549 lines
21 KiB
Python
Vendored
549 lines
21 KiB
Python
Vendored
# -*- coding: utf-8 -*-
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# Copyright (c) 2023, Songlin Yang
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# Gated Linear Attention Transformers with Hardware-Efficient Training: https://arxiv.org/abs/2312.06635
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# on-the-fly computation without materializing hidden statets into HBMs
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from typing import Tuple
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import torch
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import torch.nn.functional as F
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import triton
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import triton.language as tl
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from einops import rearrange
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from packaging import version
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from torch.cuda.amp import custom_bwd, custom_fwd
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from fla.ops.gla.chunk_util import (bwd_decay_global_cumsum, fwd_decay_cumsum,
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prepare_qg_kg)
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from fla.utils import contiguous
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inv_ln2 = 1.44269504
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@triton.jit
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def fused_chunk_gla_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_K]
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v, # value [B, H, L, D_head_V]
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g, # cumulative sum of log decay [B, H, L, D_head_K]
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o, # output [B, H, L, D_head_V]
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initial_state, # initial state of the chunk [B, H, D_head_K, D_head_V]
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final_state, # final state of the chunk [B, H, D_head_K, 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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USE_INITIAL_STATE: tl.constexpr,
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STORE_FINAL_STATE: tl.constexpr,
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CHECK: tl.constexpr
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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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b_h = tl.zeros([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), (s_qk_t, s_qk_d), (0, i_k * BK), (BT, BK), (1, 0))
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p_db = g + i_bh * s_qk_h + (BT - 1) * s_qk_t + i_k * BK + tl.arange(0, BK)
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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, BT), (0, 1))
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p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV), (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), (s_vo_t, s_vo_d), (0, i_v * BV), (BT, BV), (1, 0))
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if USE_INITIAL_STATE:
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p_h = tl.make_block_ptr(initial_state + i_bh * DK * DV, (DK, DV), (DV, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
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b_h += tl.load(p_h, boundary_check=(0, 1)).to(tl.float32)
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mask = (i_k * BK + tl.arange(0, BK)) < DK
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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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# [BT, BV]
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b_o = tl.zeros([BT, BV], dtype=tl.float32)
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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))
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d_b = tl.load(p_db, mask=mask, other=0).to(tl.float32)
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if CHECK and i == 0:
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b_o = tl.dot(b_q.to(b_v.dtype), b_h.to(b_v.dtype), allow_tf32=False)
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b_h = b_h * tl.math.exp2(d_b)[:, None] + tl.dot(b_k.to(b_v.dtype), b_v, allow_tf32=False)
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else:
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b_o = tl.dot(b_q.to(b_v.dtype), b_h.to(b_v.dtype), allow_tf32=False)
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b_h = b_h * tl.math.exp2(d_b)[:, None] + tl.dot(b_k.to(b_v.dtype), b_v, allow_tf32=False)
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tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1))
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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_db += BT * DK
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if STORE_FINAL_STATE:
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p_final = tl.make_block_ptr(final_state + i_bh * DK * DV, (DK, DV), (DV, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0))
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tl.store(p_final, b_h.to(p_final.dtype.element_ty), boundary_check=(0, 1))
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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_gla_bwd_kernel(
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q, k, v, g,
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do, # gradient of output [B, H, L, D_head_V]
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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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initial_state, # initial state of the chunk [B, H, D_head_K, 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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# clamp_min, # minimum log value of the gate for numerical stability. default: -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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USE_INITIAL_STATE: tl.constexpr,
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CHECK: tl.constexpr
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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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# [BV, BK]
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b_h = tl.zeros([BV, BK], dtype=tl.float32)
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if USE_INITIAL_STATE:
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p_h = tl.make_block_ptr(initial_state + i_bh * DK * DV, (DV, DK), (1, DV), (i_v * BV, i_k * BK), (BV, BK), (0, 1))
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b_h += tl.load(p_h, boundary_check=(0, 1)).to(tl.float32)
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mask = (i_k * BK + tl.arange(0, BK)) < DK
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for i in range(0, tl.cdiv(T, BT)):
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p_k = tl.make_block_ptr(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_db = g + i_bh * s_qk_h + ((i+1) * BT - 1) * s_qk_t + i_k * BK + tl.arange(0, BK)
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p_v = tl.make_block_ptr(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(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, (T, DK), (s_qk_t, s_qk_d), (i * BT, i_k * BK), (BT, BK), (1, 0))
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b_dq = tl.zeros([BT, BK], dtype=tl.float32)
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# [BT, DK]
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b_k = tl.load(p_k, boundary_check=(0, 1))
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# b_g = tl.load(p_g, boundary_check=(0, 1)) * inv_ln2
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d_b = tl.load(p_db, mask=mask, other=0).to(tl.float32)
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# [DV, BT]
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b_v = tl.load(p_v, boundary_check=(0, 1))
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# [BT, DV]
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b_do = tl.load(p_do, boundary_check=(0, 1))
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# [DV, DK]
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if CHECK and i == 0:
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b_dq += tl.dot(b_do, b_h.to(b_do.dtype), allow_tf32=False)
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b_h = b_h * tl.math.exp2(d_b)[None, :] + tl.dot(b_v, b_k.to(b_v.dtype), allow_tf32=False)
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else:
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b_dq += tl.dot(b_do, b_h.to(b_do.dtype), allow_tf32=False)
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b_h = b_h * tl.math.exp2(d_b)[None, :] + tl.dot(b_v, b_k.to(b_v.dtype), allow_tf32=False)
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b_dq *= scale
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tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1))
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# sync threads
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b_h = None
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tl.debug_barrier()
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# [BK, BV]
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b_dh = tl.zeros([BK, BV], dtype=tl.float32)
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# cum = tl.zeros([BK], dtype=tl.float32)
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for i in range(1, tl.cdiv(T, BT) + 1):
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p_q = tl.make_block_ptr(q + i_bh * s_qk_h, (DK, T), (s_qk_d, s_qk_t), (i_k * BK, T - i * BT), (BK, BT), (0, 1))
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p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (T - i * BT, i_k * BK), (BT, BK), (1, 0))
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p_db = g + i_bh * s_qk_h + (T - (i-1) * BT - 1) * s_qk_t + i_k * BK + tl.arange(0, BK)
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p_v = tl.make_block_ptr(v + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d), (T - i * BT, i_v * BV), (BT, BV), (1, 0))
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p_do = tl.make_block_ptr(do + i_bh * s_vo_h, (T, DV), (s_vo_t, s_vo_d), (T - i * BT, 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), (T - i * BT, 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), (T - i * BT, i_v * BV), (BT, BV), (1, 0))
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# [DK, BT]
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b_q = tl.load(p_q, boundary_check=(0, 1))
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# [BT, DK]
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b_k = tl.load(p_k, boundary_check=(0, 1))
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# [BT, DV]
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b_v = tl.load(p_v, boundary_check=(0, 1))
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b_do = tl.load(p_do, boundary_check=(0, 1))
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b_db = tl.load(p_db, mask=mask, other=0).to(tl.float32)
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# inter-chunk
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# [DK, DV]
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if CHECK and i == 1:
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b_dk = tl.trans(tl.dot(b_dh.to(b_v.dtype), tl.trans(b_v), allow_tf32=False))
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b_dv = tl.dot((b_k).to(b_v.dtype), b_dh.to(b_v.dtype), allow_tf32=False)
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b_dh = b_dh * tl.math.exp2(b_db)[:, None] + tl.dot(b_q.to(b_do.dtype), b_do, allow_tf32=False)
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else:
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b_dk = tl.trans(tl.dot(b_dh.to(b_v.dtype), tl.trans(b_v), allow_tf32=False))
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b_dv = tl.dot((b_k).to(b_v.dtype), b_dh.to(b_v.dtype), allow_tf32=False)
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b_dh = b_dh * tl.math.exp2(b_db)[:, None] + tl.dot(b_q.to(b_do.dtype), b_do, allow_tf32=False)
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tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1))
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tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1))
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@triton.jit
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def fwd_inner_chunk(
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q, k, g, A,
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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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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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# clamp_min, # minimum log value of the gate for numerical stability. default: -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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DK: tl.constexpr, # D_head_K
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):
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i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
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b_k = tl.load(p_k, boundary_check=(0, 1))
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p_g = tl.make_block_ptr(g + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
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b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32)
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mask = (i_k * BK + tl.arange(0, BK)) < DK
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o_i = tl.arange(0, BT)
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p_q = q + i_bh * s_qk_h + i_k * BK + i_t * BT * DK + tl.arange(0, BK)
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p_gq = g + i_bh * s_qk_h + i_k * BK + i_t * BT * DK + tl.arange(0, BK)
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p_A = A + (i_bh + (i_k * B * H)) * (tl.cdiv(T, BT) * BT * BT) + i_t * BT * BT + tl.arange(0, BT)
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for i in range(BT):
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_q = tl.load(p_q, mask=mask, other=0) * scale
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gq = tl.load(p_gq, mask=mask, other=0).to(tl.float32)
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s = _q[None, :] * b_k * tl.math.exp2(gq[None, :] - b_g)
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score = tl.sum(s, axis=1)
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score = tl.where(o_i <= i, score, 0)
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tl.store(p_A, score.to(p_A.dtype.element_ty))
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p_q += DK
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p_gq += DK
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p_A += BT
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@triton.jit
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def bwd_inner_chunk(
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q,
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k,
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g,
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dA,
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dq,
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dk,
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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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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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# clamp_min, # minimum log value of the gate for numerical stability. default: -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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DK: tl.constexpr, # D_head_K
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):
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i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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p_k = tl.make_block_ptr(k + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
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b_k = tl.load(p_k, boundary_check=(0, 1))
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p_g = tl.make_block_ptr(g + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
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b_g = tl.load(p_g, boundary_check=(0, 1)).to(tl.float32)
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mask = (i_k * BK + tl.arange(0, BK)) < DK
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o_i = tl.arange(0, BT)
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p_q = q + i_bh * s_qk_h + i_k * BK + i_t * BT * DK + tl.arange(0, BK)
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p_dq = dq + (i_bh) * s_qk_h + i_k * BK + i_t * BT * DK + tl.arange(0, BK)
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p_gq = g + i_bh * s_qk_h + i_k * BK + i_t * BT * DK + tl.arange(0, BK)
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p_dA = dA + i_bh * (tl.cdiv(T, BT) * BT * BT) + i_t * BT * BT + tl.arange(0, BT)
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b_dk = tl.zeros([BT, BK], dtype=tl.float32)
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for i in range(BT):
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_q = tl.load(p_q, mask=mask, other=0)
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gq = tl.load(p_gq, mask=mask, other=0).to(tl.float32)
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score = tl.math.exp2(gq[None, :] - b_g)
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score = tl.where(o_i[:, None] <= i, score, 0)
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_dA = tl.load(p_dA)
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_dA = tl.where(o_i <= i, _dA, 0)
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b_dk += (_dA[:, None] * score * _q[None, :])
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b_dq = tl.sum(_dA[:, None] * score * b_k, axis=0)
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tl.store(p_dq, b_dq, mask=mask)
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p_q += DK
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p_dq += DK
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p_gq += DK
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p_dA += BT
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p_dk = tl.make_block_ptr(dk + i_bh * s_qk_h, (T, DK), (s_qk_t, s_qk_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0))
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tl.store(p_dk, b_dk.to(dk.dtype.element_ty), boundary_check=(0, 1))
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class FusedChunkGLAFunction(torch.autograd.Function):
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@staticmethod
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@contiguous
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@custom_fwd
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def forward(ctx, q, k, v, g, scale, initial_state, output_final_state):
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ctx.g_dtype = g.dtype
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g_original = g
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# cumulative decay should be in float32, otherwise the err will be accumulated and amplified.
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g = torch.empty_like(g, dtype=torch.float32)
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batch_size, n_heads, seq_len, d_head_qk = q.shape
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d_head_v = v.shape[-1]
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ctx.scale = scale
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# inter-chunk
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BT = 16 # chunk_size
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BK, BV = min(d_head_qk, 64), min(d_head_v, 64)
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num_stages = 1
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num_warps = 2
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NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
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o = q.new_empty(NK, batch_size, n_heads, seq_len, d_head_v)
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q_g = torch.empty_like(q)
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k_g = torch.empty_like(k)
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grid = (NK, triton.cdiv(seq_len, BT), batch_size * n_heads)
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fwd_decay_cumsum[grid](
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g_original,
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g,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, BK=BK, DK=d_head_qk, num_warps=1
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)
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prepare_qg_kg[grid](
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q, k, g, q_g, k_g,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, BK=BK, DK=d_head_qk, num_warps=1
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)
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if output_final_state:
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final_state = q.new_empty(batch_size, n_heads, d_head_qk, d_head_v, dtype=torch.float, requires_grad=False)
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else:
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final_state = None
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# the bug still exists even for Triton 2.2 on H100 GPUs
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# so we always enable initial checks
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CHECK = True
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if version.parse(triton.__version__) < version.parse('2.2.0'):
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import warnings
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warnings.warn(
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"Triton<2.2.0 detected for running this kernel, "
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"which is known to have some weird compiler issues (refer to https://github.com/openai/triton/issues/2852) "
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"that lead to significant precision loss. "
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"We've add some initial condition checks to resolve this, sadly at the sacrifice of the speed. "
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"For optimal performance, it is recommended to install Triton>=2.2.0 (if possible)."
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)
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CHECK = True
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grid = (NV, NK, batch_size * n_heads)
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fused_chunk_gla_fwd_kernel[grid](
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q_g, k_g, v, g, o, initial_state, final_state,
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q.stride(1), q.stride(2), q.stride(3),
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v.stride(1), v.stride(2), v.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
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USE_INITIAL_STATE=initial_state is not None,
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STORE_FINAL_STATE=output_final_state,
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CHECK=CHECK,
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num_warps=num_warps,
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num_stages=num_stages
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)
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o = o.sum(0)
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# intra-chunk
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chunk_size = 16
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num_chunk = seq_len // chunk_size
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v2 = rearrange(v, 'b h (n c) d -> b h n c d', n=num_chunk)
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BK = min(d_head_qk, 64)
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NK = triton.cdiv(d_head_qk, BK)
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A = q.new_empty(NK, batch_size, n_heads, triton.cdiv(seq_len, BT), BT, BT)
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grid = (NK, triton.cdiv(seq_len, BT), batch_size * n_heads)
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fwd_inner_chunk[grid](
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q, k, g, A,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale, BT=BT, BK=BK, DK=d_head_qk, num_stages=3,
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num_warps=4
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)
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A = A.sum(0)
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o2 = A @ v2
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o2 = rearrange(o2, 'b h n c d -> b h (n c) d')
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# combine inner and inter
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o.add_(o2)
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ctx.save_for_backward(q, k, v, g_original, A, initial_state)
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ctx.CHECK = CHECK
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return o.to(v), final_state
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@staticmethod
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@contiguous
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@custom_bwd
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def backward(ctx, do, d_final_state=None):
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q, k, v, g_origin, A, initial_state = ctx.saved_tensors
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batch_size, n_heads, seq_len, d_head_qk = q.shape
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d_head_v = v.shape[-1]
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scale = ctx.scale
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# recomputation
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# inter-chunk
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BT = 16 # chunk_size
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g = torch.empty_like(g_origin, dtype=torch.float32)
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BK, BV = min(d_head_qk, 64), min(d_head_v, 64)
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NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
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q_g = torch.empty_like(q)
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k_g = torch.empty_like(k)
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grid = (NK, triton.cdiv(seq_len, BT), batch_size * n_heads)
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fwd_decay_cumsum[grid](
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g_origin,
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g,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, BK=BK, DK=d_head_qk, num_warps=1
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)
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prepare_qg_kg[grid](
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q, k, g, q_g, k_g,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, BK=BK, DK=d_head_qk, num_warps=1
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)
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# inter-chunk
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BT = 16
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BK, BV = min(triton.next_power_of_2(d_head_qk), 64), min(triton.next_power_of_2(d_head_v), 64)
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NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
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num_stages = 1
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num_warps = 2
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dq = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
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dk = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
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dv = q.new_empty(NK, batch_size, n_heads, seq_len, d_head_v)
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grid = (NV, NK, batch_size * n_heads)
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fused_chunk_gla_bwd_kernel[grid](
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q_g, k_g, v, g, do, dq, dk, dv, initial_state,
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q.stride(1), q.stride(2), q.stride(3),
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v.stride(1), v.stride(2), v.stride(3),
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batch_size, n_heads, seq_len, scale,
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# clamp_min=-3,
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BT=BT, DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
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USE_INITIAL_STATE=initial_state is not None,
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CHECK=ctx.CHECK,
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num_warps=num_warps,
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num_stages=num_stages,
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)
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dq = dq.sum(0)
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dk = dk.sum(0)
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dv = dv.sum(0)
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# intra chunk
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num_chunk = seq_len // BT
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v2 = rearrange(v, 'b h (n c) d -> b h n c d', n=num_chunk)
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do2 = rearrange(do, 'b h (n c) d -> b h n c d', n=num_chunk)
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dA2 = (do2 @ v2.transpose(-2, -1)) * scale
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dv2 = A.transpose(-1, -2) @ do2
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dv2 = rearrange(dv2, 'b h n c d -> b h (n c) d', n=num_chunk)
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BK = min(triton.next_power_of_2(d_head_qk), 16)
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NK = triton.cdiv(d_head_qk, BK)
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dk2 = torch.empty_like(k)
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dq2 = torch.empty_like(q)
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grid = (NK, triton.cdiv(seq_len, BT), batch_size * n_heads)
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bwd_inner_chunk[grid](
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q, k, g,
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dA2, dq2, dk2,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, DK=d_head_qk, BK=BK,
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num_warps=1,
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num_stages=3
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)
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BK = min(triton.next_power_of_2(d_head_qk), 32)
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NK = triton.cdiv(d_head_qk, BK)
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dg = torch.empty_like(g, dtype=torch.float32)
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grid = (NK, triton.cdiv(seq_len, BT), batch_size * n_heads)
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bwd_decay_global_cumsum[grid](
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dq2, dq, dk2, dk, q, k, g, dg,
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q.stride(1), q.stride(2), q.stride(3),
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batch_size, n_heads, seq_len, scale,
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BT=BT, DK=d_head_qk, BK=BK,
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num_warps=1,
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num_stages=1
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)
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dg = rearrange(dg, 'b h (n c) d -> b h n c d', c=BT)
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def rev_cumsum_exclusive(x):
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cumsum_x = x.cumsum(-2)
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rev_cumsum_x = cumsum_x[..., -1, None, :] - cumsum_x
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return rev_cumsum_x
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rev_cumsum_dg = rev_cumsum_exclusive(dg[..., 0, :])
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dg.add_(rev_cumsum_dg.unsqueeze(-2))
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dv.add_(dv2)
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dg = rearrange(dg, 'b h n c d -> b h (n c) d')
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return dq.to(q), dk.to(k), dv.to(v), dg.to(ctx.g_dtype), None, None, None
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def pad(x, chunk_size=16):
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seq_len = x.shape[-2]
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padded_seq_len = ceildiv(seq_len, chunk_size) * chunk_size
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if x.shape[-2] % chunk_size != 0:
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x = F.pad(x, (0, 0, 0, padded_seq_len - seq_len))
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return x
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def ceildiv(a, b):
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return -(a // -b)
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def fused_chunk_gla(
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q: torch.Tensor,
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k: torch.Tensor,
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v: torch.Tensor,
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g: torch.Tensor,
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scale: int = -1,
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initial_state: torch.Tensor = None,
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output_final_state: bool = False
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) -> Tuple[torch.Tensor, torch.Tensor]:
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if scale == -1:
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scale = q.shape[-1] ** -0.5
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if initial_state is not None:
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initial_state = initial_state.detach()
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seq_len = q.shape[-2]
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q, k, v, g = map(lambda x: pad(x), [q, k, v, g])
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o, final_state = FusedChunkGLAFunction.apply(
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q, k, v, g, scale, initial_state, output_final_state)
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o = o[..., :seq_len, :]
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return o, final_state
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