# -*- coding: utf-8 -*- # Copyright (c) 2023-2024, Yu Zhang, Songlin Yang from typing import Optional, Tuple import torch import triton import triton.language as tl from fla.ops.utils import chunk_reversed_cumsum_fwd from fla.utils import contiguous @triton.autotune( configs=[ triton.Config({'BS': 16}, num_warps=2), triton.Config({'BS': 16}, num_warps=4), triton.Config({'BS': 16}, num_warps=8), triton.Config({'BS': 32}, num_warps=2), triton.Config({'BS': 32}, num_warps=4), triton.Config({'BS': 32}, num_warps=8), triton.Config({'BS': 64}, num_warps=2), triton.Config({'BS': 64}, num_warps=4), triton.Config({'BS': 64}, num_warps=8), ], key=['S'] ) @triton.jit def chunk_gla_fwd_kernel_cum( s, o, s_s_h, s_s_t, s_s_d, T: tl.constexpr, S: tl.constexpr, BT: tl.constexpr, BS: tl.constexpr ): i_s, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) o_i = tl.arange(0, BT) m_s = tl.where(o_i[:, None] >= o_i[None, :], 1., 0.) p_s = tl.make_block_ptr(s + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_s * BS), (BT, BS), (1, 0)) p_o = tl.make_block_ptr(o + i_bh * s_s_h, (T, S), (s_s_t, s_s_d), (i_t * BT, i_s * BS), (BT, BS), (1, 0)) # [BT, BS] b_s = tl.load(p_s, boundary_check=(0, 1)).to(tl.float32) b_o = tl.dot(m_s, b_s, allow_tf32=False) tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) @triton.jit def chunk_gla_fwd_kernel_h( k, v, g, h, h0, ht, s_k_h, s_k_t, s_k_d, s_v_h, s_v_t, s_v_d, s_h_h, s_h_t, s_h_d, T: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, NT: tl.constexpr, USE_INITIAL_STATE: tl.constexpr, STORE_FINAL_STATE: tl.constexpr ): i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) b_h = tl.zeros([BK, BV], dtype=tl.float32) if USE_INITIAL_STATE: p_h = tl.make_block_ptr(h0 + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) b_h += tl.load(p_h, boundary_check=(0, 1)).to(tl.float32) for i_t in range(NT): p_k = tl.make_block_ptr(k + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + BT - 1) * K + i_k * BK,), (BK,), (0,)) tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1)) # [BK, BT] b_k = tl.load(p_k, boundary_check=(0, 1)) # [BT, BV] b_v = tl.load(p_v, boundary_check=(0, 1)) # [BK, BT] b_g = tl.load(p_g, boundary_check=(0, 1)) if i_t < NT - 1: # [BK,] b_gn = tl.load(p_gn, boundary_check=(0,)) else: b_gn = tl.min(b_g, axis=1) b_h *= tl.exp(b_gn)[:, None] b_k = (b_k * tl.exp(b_gn[:, None] - b_g)).to(b_k.dtype) b_h += tl.dot(b_k, b_v, allow_tf32=False) if STORE_FINAL_STATE: p_h = tl.make_block_ptr(ht + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1)) @triton.jit def chunk_gla_fwd_kernel_intra( q, k, g, A, s_k_h, s_k_t, s_k_d, scale, T: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr ): i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_t, i_i, i_j = i_c // (NC * NC), (i_c % (NC * NC)) // NC, (i_c % (NC * NC)) % NC n_bh = tl.num_programs(2) if i_i > i_j: p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gk = tl.make_block_ptr(g + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT + i_j * BC), (BK, BC), (0, 1)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_i * BC) * K + i_k * BK,), (BK,), (0,)) p_A = tl.make_block_ptr(A + (i_k*n_bh+i_bh)*T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) # [BK,] b_gn = tl.load(p_gn, boundary_check=(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).to(b_q.dtype) # [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)).to(b_k.dtype) # [BC, BC] b_A = tl.dot(b_qg, b_kg, allow_tf32=False) tl.store(p_A, b_A.to(A.dtype.element_ty), boundary_check=(0, 1)) elif i_i == i_j: p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_j * BC) * K + i_k * BK,), (BK,), (0,)) p_gk = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_j * BC) * K + i_k * BK,), (BK,), (0,)) # [BC, BK] b_q = tl.load(p_q, boundary_check=(0, 1)) b_g = tl.load(p_g, boundary_check=(0, 1)) o_i = tl.arange(0, BC) o_A = (i_bh + i_k * n_bh) * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_j * BC m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T for j in range(0, BC): # [BK,] b_k = tl.load(p_k, boundary_check=(0,)).to(tl.float32) b_gk = tl.load(p_gk, boundary_check=(0,)).to(tl.float32) # [BC,] b_A = tl.sum(b_q * b_k[None, :] * tl.exp(b_g - b_gk[None, :]) * scale, 1) b_A = tl.where(o_i >= j, b_A, 0.) tl.store(A + o_A + j, b_A.to(b_q.dtype), mask=m_A) p_k = tl.advance(p_k, (K,)) p_gk = tl.advance(p_gk, (K,)) @triton.jit def chunk_gla_fwd_kernel_inter( q, v, g, h, o, A, s_k_h, s_k_t, s_k_d, s_v_h, s_v_t, s_v_d, s_h_h, s_h_t, s_h_d, scale, T: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr ): i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) b_o = tl.zeros([BT, BV], dtype=tl.float32) for i_k in range(tl.cdiv(K, BK)): p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, s_h_d), (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, allow_tf32=False) p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_o = tl.make_block_ptr(o + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (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)) # [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_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.jit def chunk_gla_bwd_kernel_dh( q, g, do, dh, s_k_h, s_k_t, s_k_d, s_v_h, s_v_t, s_v_d, s_h_h, s_h_t, s_h_d, scale, T: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr, NT: tl.constexpr ): i_k, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) b_dh = tl.zeros([BK, BV], dtype=tl.float32) for i_t in range(NT - 1, -1, -1): p_q = tl.make_block_ptr(q + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K*V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (K, T), (s_k_d, s_k_t), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + BT - 1) * K + i_k * BK,), (BK,), (0,)) # [BK, BT] b_q = tl.load(p_q, boundary_check=(0, 1)) b_q = (b_q * scale).to(b_q.dtype) # [BT, BV] b_do = tl.load(p_do, boundary_check=(0, 1)) tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1)) # [BK,] b_gn = tl.load(p_gn, boundary_check=(0,)) # [BK, BV] b_dh *= tl.exp(b_gn)[:, None] # [BK, BT] b_g = tl.load(p_g, boundary_check=(0, 1)) b_q = (b_q * tl.exp(b_g)).to(b_q.dtype) # [BK, BV] b_dh += tl.dot(b_q, b_do, allow_tf32=False) @triton.jit def chunk_gla_bwd_kernel_inter( k, v, h, g, A, do, dh, dq, dk, dv, dA, s_k_h, s_k_t, s_k_d, s_v_h, s_v_t, s_v_d, s_h_h, s_h_t, s_h_d, scale, T: tl.constexpr, K: tl.constexpr, V: tl.constexpr, BT: tl.constexpr, BK: tl.constexpr, BV: tl.constexpr ): i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) n_bh = tl.num_programs(2) p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + BT - 1) * K + i_k * BK,), (BK,), (0,)) p_A = tl.make_block_ptr(A + i_bh * T * BT, (BT, T), (1, BT), (0, i_t * BT), (BT, BT), (0, 1)) # [BT, BK] 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, boundary_check=(0,))[None, :] - b_gk) b_k = (b_k * b_gn).to(b_k.dtype) # [BT, BT] b_A = tl.load(p_A, boundary_check=(0, 1)) b_dq = tl.zeros([BT, BK], dtype=tl.float32) b_dk = tl.zeros([BT, BK], dtype=tl.float32) b_dA = tl.zeros([BT, BT], dtype=tl.float32) for i_v in range(tl.cdiv(V, BV)): p_v = tl.make_block_ptr(v + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * V * K, (V, K), (s_h_d, s_h_t), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) p_do = tl.make_block_ptr(do + i_bh * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K*V, (K, V), (s_h_t, s_h_d), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) p_dv = tl.make_block_ptr(dv + (i_k*n_bh+i_bh) * s_v_h, (T, V), (s_v_t, s_v_d), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) # [BT, BV] b_v = tl.load(p_v, boundary_check=(0, 1)) # [BV, BK] b_h = tl.load(p_h, boundary_check=(0, 1)) # [BT, BV] b_do = tl.load(p_do, boundary_check=(0, 1)) # [BK, BV] b_dh = tl.load(p_dh, boundary_check=(0, 1)) # [BT, BV] b_dv = tl.dot(b_k, b_dh, allow_tf32=False) if i_k == 0: b_dv += tl.dot(b_A, b_do, allow_tf32=False) b_do = (b_do * scale).to(b_do.dtype) tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) # [BT, BT] b_dA += tl.dot(b_do, tl.trans(b_v), allow_tf32=False) # [BT, BK] b_dq += tl.dot(b_do, b_h, allow_tf32=False) # [BT, BK] b_dk += tl.dot(b_v, tl.trans(b_dh), allow_tf32=False) b_dq = b_dq * tl.exp(b_gk) b_dk = b_dk * b_gn p_dq = tl.make_block_ptr(dq + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dk = tl.make_block_ptr(dk + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) p_dA = tl.make_block_ptr(dA + i_bh * T * BT, (T, BT, ), (BT, 1), (i_t * BT, 0), (BT, BT), (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)) o_i = tl.arange(0, BT) m_s = o_i[:, None] >= o_i[None, :] # [BT, BT] b_dA = tl.where(m_s, b_dA, 0.).to(b_k.dtype) if i_k == 0: tl.store(p_dA, b_dA.to(p_dA.dtype.element_ty), boundary_check=(0, 1)) @triton.jit def chunk_gla_bwd_kernel_intra( q, k, g, dA, dq, dk, dg, s_k_h, s_k_t, s_k_d, T: tl.constexpr, K: tl.constexpr, BT: tl.constexpr, BC: tl.constexpr, BK: tl.constexpr, NC: tl.constexpr ): i_k, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) i_t, i_i = i_c // NC, i_c % NC p_g = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (s_k_d,), ((i_t * BT + i_i * BC) * K + i_k * BK,), (BK,), (0,)) # [BK,] b_gn = tl.load(p_gn, boundary_check=(0,)) # [BC, BK] b_g = tl.load(p_g, boundary_check=(0, 1)) b_dq = tl.zeros([BC, BK], dtype=tl.float32) for i_j in range(0, i_i): p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (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)) # [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)).to(b_k.dtype) # [BC, BC] b_dA = tl.load(p_dA, boundary_check=(0, 1)) # [BC, BK] b_dq += tl.dot(b_dA, b_kg, allow_tf32=False) b_dq *= tl.exp(b_g - b_gn[None, :]) o_i = tl.arange(0, BC) o_dA = i_bh * T * BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_i * BC m_dA = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T for j in range(0, BC): p_kj = tl.make_block_ptr(k + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i*BC+j) * K + i_k * BK,), (BK,), (0,)) p_gkj = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i*BC+j) * K + i_k * BK,), (BK,), (0,)) # [BC,] b_dA = tl.load(dA + o_dA + j, mask=m_dA, other=0) # [BK,] b_kj = tl.load(p_kj, boundary_check=(0,)).to(tl.float32) b_gkj = tl.load(p_gkj, boundary_check=(0,)).to(tl.float32) # [BC, BK] m_i = o_i[:, None] >= j # [BC, BK] b_dq += tl.where(m_i, b_dA[:, None] * b_kj[None, :] * tl.exp(b_g - b_gkj[None, :]), 0.) p_dq = tl.make_block_ptr(dq + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_dq = b_dq + tl.load(p_dq, boundary_check=(0, 1)) tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) tl.debug_barrier() p_k = tl.make_block_ptr(k + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_gk = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_gn = tl.make_block_ptr(g + i_bh * s_k_h, (T*K,), (s_k_d,), ((i_t * BT + i_i * BC + BC - 1) * K + i_k * BK,), (BK,), (0,)) # [BK,] b_gn = tl.load(p_gn, boundary_check=(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) for i_j in range(i_i + 1, NC): p_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_j * BC, i_k * BK), (BC, BK), (1, 0)) p_g = tl.make_block_ptr(g + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (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_j * BC, i_i * BC), (BC, BC), (1, 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, :])).to(b_q.dtype) # [BC, BC] b_dA = tl.load(p_dA, boundary_check=(0, 1)) # [BC, BK] b_dk += tl.dot(tl.trans(b_dA), b_qg, allow_tf32=False) b_dk *= tl.exp(b_gn[None, :] - b_gk) o_dA = i_bh * T * BT + (i_t * BT + i_i * BC) * BT + i_i * BC + tl.arange(0, BC) for j in range(0, BC): p_qj = tl.make_block_ptr(q + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i * BC + j) * K + i_k * BK,), (BK,), (0,)) p_gqj = tl.make_block_ptr(g + i_bh * s_k_h, (T * K,), (1,), ((i_t * BT + i_i * BC + j) * K + i_k * BK,), (BK,), (0,)) # [BC,] b_dA = tl.load(dA + o_dA + j * BT, mask=(i_t * BT + i_i * BC + j < T), other=0) # [BK,] b_qj = tl.load(p_qj, boundary_check=(0,)).to(tl.float32) b_gqj = tl.load(p_gqj, boundary_check=(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_q = tl.make_block_ptr(q + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_dk = tl.make_block_ptr(dk + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) p_dg = tl.make_block_ptr(dg + i_bh * s_k_h, (T, K), (s_k_t, s_k_d), (i_t * BT + i_i * BC, i_k * BK), (BC, BK), (1, 0)) b_q = tl.load(p_q, boundary_check=(0, 1)) b_dk = b_dk + tl.load(p_dk, boundary_check=(0, 1)) b_dg = b_q * b_dq - b_k * b_dk 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)) class ChunkGLAFunction(torch.autograd.Function): @staticmethod @contiguous def forward(ctx, q, k, v, g, scale, initial_state, output_final_state, checkpoint_level): B, H, T, K, V = *q.shape, v.shape[-1] BT, BC = 64, 16 BK = min(64, triton.next_power_of_2(K)) BV = min(64, triton.next_power_of_2(V)) NT, NC = triton.cdiv(T, BT), triton.cdiv(BT, BC) NK = triton.cdiv(K, BK) NV = triton.cdiv(V, BV) num_warps = 4 if BK == 64 else 2 num_stages = 1 def fwd_inner(q, k, v, g, B, H, T, K, V, BT, BK, BV, NT, h0=None, ht=None): NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV) h = q.new_empty(B, H, NT * K, V) grid = (NV, NK, B * H) chunk_gla_fwd_kernel_h[grid]( k, v, g, h, h0, ht, k.stride(1), k.stride(2), k.stride(3), v.stride(1), v.stride(2), v.stride(3), h.stride(1), h.stride(2), h.stride(3), T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, USE_INITIAL_STATE=h0 is not None, STORE_FINAL_STATE=ht is not None, num_warps=num_warps, num_stages=num_stages ) return h final_state = None if output_final_state: final_state = q.new_empty(B, H, K, V, dtype=torch.float) g_org, g = g, torch.empty_like(g, dtype=torch.float) def grid(meta): return ((triton.cdiv(meta['S'], meta['BS']), NT, B * H)) # keep cummulative normalizer in fp32 # this kernel is equivalent to # g = g.view(B, H, NT, BT, -1).cumsum(-2).view(B, H, T, -1) chunk_gla_fwd_kernel_cum[grid]( g_org, g, g.stride(1), g.stride(2), g.stride(3), T=T, S=K, BT=BT ) h = fwd_inner( q=q, k=k, v=v, g=g, B=B, H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, h0=initial_state if initial_state is not None else None, ht=final_state if final_state is not None else None ) A = q.new_zeros(NK, B, H, T, BT) grid = (NK, NT * NC * NC, B * H) chunk_gla_fwd_kernel_intra[grid]( q, k, g, A, k.stride(1), k.stride(2), k.stride(3), scale, T=T, K=K, BT=BT, BC=BC, BK=BK, NC=NC, num_warps=num_warps, num_stages=num_stages ) A = A.sum(0, dtype=A.dtype) o = torch.empty_like(v) grid = (NV, NT, B * H) chunk_gla_fwd_kernel_inter[grid]( q, v, g, h, o, A, k.stride(1), k.stride(2), k.stride(3), v.stride(1), v.stride(2), v.stride(3), h.stride(1), h.stride(2), h.stride(3), scale, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, num_warps=num_warps, num_stages=num_stages ) if checkpoint_level >= 1: del g g = g_org if checkpoint_level > 1: del h h, initial_state = None, None ctx.save_for_backward(q, k, v, g, h, initial_state, A) ctx.BT = BT ctx.scale = scale ctx.checkpoint_level = checkpoint_level return o, final_state @staticmethod @contiguous def backward(ctx, do, dht=None): q, k, v, g, h, initial_state, A = ctx.saved_tensors B, H, T, K, V = *q.shape, v.shape[-1] BT, BC = ctx.BT, 16 BK = min(64, triton.next_power_of_2(K)) BV = min(64, triton.next_power_of_2(V)) NT, NC = triton.cdiv(T, BT), triton.cdiv(BT, BC) NK = triton.cdiv(K, BK) num_warps = 4 if BK == 64 else 2 num_stages = 1 def fwd_inner(q, k, v, g, B, H, T, K, V, BT, BK, BV, NT, h0=None, ht=None): NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV) h = q.new_empty(B, H, NT * K, V) grid = (NV, NK, B * H) chunk_gla_fwd_kernel_h[grid]( k, v, g, h, h0, ht, k.stride(1), k.stride(2), k.stride(3), v.stride(1), v.stride(2), v.stride(3), h.stride(1), h.stride(2), h.stride(3), T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, USE_INITIAL_STATE=h0 is not None, STORE_FINAL_STATE=ht is not None, num_warps=num_warps, num_stages=num_stages ) return h def bwd_inner(q, g, do, B, H, T, K, V, BT, BK, BV, NT, scale): NK, NV = triton.cdiv(K, BK), triton.cdiv(V, BV) dh = q.new_empty(B, H, NT * K, V) grid = (NK, NV, B * H) chunk_gla_bwd_kernel_dh[grid]( q, g, do, dh, q.stride(1), q.stride(2), q.stride(3), do.stride(1), do.stride(2), do.stride(3), dh.stride(1), dh.stride(2), dh.stride(3), scale, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, num_warps=num_warps, num_stages=num_stages ) return dh if ctx.checkpoint_level >= 1: # save the original g and compute its fp32 cumsum during the backward pass for memory consideration g_org, g = g, torch.zeros_like(g, dtype=torch.float) def grid(meta): return ((triton.cdiv(meta['S'], meta['BS']), NT, B * H)) # keep cummulative normalizer in fp32 # this kernel is equivalent to # g = g.view(B, H, NT, BT, -1).cumsum(-2).view(B, H, T, -1) chunk_gla_fwd_kernel_cum[grid]( g_org, g, g.stride(1), g.stride(2), g.stride(3), T=T, S=K, BT=BT ) # rerun the forward pass to get h if checkpoint_level >= 1 if ctx.checkpoint_level > 1: h = fwd_inner( q=q, k=k, v=v, g=g, B=B, H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, h0=initial_state if initial_state is not None else None, ht=None ) scale = ctx.scale dh = bwd_inner( q, g, do, B=B, H=H, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, scale=scale ) dq = torch.empty_like(q, dtype=torch.float) dk = torch.empty_like(k, dtype=torch.float) dg = torch.empty_like(k, dtype=torch.float) dv = v.new_empty(NK, *v.shape) dA = q.new_zeros(B, H, T, BT) grid = (NK, NT, B * H) chunk_gla_bwd_kernel_inter[grid]( k, v, h, g, A, do, dh, dq, dk, dv, dA, k.stride(1), k.stride(2), k.stride(3), v.stride(1), v.stride(2), v.stride(3), h.stride(1), h.stride(2), h.stride(3), scale, T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, num_warps=num_warps, num_stages=num_stages ) dv = dv.sum(0, dtype=dv.dtype) grid = (NK, NT * NC, B * H) chunk_gla_bwd_kernel_intra[grid]( q, k, g, dA, dq, dk, dg, k.stride(1), k.stride(2), k.stride(3), T=T, K=K, BT=BT, BC=BC, BK=BK, NC=NC, num_warps=num_warps, num_stages=num_stages ) dq = dq.to(q.dtype) dk = dk.to(q.dtype) # reversed cumsum, equivalent to: # # def reversed_cumsum(x, dim=-1): # c = x.cumsum(dim) # return x + c.index_select(dim, x.new_tensor([c.shape[dim]-1], dtype=torch.long)) - c dg = chunk_reversed_cumsum_fwd(dg).to(k.dtype) return dq, dk, dv, dg, None, 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, checkpoint_level: Optional[int] = 2 ) -> Tuple[torch.Tensor, torch.Tensor]: r""" Args: q (torch.Tensor): queries of shape `(B, H, T, K)` k (torch.Tensor): keys of shape `(B, H, T, K)` v (torch.Tensor): values of shape `(B, H, T, V)` g (torch.Tensor): Forget gates of shape `(B, H, T, K)` applied to keys. scale (Optional[int]): Scale factor for the GLA attention scores. If not provided, it will default to `1 / sqrt(K)`. Default: `None`. initial_state (Optional[torch.Tensor]): Initial state of shape `(B, H, K, V)`. Default: `None`. output_final_state (Optional[bool]): Whether to output the final state of shape `(B, H, K, V)`. Default: `False`. checkpoint_level (Optional[int]): Checkpointing level; higher values will save more memories and do more recomputations during backward. Default: `0`: - Level `0`: no memory saved, no recomputation. - Level `1`: recompute the fp32 cumulative values during backward. - Level `2`: recompute the fp32 cumulative values and forward hidden states during backward. """ assert checkpoint_level in [0, 1, 2] if scale is None: scale = q.shape[-1] ** -0.5 if initial_state is not None: initial_state = initial_state.detach() o, final_state = ChunkGLAFunction.apply(q, k, v, g, scale, initial_state, output_final_state, checkpoint_level) return o, final_state