# -*- coding: utf-8 -*- # Copyright (c) 2024, Songlin Yang, Yu Zhang from typing import Optional, Tuple import torch import triton import triton.language as tl from fla.ops.common.chunk_h import chunk_bwd_dh, chunk_fwd_h from fla.ops.utils import chunk_local_cumsum from fla.utils import contiguous @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BC", "BK"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_fwd_A_kernel_intra_sub_inter( q, k, g, A, offsets, indices, scale, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_t, 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 i_i, i_j = i_c // NC, i_c % NC if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos else: bos, eos = i_b * T, i_b * T + T if i_t * BT + i_i * BC >= T: return if i_i <= i_j: return b_A = tl.zeros([BC, BC], dtype=tl.float32) for i_k in range(tl.cdiv(K, BK)): o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K if HEAD_FIRST: p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k + i_bh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gk = tl.make_block_ptr(g + i_bh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gn = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) else: p_q = tl.make_block_ptr(q + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k + (bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gk = tl.make_block_ptr(g + (bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k, BK), BK) # [BK,] b_gn = tl.load(p_gn, mask=m_k, other=0) # [BC, BK] b_q = tl.load(p_q, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) b_qg = b_q * tl.exp(b_g - b_gn[None, :]) * scale # [BK, BC] b_k = tl.load(p_k, boundary_check=(0, 1)) b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_kg = b_k * tl.exp(b_gn[:, None] - b_gk) # [BC, BC] using tf32 to improve precision here. b_A += tl.dot(b_qg, b_kg) if HEAD_FIRST: p_A = tl.make_block_ptr(A + i_bh*T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) else: p_A = tl.make_block_ptr(A + (bos*H + i_h)*BT, (T, BT), (H*BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) tl.store(p_A, b_A.to(A.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BK", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_fwd_A_kernel_intra_sub_intra( q, k, g, A, offsets, indices, scale, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_t, i_i, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H i_j = i_i if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos else: bos, eos = i_b * T, i_b * T + T if i_t * BT + i_i * BC >= T: return o_i = tl.arange(0, BC) o_k = tl.arange(0, BK) m_k = o_k < K m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T if HEAD_FIRST: o_A = i_bh * T*BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_j * BC p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_k = tl.max_contiguous(tl.multiple_of(k + (i_bh * T + i_t * BT + i_j * BC) * K + o_k, BK), BK) p_gk = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_j * BC) * K + o_k, BK), BK) else: o_A = (bos + i_t * BT + i_i * BC + tl.arange(0, BC)) * H*BT + i_h * BT + i_j * BC p_q = tl.make_block_ptr(q + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, 0), (BC, BK), (1, 0)) p_k = tl.max_contiguous(tl.multiple_of(k + (bos + i_t * BT + i_j * BC) * H*K + i_h * K + o_k, BK), BK) p_gk = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_j * BC) * H*K + i_h * K + o_k, BK), BK) b_q = tl.load(p_q, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) for j in range(0, min(BC, T - i_t * BT - i_i * BC)): b_k = tl.load(p_k, mask=m_k, other=0).to(tl.float32) b_gk = tl.load(p_gk, mask=m_k, other=0).to(tl.float32) b_A = tl.sum(b_q * b_k[None, :] * tl.exp(b_g - b_gk[None, :]), 1) b_A = tl.where(o_i >= j, b_A * scale, 0.) tl.store(A + o_A + j, b_A, mask=m_A) p_k += K if HEAD_FIRST else H*K p_gk += K if HEAD_FIRST else H*K @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BC", "BK"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_fwd_A_kernel_intra_sub_intra_split( q, k, g, A, offsets, indices, scale, B: tl.constexpr, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_k, i_tc, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_b, i_h = i_bh // H, i_bh % H i_t, i_i = i_tc // NC, i_tc % NC i_j = i_i if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) all = T T = eos - bos else: bos, eos = i_b * T, i_b * T + T all = B * T if i_t * BT + i_i * BC >= T: return o_i = tl.arange(0, BC) o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T if HEAD_FIRST: o_A = (i_k * B*H + i_bh) * T * BC + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BC p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.max_contiguous(tl.multiple_of(k + (i_bh * T + i_t * BT + i_j * BC) * K + o_k, BK), BK) p_gk = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_j * BC) * K + o_k, BK), BK) else: o_A = (i_k * all + bos + i_t * BT + i_i * BC + tl.arange(0, BC)) * H*BC + i_h * BC p_q = tl.make_block_ptr(q + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.max_contiguous(tl.multiple_of(k + (bos + i_t * BT + i_j * BC) * H*K + i_h * K + o_k, BK), BK) p_gk = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_j * BC) * H*K + i_h * K + o_k, BK), BK) b_q = tl.load(p_q, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) for j in range(0, min(BC, T - i_t * BT - i_i * BC)): b_A = tl.zeros([BC], dtype=tl.float32) b_k = tl.load(p_k, mask=m_k, other=0).to(tl.float32) b_gk = tl.load(p_gk, mask=m_k, other=0).to(tl.float32) b_A += tl.sum(b_q * b_k[None, :] * tl.exp(b_g - b_gk[None, :]), 1) b_A = tl.where(o_i >= j, b_A * scale, 0.) tl.store(A + o_A + j, b_A, mask=m_A) p_k += K if HEAD_FIRST else H*K p_gk += K if HEAD_FIRST else H*K @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BC"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_fwd_A_kernel_intra_sub_intra_merge( A, A2, offsets, indices, B: tl.constexpr, T: tl.constexpr, H: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, NK: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_t, 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 if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) all = T T = eos - bos else: bos, eos = i_b * T, i_b * T + T all = B * T if i_t * BT + i_c * BC >= T: return b_A = tl.zeros([BC, BC], dtype=tl.float32) for i_k in range(0, NK): if HEAD_FIRST: p_A = tl.make_block_ptr(A + (i_k*B*H+i_bh)*T*BC, (T, BC), (BC, 1), (i_t*BT + i_c*BC, 0), (BC, BC), (1, 0)) else: p_A = tl.make_block_ptr(A + (i_k*all+bos)*H*BC+i_h*BC, (T, BC), (H*BC, 1), (i_t*BT + i_c*BC, 0), (BC, BC), (1, 0)) b_A += tl.load(p_A, boundary_check=(0, 1)) if HEAD_FIRST: p_A2 = tl.make_block_ptr(A2 + i_bh*T*BT, (T, BT), (BT, 1), (i_t * BT + i_c * BC, i_c * BC), (BC, BC), (1, 0)) else: p_A2 = tl.make_block_ptr(A2 + (bos*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t * BT + i_c * BC, i_c * BC), (BC, BC), (1, 0)) tl.store(p_A2, b_A.to(A2.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BK", "BV", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_fwd_kernel_o( q, v, g, h, o, A, offsets, indices, scale, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_v, i_t, 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 USE_OFFSETS: i_tg = i_t i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos NT = tl.cdiv(T, BT) else: NT = tl.cdiv(T, BT) i_tg = i_b * NT + i_t bos, eos = i_b * T, i_b * T + T m_s = tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :] b_o = tl.zeros([BT, BV], dtype=tl.float32) for i_k in range(tl.cdiv(K, BK)): if HEAD_FIRST: p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_h = tl.make_block_ptr(h + (i_bh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) else: p_q = tl.make_block_ptr(q + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) # [BT, BK] b_q = tl.load(p_q, boundary_check=(0, 1)) b_q = (b_q * scale).to(b_q.dtype) # [BT, BK] b_g = tl.load(p_g, boundary_check=(0, 1)) # [BT, BK] b_qg = (b_q * tl.exp(b_g)).to(b_q.dtype) # [BK, BV] b_h = tl.load(p_h, boundary_check=(0, 1)) # works but dkw, owing to divine benevolence # [BT, BV] if i_k >= 0: b_o += tl.dot(b_qg, b_h.to(b_qg.dtype)) if HEAD_FIRST: p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_o = tl.make_block_ptr(o + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_A = tl.make_block_ptr(A + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) else: p_v = tl.make_block_ptr(v + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_o = tl.make_block_ptr(o + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_A = tl.make_block_ptr(A + (bos * H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) # [BT, BV] b_v = tl.load(p_v, boundary_check=(0, 1)) # [BT, BT] b_A = tl.load(p_A, boundary_check=(0, 1)) b_A = tl.where(m_s, b_A, 0.).to(b_v.dtype) b_o += tl.dot(b_A, b_v, allow_tf32=False) tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BK", "NC", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_bwd_kernel_intra( q, k, g, dA, dq, dk, offsets, indices, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_k, 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 i_t, i_i = i_c // NC, i_c % NC if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) else: bos, eos = i_b * T, i_b * T + T T = eos - bos if i_t * BT + i_i * BC >= T: return o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K if HEAD_FIRST: p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) else: p_g = tl.make_block_ptr(g + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) # [BC, BK] b_g = tl.load(p_g, boundary_check=(0, 1)) b_dq = tl.zeros([BC, BK], dtype=tl.float32) if i_i > 0: if HEAD_FIRST: p_gn = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) else: p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC) * H*K + i_h*K + o_k, BK), BK) # [BK,] b_gn = tl.load(p_gn, mask=m_k, other=0) for i_j in range(0, i_i): if HEAD_FIRST: p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_dA = tl.make_block_ptr(dA + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) else: p_k = tl.make_block_ptr(k+(bos*H+i_h)*K, (T, K), (H*K, 1), (i_t*BT+i_j*BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g+(bos*H+i_h)*K, (T, K), (H*K, 1), (i_t*BT+i_j*BC, i_k * BK), (BC, BK), (1, 0)) p_dA = tl.make_block_ptr(dA+(bos*H+i_h)*BT, (T, BT), (H*BT, 1), (i_t*BT+i_i*BC, i_j * BC), (BC, BC), (1, 0)) # [BC, BK] b_k = tl.load(p_k, boundary_check=(0, 1)) b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_kg = (b_k * tl.exp(b_gn[None, :] - b_gk)) # [BC, BC] b_dA = tl.load(p_dA, boundary_check=(0, 1)) # [BC, BK] b_dq += tl.dot(b_dA, b_kg) b_dq *= tl.exp(b_g - b_gn[None, :]) o_i = tl.arange(0, BC) m_dA = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T if HEAD_FIRST: o_dA = i_bh * T*BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_i * BC p_kj = tl.max_contiguous(tl.multiple_of(k + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) p_gkj = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) p_dq = tl.make_block_ptr(dq + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) else: o_dA = bos*H*BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * H*BT + i_h * BT + i_i * BC p_kj = tl.max_contiguous(tl.multiple_of(k + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k, BK), BK) p_gkj = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k, BK), BK) p_dq = tl.make_block_ptr(dq + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) for j in range(0, min(BC, T - i_t * BT - i_i * BC)): # [BC,] b_dA = tl.load(dA + o_dA + j, mask=m_dA, other=0) # [BK,] b_kj = tl.load(p_kj, mask=m_k, other=0).to(tl.float32) b_gkj = tl.load(p_gkj, mask=m_k, other=0).to(tl.float32) # [BC, BK] m_i = o_i[:, None] >= j # [BC, BK] # (SY 09/17) important to not use bf16 here to have a good precision. b_dq += tl.where(m_i, b_dA[:, None] * b_kj[None, :] * tl.exp(b_g - b_gkj[None, :]), 0.) p_kj += K if HEAD_FIRST else H*K p_gkj += K if HEAD_FIRST else H*K tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) tl.debug_barrier() if HEAD_FIRST: p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) else: p_k = tl.make_block_ptr(k + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g + (bos*H + i_h) * K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) # [BC, BK] b_k = tl.load(p_k, boundary_check=(0, 1)) b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_dk = tl.zeros([BC, BK], dtype=tl.float32) NC = min(NC, tl.cdiv(T - i_t * BT, BC)) if i_i < NC - 1: if HEAD_FIRST: p_gn = tl.max_contiguous(tl.multiple_of(g + i_bh*T*K + (i_t * BT + i_i * BC + BC - 1)*K + o_k, BK), BK) else: p_gn = tl.max_contiguous(tl.multiple_of(g + bos*H*K + (i_t * BT + i_i * BC + BC - 1)*H*K + i_h*K + o_k, BK), BK) # [BK,] b_gn = tl.load(p_gn, mask=m_k, other=0) for i_j in range(i_i + 1, NC): if HEAD_FIRST: p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (BT, T), (1, BT), (i_i*BC, i_t*BT + i_j*BC), (BC, BC), (0, 1)) else: p_q = tl.make_block_ptr(q + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_dA = tl.make_block_ptr(dA + (bos*H+i_h)*BT, (BT, T), (1, H*BT), (i_i*BC, i_t*BT + i_j*BC), (BC, BC), (0, 1)) # [BC, BK] b_q = tl.load(p_q, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) b_qg = (b_q * tl.exp(b_g - b_gn[None, :])) # [BC, BC] b_dA = tl.load(p_dA, boundary_check=(0, 1)) # [BC, BK] # (SY 09/17) important to not use bf16 here to have a good precision. b_dk += tl.dot(b_dA, b_qg) b_dk *= tl.exp(b_gn[None, :] - b_gk) if HEAD_FIRST: o_dA = i_bh * T * BT + (i_t * BT + i_i * BC) * BT + i_i * BC + tl.arange(0, BC) p_qj = tl.max_contiguous(tl.multiple_of(q + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) p_gqj = tl.max_contiguous(tl.multiple_of(g + (i_bh * T + i_t * BT + i_i * BC) * K + o_k, BK), BK) p_dk = tl.make_block_ptr(dk + i_bh*T*K, (T, K), (K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) else: o_dA = bos*H*BT + (i_t * BT + i_i * BC) * H*BT + i_h * BT + i_i * BC + tl.arange(0, BC) p_qj = tl.max_contiguous(tl.multiple_of(q + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k, BK), BK) p_gqj = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC) * H*K + i_h * K + o_k, BK), BK) p_dk = tl.make_block_ptr(dk + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) for j in range(0, min(BC, T - i_t * BT - i_i * BC)): # [BC,] b_dA = tl.load(dA + o_dA + j * (1 if HEAD_FIRST else H) * BT) # [BK,] b_qj = tl.load(p_qj, mask=m_k, other=0).to(tl.float32) b_gqj = tl.load(p_gqj, mask=m_k, other=0).to(tl.float32) # [BC, BK] m_i = o_i[:, None] <= j b_dk += tl.where(m_i, b_dA[:, None] * b_qj[None, :] * tl.exp(b_gqj[None, :] - b_gk), 0.) p_qj += K if HEAD_FIRST else H*K p_gqj += K if HEAD_FIRST else H*K tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BV", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_bwd_kernel_dA( v, do, dA, offsets, indices, scale, T: tl.constexpr, H: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_t, i_bh = tl.program_id(0), tl.program_id(1) i_b, i_h = i_bh // H, i_bh % H if USE_OFFSETS: i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) else: bos, eos = i_b * T, i_b * T + T T = eos - bos b_dA = tl.zeros([BT, BT], dtype=tl.float32) for i_v in range(tl.cdiv(V, BV)): if HEAD_FIRST: p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_v = tl.make_block_ptr(v + i_bh * T*V, (V, T), (1, V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) else: p_do = tl.make_block_ptr(do + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t * BT), (BV, BT), (0, 1)) b_v = tl.load(p_v, boundary_check=(0, 1)) b_do = tl.load(p_do, boundary_check=(0, 1)) b_dA += tl.dot(b_do, b_v) if HEAD_FIRST: p_dA = tl.make_block_ptr(dA + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) else: p_dA = tl.make_block_ptr(dA + (bos * H + i_h) * BT, (T, BT), (H*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) m_s = tl.arange(0, BT)[:, None] >= tl.arange(0, BT)[None, :] b_dA = tl.where(m_s, b_dA * scale, 0.) tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BK", "BV", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_bwd_kernel_dv( k, g, A, do, dh, dv, offsets, indices, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_v, i_t, 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 USE_OFFSETS: i_tg = i_t i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos NT = tl.cdiv(T, BT) else: NT = tl.cdiv(T, BT) i_tg = i_b * NT + i_t bos, eos = i_b * T, i_b * T + T if HEAD_FIRST: p_A = tl.make_block_ptr(A + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1)) p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_dv = tl.make_block_ptr(dv + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) else: p_A = tl.make_block_ptr(A + (bos * H + i_h) * BT, (BT, T), (1, H*BT), (0, i_t * BT), (BT, BT), (0, 1)) p_do = tl.make_block_ptr(do + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_dv = tl.make_block_ptr(dv + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) b_A = tl.load(p_A, boundary_check=(0, 1)) b_A = tl.where(tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :], b_A, 0.) b_do = tl.load(p_do, boundary_check=(0, 1)) # (SY 09/17) important to disallow tf32 here to maintain a good precision. b_dv = tl.dot(b_A, b_do.to(b_A.dtype), allow_tf32=False) for i_k in range(tl.cdiv(K, BK)): o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K if HEAD_FIRST: p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gn = tl.max_contiguous(tl.multiple_of(g + i_bh * T*K + min(i_t * BT + BT, T) * K - K + o_k, BK), BK) p_dh = tl.make_block_ptr(dh + (i_bh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) else: p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gk = tl.make_block_ptr(g + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + min(i_t * BT + BT, T) - 1)*H*K + i_h * K + o_k, BK), BK) p_dh = tl.make_block_ptr(dh + (i_tg * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) b_k = tl.load(p_k, boundary_check=(0, 1)) b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_gn = tl.exp(tl.load(p_gn, mask=m_k, other=0)[None, :] - b_gk) b_k = (b_k * b_gn).to(b_k.dtype) b_dh = tl.load(p_dh, boundary_check=(0, 1)) # [BT, BV] # (SY 09/17) it is ok to have bf16 interchunk gradient contribution here b_dv += tl.dot(b_k, b_dh.to(b_k.dtype)) tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) @triton.autotune( configs=[ triton.Config({}, num_warps=1), triton.Config({}, num_warps=2), triton.Config({}, num_warps=4), triton.Config({}, num_warps=8), ], key=["BK", "BV", "BT"], ) @triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) @triton.jit def chunk_gla_bwd_kernel_inter( q, k, v, h, g, do, dh, dq, dk, dq2, dk2, dg, offsets, indices, scale, T: tl.constexpr, H: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, USE_OFFSETS: tl.constexpr, HEAD_FIRST: tl.constexpr ): i_k, i_t, 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 USE_OFFSETS: i_tg = i_t i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) T = eos - bos NT = tl.cdiv(T, BT) else: NT = tl.cdiv(T, BT) i_tg = i_b * NT + i_t bos, eos = i_b * T, i_b * T + T o_k = i_k * BK + tl.arange(0, BK) m_k = o_k < K if HEAD_FIRST: p_gk = tl.make_block_ptr(g + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gn = tl.max_contiguous(tl.multiple_of(g + i_bh * T*K + (min(T, i_t * BT + BT)-1) * K + o_k, BK), BK) else: p_gk = tl.make_block_ptr(g + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + min(T, i_t * BT + BT)-1) * H*K + i_h * K + o_k, BK), BK) b_gn = tl.load(p_gn, mask=m_k, other=0) b_dq = tl.zeros([BT, BK], dtype=tl.float32) b_dk = tl.zeros([BT, BK], dtype=tl.float32) b_dgk = tl.zeros([BK,], dtype=tl.float32) for i_v in range(tl.cdiv(V, BV)): if HEAD_FIRST: p_v = tl.make_block_ptr(v + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_h = tl.make_block_ptr(h + i_bh * NT*K*V + i_t * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) p_dh = tl.make_block_ptr(dh + i_bh * NT*K*V + i_t * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) else: p_v = tl.make_block_ptr(v + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_do = tl.make_block_ptr(do + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_h = tl.make_block_ptr(h + (i_tg * H + i_h) * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) p_dh = tl.make_block_ptr(dh + (i_tg * H + i_h) * K*V, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) # [BT, BV] b_v = tl.load(p_v, boundary_check=(0, 1)) b_do = tl.load(p_do, boundary_check=(0, 1)) # [BV, BK] b_h = tl.load(p_h, boundary_check=(0, 1)) b_dh = tl.load(p_dh, boundary_check=(0, 1)) # [BK] b_dgk += tl.sum(b_h * b_dh, axis=0) # [BT, BK] b_dq += tl.dot(b_do, b_h.to(b_do.dtype)) b_dk += tl.dot(b_v, b_dh.to(b_v.dtype)) b_dgk *= tl.exp(b_gn) b_dq *= scale b_gk = tl.load(p_gk, boundary_check=(0, 1)) b_dq = b_dq * tl.exp(b_gk) b_dk = b_dk * tl.exp(b_gn[None, :] - b_gk) if HEAD_FIRST: p_q = tl.make_block_ptr(q + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_k = tl.make_block_ptr(k + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dq = tl.make_block_ptr(dq + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) else: p_q = tl.make_block_ptr(q + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_k = tl.make_block_ptr(k + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dq = tl.make_block_ptr(dq + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk + (bos*H+i_h)*K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) b_q = tl.load(p_q, boundary_check=(0, 1)) b_k = tl.load(p_k, boundary_check=(0, 1)) b_dgk += tl.sum(b_dk * b_k, axis=0) b_dq += tl.load(p_dq, boundary_check=(0, 1)) b_dk += tl.load(p_dk, boundary_check=(0, 1)) b_dg = b_q * b_dq - b_k * b_dk # tl.debug_barrier() b_dg = b_dg - tl.cumsum(b_dg, axis=0) + tl.sum(b_dg, axis=0)[None, :] + b_dgk[None, :] # Buggy due to strange triton compiler issue. # m_s = tl.where(tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :], 1., 0.) # b_dg = tl.dot(m_s, b_dg, allow_tf32=False) + b_dgk[None, :] if HEAD_FIRST: p_dq = tl.make_block_ptr(dq2 + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk2 + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dg = tl.make_block_ptr(dg + i_bh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) else: p_dq = tl.make_block_ptr(dq2 + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk2 + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dg = tl.make_block_ptr(dg + (bos * H + i_h) * K, (T, K), (H*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) tl.store(p_dg, b_dg.to(p_dg.dtype.element_ty), boundary_check=(0, 1)) def chunk_gla_fwd_intra_gk( q: torch.Tensor, k: torch.Tensor, g: torch.Tensor, scale: float, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, K = k.shape else: B, T, H, K = k.shape BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BC = min(16, triton.next_power_of_2(T)) BK = min(64, triton.next_power_of_2(K)) NC = triton.cdiv(BT, BC) A = q.new_empty(B, *((H, T) if head_first else (T, H)), BT, dtype=torch.float32) grid = (NT, NC * NC, B * H) chunk_gla_fwd_A_kernel_intra_sub_inter[grid]( q, k, g, A, offsets, indices, scale, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, NC=NC, HEAD_FIRST=head_first ) grid = (NT, NC, B * H) # load the entire [BC, K] blocks into SRAM at once if K <= 256: BK = triton.next_power_of_2(K) chunk_gla_fwd_A_kernel_intra_sub_intra[grid]( q, k, g, A, offsets, indices, scale, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, HEAD_FIRST=head_first ) # split then merge else: BK = min(128, triton.next_power_of_2(K)) NK = triton.cdiv(K, BK) A_intra = q.new_empty(NK, B, *((H, T) if head_first else (T, H)), BC, dtype=torch.float32) grid = (NK, NT * NC, B * H) chunk_gla_fwd_A_kernel_intra_sub_intra_split[grid]( q, k, g, A_intra, offsets, indices, scale, B=B, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, NC=NC, HEAD_FIRST=head_first ) grid = (NT, NC, B * H) chunk_gla_fwd_A_kernel_intra_sub_intra_merge[grid]( A_intra, A, offsets, indices, B=B, T=T, H=H, BT=BT, BC=BC, NK=NK, HEAD_FIRST=head_first ) return A def chunk_gla_fwd_o_gk( q: torch.Tensor, v: torch.Tensor, g: torch.Tensor, A: torch.Tensor, h: torch.Tensor, scale: float, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, K, V = *q.shape, v.shape[-1] else: B, T, H, K, V = *q.shape, v.shape[-1] BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BK = min(32, triton.next_power_of_2(K)) BV = min(32, triton.next_power_of_2(V)) NV = triton.cdiv(V, BV) grid = (NV, NT, B * H) o = torch.empty_like(v) chunk_gla_fwd_kernel_o[grid]( q, v, g, h, o, A, offsets, indices, scale, T=T, H=H, K=K, V=V, BT=BT, BK=BK, BV=BV, HEAD_FIRST=head_first ) return o def chunk_gla_bwd_dA( v: torch.Tensor, do: torch.Tensor, scale: float, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, V = v.shape else: B, T, H, V = v.shape BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BV = min(64, triton.next_power_of_2(V)) dA = v.new_empty(B, *((H, T) if head_first else (T, H)), BT, dtype=torch.float32) grid = (NT, B * H) chunk_gla_bwd_kernel_dA[grid]( v, do, dA, offsets, indices, scale, T=T, H=H, V=V, BT=BT, BV=BV, HEAD_FIRST=head_first ) return dA def chunk_gla_bwd_dv( k: torch.Tensor, g: torch.Tensor, A: torch.Tensor, do: torch.Tensor, dh: torch.Tensor, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, K, V = *k.shape, do.shape[-1] else: B, T, H, K, V = *k.shape, do.shape[-1] BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BK = min(64, triton.next_power_of_2(K)) BV = min(32, triton.next_power_of_2(V)) dv = torch.empty_like(do) grid = (triton.cdiv(V, BV), NT, B * H) chunk_gla_bwd_kernel_dv[grid]( k, g, A, do, dh, dv, offsets, indices, T=T, H=H, K=K, V=V, BT=BT, BK=BK, BV=BV, HEAD_FIRST=head_first ) return dv def chunk_gla_bwd_dqk_intra( q: torch.Tensor, k: torch.Tensor, g: torch.Tensor, dA: torch.Tensor, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, K = q.shape else: B, T, H, K = q.shape BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], BT).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BC = min(16, triton.next_power_of_2(T)) BK = min(64, triton.next_power_of_2(K)) NK = triton.cdiv(K, BK) NC = triton.cdiv(BT, BC) dq = torch.empty_like(q, dtype=torch.float32) dk = torch.empty_like(k, dtype=torch.float32) grid = (NK, NT * NC, B * H) chunk_gla_bwd_kernel_intra[grid]( q, k, g, dA, dq, dk, offsets, indices, T=T, H=H, K=K, BT=BT, BC=BC, BK=BK, NC=NC, HEAD_FIRST=head_first ) return dq, dk def chunk_gla_bwd_dqkg( q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, h: torch.Tensor, g: torch.Tensor, do: torch.Tensor, dh: torch.Tensor, dq: torch.Tensor, dk: torch.Tensor, scale: float, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): if head_first: B, H, T, K, V = *k.shape, v.shape[-1] else: B, T, H, K, V = *k.shape, v.shape[-1] BT = min(chunk_size, triton.next_power_of_2(T)) if offsets is None: NT = triton.cdiv(T, BT) else: if indices is None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], chunk_size).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) NT = len(indices) BK = min(64, triton.next_power_of_2(K)) BV = min(64, triton.next_power_of_2(V)) NK = triton.cdiv(K, BK) dg = torch.empty_like(g) grid = (NK, NT, B * H) # work around triton compiler bugs. dq2 = torch.empty_like(dq) dk2 = torch.empty_like(dk) chunk_gla_bwd_kernel_inter[grid]( q, k, v, h, g, do, dh, dq, dk, dq2, dk2, dg, offsets, indices, scale, T=T, H=H, K=K, V=V, BT=BT, BK=BK, BV=BV, HEAD_FIRST=head_first ) return dq2, dk2, dg def chunk_gla_fwd( q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, g: torch.Tensor, g_cumsum: Optional[torch.Tensor], scale: float, initial_state: torch.Tensor, output_final_state: bool, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]: T = q.shape[2] if head_first else q.shape[1] BT = min(chunk_size, triton.next_power_of_2(T)) if g_cumsum is None: g_cumsum = chunk_local_cumsum(g, BT, offsets=offsets, head_first=head_first) h, ht = chunk_fwd_h( k=k, v=v, g=None, gk=g_cumsum, gv=None, h0=initial_state, output_final_state=output_final_state, states_in_fp32=False, offsets=offsets, head_first=head_first, chunk_size=BT ) # the intra A is kept in fp32 # the computation has very marginal effect on the entire throughput A = chunk_gla_fwd_intra_gk( q=q, k=k, g=g_cumsum, scale=scale, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) o = chunk_gla_fwd_o_gk( q=q, v=v, g=g_cumsum, A=A, h=h, scale=scale, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) return g_cumsum, A, h, ht, o def chunk_gla_bwd( q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, g: torch.Tensor, g_cumsum: Optional[torch.Tensor], scale: float, initial_state: torch.Tensor, h: torch.Tensor, A: torch.Tensor, do: torch.Tensor, dht: torch.Tensor, offsets: Optional[torch.LongTensor] = None, indices: Optional[torch.LongTensor] = None, head_first: bool = True, chunk_size: int = 64 ): T = q.shape[2] if head_first else q.shape[1] BT = min(chunk_size, triton.next_power_of_2(T)) if g_cumsum is None: g_cumsum = chunk_local_cumsum(g, BT, offsets=offsets, head_first=head_first) if h is None: h, _ = chunk_fwd_h( k=k, v=v, g=None, gk=g_cumsum, gv=None, h0=initial_state, output_final_state=False, states_in_fp32=True, offsets=offsets, head_first=head_first, chunk_size=BT ) dh, dh0 = chunk_bwd_dh( q=q, k=k, v=v, g=None, gk=g_cumsum, gv=None, do=do, h0=initial_state, dht=dht, scale=scale, states_in_fp32=True, offsets=offsets, head_first=head_first, chunk_size=BT ) dv = chunk_gla_bwd_dv( k=k, g=g_cumsum, A=A, do=do, dh=dh, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) # dq dk in fp32 dA = chunk_gla_bwd_dA( v=v, do=do, scale=scale, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) dq, dk = chunk_gla_bwd_dqk_intra( q=q, k=k, g=g_cumsum, dA=dA, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) dq, dk, dg = chunk_gla_bwd_dqkg( q=q, k=k, v=v, h=h, g=g_cumsum, do=do, dh=dh, dq=dq, dk=dk, scale=scale, offsets=offsets, indices=indices, head_first=head_first, chunk_size=BT ) return dq, dk, dv, dg, dh0 class ChunkGLAFunction(torch.autograd.Function): @staticmethod @contiguous def forward( ctx, q, k, v, g, scale, initial_state, output_final_state, offsets, head_first ): T = q.shape[2] if head_first else q.shape[1] chunk_size = min(64, triton.next_power_of_2(T)) # 2-d indices denoting the offsets of chunks in each sequence # for example, if the passed `offsets` is [0, 100, 356] and `chunk_size` is 64, # then there are 2 and 4 chunks in the 1st and 2nd sequences respectively, and `indices` will be # [[0, 0], [0, 1], [1, 0], [1, 1], [1, 2], [1, 3]] indices = None if offsets is not None: indices = torch.cat([torch.arange(n) for n in triton.cdiv(offsets[1:] - offsets[:-1], chunk_size).tolist()]) indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) g_cumsum, A, h, ht, o = chunk_gla_fwd( q=q, k=k, v=v, g=g, g_cumsum=None, scale=scale, initial_state=initial_state, output_final_state=output_final_state, offsets=offsets, indices=indices, head_first=head_first, chunk_size=chunk_size ) # recompute g_cumsum in bwd pass if g.dtype != torch.float32: g_cumsum = None else: g = None ctx.save_for_backward(q, k, v, g, g_cumsum, initial_state, A) ctx.chunk_size = chunk_size ctx.scale = scale ctx.offsets = offsets ctx.indices = indices ctx.head_first = head_first return o, ht @staticmethod @contiguous def backward(ctx, do, dht): q, k, v, g, g_cumsum, initial_state, A = ctx.saved_tensors chunk_size, scale, offsets, indices, head_first = ctx.chunk_size, ctx.scale, ctx.offsets, ctx.indices, ctx.head_first dq, dk, dv, dg, dh0 = chunk_gla_bwd( q=q, k=k, v=v, g=g, g_cumsum=g_cumsum, scale=scale, h=None, A=A, initial_state=initial_state, do=do, dht=dht, offsets=offsets, indices=indices, head_first=head_first, chunk_size=chunk_size ) return dq.to(q), dk.to(k), dv.to(v), dg, None, dh0, None, None, None def chunk_gla( q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, g: torch.Tensor, scale: Optional[int] = None, initial_state: torch.Tensor = None, output_final_state: bool = False, offsets: Optional[torch.LongTensor] = None, head_first: bool = True ) -> Tuple[torch.Tensor, torch.Tensor]: r""" Args: q (torch.Tensor): queries of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]`. k (torch.Tensor): keys of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]`. v (torch.Tensor): values of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]`. g (torch.Tensor): Forget gates of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]` applied to keys. scale (Optional[int]): Scale factor for the attention scores. If not provided, it will default to `1 / sqrt(K)`. Default: `None`. initial_state (Optional[torch.Tensor]): Initial state of shape `[N, H, K, V]` for `N` input sequences. For equal-length input sequences, `N` equals the batch size `B`. Default: `None`. output_final_state (Optional[bool]): Whether to output the final state of shape `[N, H, K, V]`. Default: `False`. offsets (Optional[torch.LongTensor]): Offsets of shape `[N+1]` defining the bos/eos positions of `N` variable-length sequences in the batch. For example, if `offsets` is `[0, 1, 3, 6, 10, 15]`, there are `N=5` sequences with lengths 1, 2, 3, 4 and 5 respectively. If provided, the inputs are concatenated and the batch size `B` is expected to be 1. Default: `None`. head_first (Optional[bool]): Whether the inputs are in the head-first format, which is not supported for variable-length inputs. Default: `True`. Returns: o (torch.Tensor): Outputs of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]`. final_state (torch.Tensor): Final state of shape `[N, H, K, V]` if `output_final_state=True` else `None`. Examples:: >>> import torch >>> import torch.nn.functional as F >>> from einops import rearrange >>> from fla.ops.gla import chunk_gla # inputs with equal lengths >>> B, T, H, K, V = 4, 2048, 4, 512, 512 >>> q = torch.randn(B, T, H, K, device='cuda') >>> k = torch.randn(B, T, H, K, device='cuda') >>> v = torch.randn(B, T, H, V, device='cuda') >>> g = F.logsigmoid(torch.randn(B, T, H, K, device='cuda')) >>> h0 = torch.randn(B, H, K, V, device='cuda') >>> o, ht = chunk_gla(q, k, v, g, initial_state=h0, output_final_state=True, head_first=False) # for variable-length inputs, the batch size `B` is expected to be 1 and `offsets` is required >>> q, k, v, g = map(lambda x: rearrange(x, 'b t h d -> 1 (b t) h d'), (q, k, v, g)) # for a batch with 4 sequences, offsets with 5 start/end positions are expected >>> offsets = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long) >>> o_var, ht_var = chunk_gla(q, k, v, g, initial_state=h0, output_final_state=True, offsets=offsets, head_first=False) >>> assert o.allclose(o_var.view(o.shape)) >>> assert ht.allclose(ht_var) """ if offsets is not None: if q.shape[0] != 1: raise ValueError(f"The batch size is expected to be 1 rather than {q.shape[0]} when using `offsets`." f"Please flatten variable-length inputs before processing.") if head_first: raise RuntimeError("Sequences with variable lengths are not supported for head-first mode") if initial_state is not None and initial_state.shape[0] != len(offsets) - 1: raise ValueError(f"The number of initial states is expected to be equal to the number of input sequences, " f"i.e., {len(offsets) - 1} rather than {initial_state.shape[0]}.") if scale is None: scale = q.shape[-1] ** -0.5 o, final_state = ChunkGLAFunction.apply(q, k, v, g, scale, initial_state, output_final_state, offsets, head_first) return o, final_state