallel_retention_bwd_dq(
        i_bh, i_c, i_k, i_v, i_h,
        k, v, do, dq, s_qk_h, s_qk_t, s_qk_d, s_vo_h,
        s_vo_t, s_vo_d, B, H, T, scale,  BTL=BTL, BTS=BTS, BK=BK, BV=BV, DK=DK, DV=DV
    )
    tl.debug_barrier()
    _parallel_retention_bwd_dkv(
        i_bh, i_c, i_k, i_v, i_h,
        q, k, v, do, dk, dv, s_qk_h, s_qk_t, s_qk_d, s_vo_h,
        s_vo_t, s_vo_d, B, H, T, scale, BTL, BTS, BK, BV, DK, DV
    )


class ParallelRetentionFunction(torch.autograd.Function):
    @staticmethod
    @contiguous
    @custom_fwd
    def forward(ctx, q, k, v):
        BTL, BTS = 128, 32
        assert BTL % BTS == 0
        BK = min(128, triton.next_power_of_2(k.shape[-1]))
        BV = min(128, triton.next_power_of_2(v.shape[-1]))
        batch_size, n_heads, seq_len, d_head_qk = q.shape
        d_head_v = v.shape[-1]
        num_stages = 3 if d_head_qk <= 64 else 2
        num_warps = 4
        NK = triton.cdiv(d_head_qk, BK)
        NV = triton.cdiv(d_head_v, BV)

        grid = (NK * NV, triton.cdiv(seq_len, BTL), batch_size * n_heads)
        scale = d_head_qk ** -0.5
        o = torch.empty(NK, batch_size, n_heads, seq_len,
                        d_head_v, dtype=q.dtype, device=q.device)
        parallel_retention_fwd_kernel[grid](
            q, k, v, o,
            q.stride(1), q.stride(2), q.stride(3),
            v.stride(1), v.stride(2), v.stride(3),
            batch_size, n_heads, seq_len, scale,
            BTL=BTL, BTS=BTS, BK=BK, BV=BV, DK=d_head_qk, DV=d_head_v,
            num_warps=num_warps,
            num_stages=num_stages
        )
        ctx.save_for_backward(q, k, v)
        return o.sum(0).to(q.dtype)

    @staticmethod
    @contiguous
    @custom_bwd
    def backward(ctx, do):
        q, k, v = ctx.saved_tensors
        BTL, BTS = 64, 32
        assert BTL % BTS == 0
        BK = min(128, triton.next_power_of_2(k.shape[-1]))
        BV = min(128, triton.next_power_of_2(v.shape[-1]))
        batch_size, n_heads, seq_len, d_head_qk = q.shape
        d_head_v = v.shape[-1]
        num_stages = 3 if d_head_qk <= 64 else 2
        num_warps = 4
        NK = triton.cdiv(d_head_qk, BK)
        NV = triton.cdiv(d_head_v, BV)
        grid = (NK * NV, triton.cdiv(seq_len, BTL), batch_size * n_heads)
        scale = d_head_qk ** -0.5

        dq = torch.empty(NV, batch_size, n_heads, seq_len,
                         d_head_qk, dtype=q.dtype, device=q.device)
        dk = torch.empty(NV, batch_size, n_heads, seq_len,
                         d_head_qk, dtype=q.dtype, device=q.device)
        dv = torch.empty(NK, batch_size, n_heads, seq_len,
                         d_head_v, dtype=q.dtype, device=q.device)

        parallel_retention_bwd_kernel[grid](
            q, k, v, do, dq, dk, dv,
            q.stride(1), q.stride(2), q.stride(3),
            v.stride(1), v.stride(2), v.stride(3),
            batch_size, n_heads, seq_len, scale,
            BTL=BTL, BTS=BTS, BK=BK, BV=BV, DK=d_head_qk, DV=d_head_v,
            num_warps=num_warps,
            num_stages=num_stages
        )

        return dq.sum(0).to(q.dtype), dk.sum(0).to(k.dtype), dv.sum(0).to(v.dtype)


parallel_retention = ParallelRetentionFunction.apply