411 lines
15 KiB
Python
411 lines
15 KiB
Python
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# -*- coding: utf-8 -*-
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import torch
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import triton
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import triton.language as tl
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from torch.cuda.amp import custom_bwd, custom_fwd
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from fla.utils import contiguous
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# on-the-fly computation without materializing hidden statets into HBMs
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@triton.jit
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def fused_chunk_based_fwd_kernel(
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# B: batch_size, H: n_heads, T: seq_len, D: d_head
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q, # query [B, H, L, D_head_K]
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k, # key [B, H, L, D_head_V]
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v, # value [B, H, L, D_head_V]
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o, # output [B, H, L, D_head_V]
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z, # normalizer [B, H, L, 1]
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s_qk_h, # stride size: L * D_head_K
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s_qk_t, # stride size: D_head_K
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s_qk_d, # stride size: 1
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s_vo_h, # stride size: L * D_head_V
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s_vo_t, # stride size: D_head_V
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s_vo_d, # stride size: 1
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B, # batch size
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H, # n_heads
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T, # seq_len
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scale, # D_head_K ** -0.5
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BT: tl.constexpr, # BLOCK SIZE along the sequence dimension, a.k.a. chunk size
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BK: tl.constexpr, # BLOCK SIZE along the K dimension
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BV: tl.constexpr, # BLOCK SIZE along the V dimension
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DK: tl.constexpr, # D_head_K
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DV: tl.constexpr, # D_head_V
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):
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# indices
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i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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o_i = tl.arange(0, BT)
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# [BT, BT]
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m_s = o_i[:, None] >= o_i[None, :]
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# [BV], zero-order taylor expansion
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b_h_0o = tl.zeros([BV], dtype=tl.float32)
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# [BK, BV], first-order taylor expansion
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b_h_1o = tl.zeros([BK, BV], dtype=tl.float32)
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# [BK, BK, BV] second-order taylor expansion
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b_h_2o = tl.zeros([BK*BK, BV], dtype=tl.float32)
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# make block pointers
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p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (T, DK),
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(s_qk_t, s_qk_d), (0, i_k * BK), (BT, BK), (1, 0))
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p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (DK, T),
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(s_qk_d, s_qk_t), (i_k * BK, 0), (BK, BT), (0, 1))
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p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV),
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(s_vo_t, s_vo_d), (0, i_v * BV), (BT, BV), (1, 0))
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p_o = tl.make_block_ptr(o + (i_bh + i_k*B*H) * s_vo_h, (T, DV),
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(s_vo_t, s_vo_d), (0, i_v * BV), (BT, BV), (1, 0))
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p_z = z + (i_bh + i_k * B * H) * T + tl.arange(0, BT)
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k_2o = tl.zeros([1, BK * BK], dtype=tl.float32)
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k_1o = tl.zeros([1, BK], dtype=tl.float32)
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k_0o = 0
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for i in range(0, tl.cdiv(T, BT)):
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# [BK, BT]
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b_k = tl.load(p_k, boundary_check=(0, 1))
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# [BK*BK, BT]
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b_k_2o = b_k[:, None, :] * b_k[None, :, :]
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b_k_2o = tl.reshape(b_k_2o, [BK * BK, BT]).to(b_k.dtype)
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# [BT, BV]
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b_v = tl.load(p_v, boundary_check=(0, 1))
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# [BT, BK]
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b_q = (tl.load(p_q, boundary_check=(0, 1)) * scale).to(b_k.dtype)
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b_o = tl.zeros([BT, BV], dtype=tl.float32)
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b_z = tl.zeros([BT], dtype=tl.float32)
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# interchunk
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# zero-order
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b_o += b_h_0o
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b_z += k_0o
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# first-order
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b_o += tl.dot(b_q, b_h_1o.to(b_q.dtype), allow_tf32=False)
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b_z += tl.sum(b_q * k_1o, axis=1)
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# second-order
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b_q_2o = b_q[:, :, None] * b_q[:, None, :]
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b_q_2o = tl.reshape(b_q_2o, [BT, BK * BK]).to(b_k.dtype)
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b_o += tl.dot(b_q_2o, b_h_2o.to(b_q_2o.dtype), allow_tf32=False) * 0.5
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b_z += tl.sum(b_q_2o * k_2o, axis=1) * 0.5
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# update running statistics
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k_1o += tl.sum(b_k, axis=1)[None, :]
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k_2o += tl.sum(b_k_2o, axis=1)[None, :]
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k_0o += BT
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# intrachunk
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# [BT, BT]
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b_s = tl.dot(b_q, b_k, allow_tf32=False)
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b_s = 1 + b_s + 0.5 * b_s * b_s
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b_s = tl.where(m_s, b_s, 0)
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b_z += tl.sum(b_s, axis=1)
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b_o += tl.dot(b_s.to(b_q.dtype), b_v, allow_tf32=False)
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# [TB, BV]
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tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
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tl.store(p_z, b_z.to(p_z.dtype.element_ty),
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mask=(i * BT + tl.arange(0, BT)) < T)
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# update hidden state
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# [BK, BV]
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b_h_2o = b_h_2o + tl.dot(b_k_2o.to(b_v.dtype), b_v, allow_tf32=False)
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b_h_1o = b_h_1o + tl.dot(b_k, b_v, allow_tf32=False)
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b_h_0o = b_h_0o + tl.sum(b_v, axis=0)
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p_q = tl.advance(p_q, (BT, 0))
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p_k = tl.advance(p_k, (0, BT))
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p_v = tl.advance(p_v, (BT, 0))
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p_o = tl.advance(p_o, (BT, 0))
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p_z += BT
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# Similar to Algorithm1 of https://arxiv.org/abs/2006.16236
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@triton.jit
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def fused_chunk_based_bwd_kernel(
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# B: batch_size, H: n_heads, T: seq_len, D: d_head
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# NV: number of split in the V dimension. NK: number of split in the K dimension
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q, # query [B, H, L, D_head_K]
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k, # key [B, H, L, D_head_V]
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v, # value [B, H, L, D_head_V]
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do, # gradient of output [B, H, L, D_head_V]
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dz, # gradient of normalizer [B, H, L]
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dq, # gradient of query [NV, B, H, L, D_head_K]
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dk, # gradient of key [NV, B, H, L, D_head_K]
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dv, # gradient of value [NK, B, H, L, D_head_V]
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s_qk_h, # stride size: L * D_head_K
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s_qk_t, # stride size: D_head_K
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s_qk_d, # stride size: 1
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s_vo_h, # stride size: L * D_head_V
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s_vo_t, # stride size: D_head_V
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s_vo_d, # stride size: 1
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B, # batch_size
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H, # n_heads
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T, # seq_len
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scale, # D_head_K ** -0.5
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BT: tl.constexpr, # BLOCK SIZE along the sequence dimension, a.k.a. chunk size
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BK: tl.constexpr, # BLOCK SIZE along the K dimension
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BV: tl.constexpr, # BLOCK SIZE along the V dimension
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DK: tl.constexpr, # D_head_K
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DV: tl.constexpr, # D_head_V
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):
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i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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o_i = tl.arange(0, BT)
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m_s = o_i[:, None] >= o_i[None, :]
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# [BV], zero-order taylor expansion
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# b_h_0o = tl.zeros([BV], dtype=tl.float32)
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# [BK, BV], first-order taylor expansion
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b_h_1o = tl.zeros([BV, BK], dtype=tl.float32)
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# [BK, BK, BV] second-order taylor expansion
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b_h_2o = tl.zeros([BV, BK*BK], dtype=tl.float32)
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k_1o = tl.zeros([1, BK], dtype=tl.float32)
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k_2o = tl.zeros([1, BK * BK], dtype=tl.float32)
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for i in range(0, tl.cdiv(T, BT)):
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p_q = tl.make_block_ptr(
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q + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i * BT, i_k * BK), (BT, BK), (1, 0))
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p_k = tl.make_block_ptr(
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k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i * BT, i_k * BK), (BT, BK), (1, 0))
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p_v = tl.make_block_ptr(
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v + i_bh * s_vo_h, (DV, T), (s_vo_d, s_vo_t), (i_v * BV, i * BT), (BV, BT), (0, 1))
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p_do = tl.make_block_ptr(
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do + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d), (i * BT, i_v * BV), (BT, BV), (1, 0))
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p_dq = tl.make_block_ptr(dq + (i_bh + i_v*B*H) * s_qk_h,
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(T, DK), (s_qk_t, s_qk_d), (i*BT, i_k*BK), (BT, BK), (1, 0))
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p_dz = dz + (i_bh) * T + tl.arange(0, BT) + i * BT
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b_dq = tl.zeros([BT, BK], dtype=tl.float32)
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# load tensors
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# [BT, BK]
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b_dz = tl.load(p_dz, mask=(tl.arange(0, BT) + i * BT) < T)
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b_q = tl.load(p_q, boundary_check=(0, 1))
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b_q = (b_q * scale).to(b_q.dtype)
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b_do = tl.load(p_do, boundary_check=(0, 1)).to(b_q.dtype)
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b_k = tl.load(p_k, boundary_check=(0, 1))
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# [BV, BT]
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b_v = tl.load(p_v, boundary_check=(0, 1))
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# inter-chunk
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b_dq += tl.dot(b_do, (b_h_1o).to(b_do.dtype), allow_tf32=False)
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if i_v == 0:
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b_dq += b_dz[:, None] * k_1o
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b_dq_2o = tl.dot(b_do, (b_h_2o).to(b_do.dtype), allow_tf32=False) * 0.5
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if i_v == 0:
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b_dq_2o += (b_dz[:, None] * k_2o) * 0.5
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b_dq_2o = tl.reshape(b_dq_2o, [BT, BK, BK])
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b_dq += tl.sum(b_dq_2o * b_q[:, :, None], axis=1)
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b_dq += tl.sum(b_dq_2o * b_q[:, None, :], axis=2)
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b_dq *= scale
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# intra-chunk
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# [BT, BT]
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b_ds = tl.dot(b_do, b_v, allow_tf32=False)
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if i_v == 0:
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b_ds += b_dz[:, None]
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b_ds = tl.where(m_s, b_ds, 0) * scale
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b_s = tl.dot(b_q, tl.trans(b_k), allow_tf32=False)
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b_s = tl.where(m_s, b_s, 0)
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b_dq += tl.dot((b_ds * (1 + b_s)).to(b_q.dtype), b_k, allow_tf32=False)
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# store
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tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
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# update hidden state
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# [BT, BK*BK]
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b_k_2o = b_k[:, :, None] * b_k[:, None, :]
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b_k_2o = tl.reshape(b_k_2o, [BT, BK * BK]).to(b_k.dtype)
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# [BV, BK*BK]
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b_h_2o = b_h_2o + tl.dot(b_v, b_k_2o.to(b_v.dtype), allow_tf32=False)
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# [BV, BK]
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b_h_1o = b_h_1o + tl.dot(b_v, b_k, allow_tf32=False)
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if i_v == 0:
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# update running statistics
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k_1o += tl.sum(b_k, axis=0)[None, :]
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k_2o += tl.sum(b_k_2o, axis=0)[None, :]
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tl.debug_barrier()
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b_h_1o = None
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b_h_2o = None
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# [BK, BV], first-order taylor expansion
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b_dh_1o = tl.zeros([BK, BV], dtype=tl.float32)
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# [BK, BK, BV] second-order taylor expansion
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b_dh_2o = tl.zeros([BK*BK, BV], dtype=tl.float32)
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b_dh_0o = tl.zeros([BV], dtype=tl.float32)
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m_s = tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :]
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dq_1o = tl.zeros([1, BK], dtype=tl.float32)
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dq_2o = tl.zeros([BK * BK, 1], dtype=tl.float32)
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for i in range(tl.cdiv(T, BT) * BT - BT, -BT, -BT):
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p_q = tl.make_block_ptr(
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q + i_bh * s_qk_h, (DK, T), (s_qk_d, s_qk_t), (i_k * BK, i), (BK, BT), (0, 1))
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p_k = tl.make_block_ptr(
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k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i, i_k * BK), (BT, BK), (1, 0))
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p_v = tl.make_block_ptr(
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v + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d), (i, i_v * BV), (BT, BV), (1, 0))
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p_do = tl.make_block_ptr(
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do + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d), (i, i_v * BV), (BT, BV), (1, 0))
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p_dk = tl.make_block_ptr(dk + (i_bh+i_v*B*H) * s_qk_h, (T, DK),
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(s_qk_t, s_qk_d), (i, i_k*BK), (BT, BK), (1, 0))
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p_dv = tl.make_block_ptr(dv + (i_bh+i_k*B*H) * s_vo_h, (T, DV),
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(s_vo_t, s_vo_d), (i, i_v*BV), (BT, BV), (1, 0))
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p_dz = dz + (i_bh) * T + tl.arange(0, BT) + i
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b_dk = tl.zeros([BT, BK], dtype=tl.float32)
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b_dv = tl.zeros([BT, BV], dtype=tl.float32)
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b_dz = tl.load(p_dz, mask=(tl.arange(0, BT)+i) < T)
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b_q = tl.load(p_q, boundary_check=(0, 1))
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b_k = tl.load(p_k, boundary_check=(0, 1))
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b_v = tl.load(p_v, boundary_check=(0, 1))
|
||
|
|
b_do = tl.load(p_do, boundary_check=(0, 1)).to(b_q.dtype)
|
||
|
|
b_q = (b_q * scale).to(b_k.dtype)
|
||
|
|
|
||
|
|
# intra chunk
|
||
|
|
b_ds = tl.dot(b_v, tl.trans(b_do), allow_tf32=False)
|
||
|
|
if i_v == 0:
|
||
|
|
b_ds += b_dz[None, :]
|
||
|
|
b_ds = tl.where(m_s, b_ds, 0)
|
||
|
|
b_s = tl.dot(b_k, b_q, allow_tf32=False)
|
||
|
|
b_s2 = 1 + b_s + 0.5 * b_s * b_s
|
||
|
|
b_s = tl.where(m_s, b_s, 0)
|
||
|
|
b_s2 = tl.where(m_s, b_s2, 0)
|
||
|
|
b_ds *= (1+b_s)
|
||
|
|
|
||
|
|
b_dk += tl.dot(b_ds.to(b_k.dtype), tl.trans(b_q), allow_tf32=False)
|
||
|
|
b_dv += tl.dot(b_s2.to(b_do.dtype), b_do, allow_tf32=False)
|
||
|
|
|
||
|
|
# inter chunk
|
||
|
|
b_k_2o = b_k[:, :, None] * b_k[:, None, :]
|
||
|
|
b_k_2o = tl.reshape(b_k_2o, [BT, BK * BK]).to(b_k.dtype)
|
||
|
|
|
||
|
|
b_dv += tl.dot(b_k, b_dh_1o.to(b_k.dtype), allow_tf32=False)
|
||
|
|
b_dv += tl.dot(b_k_2o, b_dh_2o.to(b_k.dtype), allow_tf32=False)
|
||
|
|
b_dv += b_dh_0o
|
||
|
|
|
||
|
|
b_dk += tl.dot(b_v, tl.trans(b_dh_1o).to(b_k.dtype), allow_tf32=False)
|
||
|
|
|
||
|
|
if i_v == 0:
|
||
|
|
b_dk += dq_1o
|
||
|
|
|
||
|
|
b_dk_2o = tl.dot(b_dh_2o.to(b_k.dtype),
|
||
|
|
tl.trans(b_v), allow_tf32=False)
|
||
|
|
if i_v == 0:
|
||
|
|
b_dk_2o += dq_2o
|
||
|
|
b_dk_2o = tl.reshape(b_dk_2o, [BK, BK, BT])
|
||
|
|
b_k_fp32 = tl.trans(b_k.to(tl.float32))
|
||
|
|
b_dk2 = tl.sum(b_dk_2o * b_k_fp32[:, None, :], axis=0)
|
||
|
|
b_dk2 += tl.sum(b_dk_2o * b_k_fp32[None, :, :], axis=1)
|
||
|
|
b_dk += tl.trans(b_dk2)
|
||
|
|
|
||
|
|
# hidden state update
|
||
|
|
b_dh_0o += tl.sum(b_do, axis=0)
|
||
|
|
b_dh_1o = b_dh_1o + tl.dot(b_q, b_do, allow_tf32=False)
|
||
|
|
b_q_2o = b_q[None, :, :] * b_q[:, None, :]
|
||
|
|
b_q_2o = tl.reshape(b_q_2o, [BK * BK, BT]).to(b_k.dtype)
|
||
|
|
b_dh_2o = b_dh_2o + tl.dot(b_q_2o, b_do, allow_tf32=False) * 0.5
|
||
|
|
|
||
|
|
if i_v == 0:
|
||
|
|
dq_1o += (tl.sum(b_dz[None, :] * b_q, axis=1))[None, :]
|
||
|
|
dq_2o += (tl.sum(b_dz[None, :] * b_q_2o, axis=1) * 0.5)[:, None]
|
||
|
|
|
||
|
|
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))
|
||
|
|
|
||
|
|
|
||
|
|
class FusedChunkBasedFunction(torch.autograd.Function):
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
@contiguous
|
||
|
|
@custom_fwd
|
||
|
|
def forward(ctx, q, k, v, scale=1):
|
||
|
|
batch_size, n_heads, seq_len, d_head_qk = q.shape
|
||
|
|
# assert d_head_qk == 16, "currently we do not support feature dim other than 16"
|
||
|
|
d_head_v = v.shape[-1]
|
||
|
|
|
||
|
|
scale = scale
|
||
|
|
BT = 16
|
||
|
|
BK, BV = min(d_head_qk, 16), min(d_head_v, 32)
|
||
|
|
BK, BV = max(BK, 16), max(BV, 16)
|
||
|
|
NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
|
||
|
|
|
||
|
|
num_warps = 4
|
||
|
|
|
||
|
|
# the norm of o might explode, so we need to use float32 here
|
||
|
|
o = q.new_empty(NK, batch_size, n_heads, seq_len,
|
||
|
|
d_head_v, dtype=torch.float32)
|
||
|
|
z = q.new_empty(NK, batch_size, n_heads, seq_len, dtype=torch.float32)
|
||
|
|
|
||
|
|
grid = (NV, NK, batch_size * n_heads)
|
||
|
|
fused_chunk_based_fwd_kernel[grid](
|
||
|
|
q, k, v, o, z,
|
||
|
|
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,
|
||
|
|
BT=BT, DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
|
||
|
|
num_warps=num_warps,
|
||
|
|
)
|
||
|
|
o = o.sum(0)
|
||
|
|
z = z.sum(0)
|
||
|
|
ctx.save_for_backward(q, k, v)
|
||
|
|
ctx.scale = scale
|
||
|
|
return o.to(q.dtype), z.to(z.dtype)
|
||
|
|
|
||
|
|
@staticmethod
|
||
|
|
@contiguous
|
||
|
|
@custom_bwd
|
||
|
|
def backward(ctx, do, dz):
|
||
|
|
q, k, v = ctx.saved_tensors
|
||
|
|
batch_size, n_heads, seq_len, d_head_qk = q.shape
|
||
|
|
d_head_v = v.shape[-1]
|
||
|
|
scale = ctx.scale
|
||
|
|
|
||
|
|
BT = 16
|
||
|
|
BK, BV = min(d_head_qk, 16), min(d_head_v, 32)
|
||
|
|
BK, BV = max(BK, 16), max(BV, 16)
|
||
|
|
NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
|
||
|
|
num_stages = 1
|
||
|
|
num_warps = 4
|
||
|
|
|
||
|
|
dq = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
|
||
|
|
dk = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
|
||
|
|
dv = q.new_empty(NK, batch_size, n_heads, seq_len, d_head_v)
|
||
|
|
grid = (NV, NK, batch_size * n_heads)
|
||
|
|
|
||
|
|
fused_chunk_based_bwd_kernel[grid](
|
||
|
|
q, k, v, do, dz, 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,
|
||
|
|
BT=BT, DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
|
||
|
|
num_warps=num_warps,
|
||
|
|
num_stages=num_stages
|
||
|
|
)
|
||
|
|
dq = dq.sum(0)
|
||
|
|
dk = dk.sum(0)
|
||
|
|
dv = dv.sum(0)
|
||
|
|
return dq.to(q.dtype), dk.to(k.dtype), dv.to(v.dtype), None
|
||
|
|
|
||
|
|
|
||
|
|
triton_fused_chunk_based = FusedChunkBasedFunction.apply
|
||
|
|
|
||
|
|
|
||
|
|
def fused_chunk_based(q, k, v, use_scale=True, use_normalize=True):
|
||
|
|
assert q.shape[-1] <= 16, 'only support feature dimension up to 16.'
|
||
|
|
if use_scale:
|
||
|
|
scale = q.shape[-1] ** -0.5
|
||
|
|
else:
|
||
|
|
scale = 1
|
||
|
|
o, z = triton_fused_chunk_based(q, k, v, scale)
|
||
|
|
if use_normalize:
|
||
|
|
o = o / (z[..., None] + 1e-6)
|
||
|
|
else:
|
||
|
|
o = o
|
||
|
|
|
||
|
|
return o.to(q.dtype)
|