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from typing import Optional, Tuple |
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import torch |
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import triton |
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import triton.language as tl |
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from einops import reduce |
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from fla.ops.common.chunk_h import chunk_bwd_dh, chunk_fwd_h |
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from fla.ops.gla.chunk import chunk_gla_bwd, chunk_gla_fwd |
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from fla.ops.utils import chunk_local_cumsum, softmax_bwd, softmax_fwd |
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from fla.utils import contiguous |
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@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) |
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@triton.jit |
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def chunk_gsa_fwd_k_kernel_inter( |
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q, |
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k, |
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h, |
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g, |
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o, |
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A, |
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offsets, |
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indices, |
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scale, |
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T: tl.constexpr, |
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HQ: tl.constexpr, |
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H: tl.constexpr, |
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K: tl.constexpr, |
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V: tl.constexpr, |
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BT: tl.constexpr, |
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BK: tl.constexpr, |
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BV: tl.constexpr, |
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NG: tl.constexpr, |
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USE_OFFSETS: tl.constexpr, |
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HEAD_FIRST: tl.constexpr |
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): |
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i_v, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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i_bg = i_bh // NG |
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i_b, i_hq = i_bh // HQ, i_bh % HQ |
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i_h = i_hq // NG |
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if USE_OFFSETS: |
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i_tg = i_t |
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i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) |
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bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
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T = eos - bos |
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NT = tl.cdiv(T, BT) |
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else: |
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NT = tl.cdiv(T, BT) |
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i_tg = i_b * NT + i_t |
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bos, eos = i_b * T, i_b * T + T |
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o_i = tl.arange(0, BT) |
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m_s = o_i[:, None] >= o_i[None, :] |
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b_o = tl.zeros([BT, BV], dtype=tl.float32) |
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b_A = tl.zeros([BT, BT], dtype=tl.float32) |
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for i_k in range(tl.cdiv(K, BK)): |
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if HEAD_FIRST: |
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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)) |
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p_k = tl.make_block_ptr(k + i_bg * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
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p_h = tl.make_block_ptr(h + (i_bg * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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else: |
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p_q = tl.make_block_ptr(q + (bos * HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
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p_k = tl.make_block_ptr(k + (bos * H + i_h) * K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
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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)) |
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b_q = tl.load(p_q, boundary_check=(0, 1)) |
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b_q = (b_q * scale).to(b_q.dtype) |
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b_k = tl.load(p_k, boundary_check=(0, 1)) |
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b_h = tl.load(p_h, boundary_check=(0, 1)) |
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b_o += tl.dot(b_q, b_h) |
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b_A += tl.dot(b_q, b_k) |
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if HEAD_FIRST: |
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p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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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)) |
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p_A = tl.make_block_ptr(A + i_bh * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) |
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else: |
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p_g = tl.make_block_ptr(g + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_o = tl.make_block_ptr(o + (bos * HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_A = tl.make_block_ptr(A + (bos * HQ + i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) |
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b_g = tl.load(p_g, boundary_check=(0, 1)) |
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b_o = b_o * tl.exp(b_g) |
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tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) |
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b_A = tl.where(m_s, b_A, 0.) |
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if i_v == 0: |
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tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1)) |
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@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) |
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@triton.jit |
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def chunk_gsa_fwd_k_kernel_intra( |
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v, |
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g, |
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o, |
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A, |
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offsets, |
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indices, |
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T: tl.constexpr, |
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HQ: tl.constexpr, |
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H: tl.constexpr, |
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V: tl.constexpr, |
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BT: tl.constexpr, |
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BC: tl.constexpr, |
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BV: tl.constexpr, |
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NC: tl.constexpr, |
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NG: tl.constexpr, |
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USE_OFFSETS: tl.constexpr, |
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HEAD_FIRST: tl.constexpr |
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): |
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i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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i_bg = i_bh // NG |
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i_b, i_hq = i_bh // HQ, i_bh % HQ |
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i_h = i_hq // NG |
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i_t, i_i = i_c // NC, i_c % NC |
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if USE_OFFSETS: |
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i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) |
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bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
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T = eos - bos |
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else: |
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bos, eos = i_b * T, i_b * T + T |
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o_v = i_v * BV + tl.arange(0, BV) |
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m_v = o_v < V |
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if i_t * BT + i_i * BC > T: |
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return |
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if HEAD_FIRST: |
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p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_gn = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + min(i_t * BT + i_i * BC, T) * V + o_v, BV), BV) |
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else: |
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p_g = tl.make_block_ptr(g + (bos * H + i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + min(i_t * BT + i_i * BC, T)) * H*V + i_h * V + o_v, BV), BV) |
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b_gn = tl.load(p_gn, mask=m_v, other=0) |
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b_o = tl.zeros([BC, BV], dtype=tl.float32) |
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for i_j in range(0, i_i): |
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if HEAD_FIRST: |
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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)) |
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p_v = tl.make_block_ptr(v + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_gv = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
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else: |
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p_A = tl.make_block_ptr(A + (bos*HQ+i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t*BT+i_i*BC, i_j * BC), (BC, BC), (1, 0)) |
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p_v = tl.make_block_ptr(v + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_gv = tl.make_block_ptr(g + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
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b_v = tl.load(p_v, boundary_check=(0, 1)) |
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b_gv = tl.load(p_gv, boundary_check=(0, 1)) |
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b_vg = (b_v * tl.exp(b_gn[None, :] - b_gv)).to(b_v.dtype) |
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b_A = tl.load(p_A, boundary_check=(0, 1)) |
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b_o += tl.dot(b_A, b_vg) |
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b_g = tl.load(p_g, boundary_check=(0, 1)) |
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b_o *= tl.exp(b_g - b_gn[None, :]) |
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o_i = tl.arange(0, BC) |
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if HEAD_FIRST: |
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o_A = i_bh * T*BT + (i_t * BT + i_i * BC + tl.arange(0, BC)) * BT + i_i * BC |
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else: |
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o_A = (bos + i_t * BT + i_i * BC + tl.arange(0, BC)) * HQ*BT + i_hq * BT + i_i * BC |
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m_A = (i_t * BT + i_i * BC + tl.arange(0, BC)) < T |
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for j in range(0, min(BC, T - i_t * BT - i_i * BC)): |
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if HEAD_FIRST: |
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p_v = tl.max_contiguous(tl.multiple_of(v + i_bg * T*V + (i_t * BT + i_i * BC + j) * V + o_v, BV), BV) |
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p_gv = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (i_t * BT + i_i * BC + j) * V + o_v, BV), BV) |
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else: |
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p_v = tl.max_contiguous(tl.multiple_of(v + (bos + i_t * BT + i_i * BC + j) * H*V + i_h * V + o_v, BV), BV) |
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p_gv = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC + j) * H*V + i_h * V + o_v, BV), BV) |
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b_A = tl.load(A + o_A + j, mask=m_A, other=0) |
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b_v = tl.load(p_v, mask=m_v, other=0).to(tl.float32) |
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b_gv = tl.load(p_gv, mask=m_v, other=0).to(tl.float32) |
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b_vg = b_v[None, :] * tl.exp(b_g - b_gv[None, :]) |
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b_o += tl.where(o_i[:, None] >= j, b_A[:, None] * b_vg, 0.) |
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if HEAD_FIRST: |
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p_o = tl.make_block_ptr(o + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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else: |
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p_o = tl.make_block_ptr(o + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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b_o += tl.load(p_o, boundary_check=(0, 1)) |
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tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) |
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@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) |
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@triton.jit |
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def chunk_gsa_bwd_k_kernel_dA( |
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v, |
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g, |
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do, |
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dA, |
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indices, |
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offsets, |
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scale, |
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B: tl.constexpr, |
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T: tl.constexpr, |
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HQ: tl.constexpr, |
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H: tl.constexpr, |
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V: tl.constexpr, |
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BT: tl.constexpr, |
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BC: tl.constexpr, |
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BV: tl.constexpr, |
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NC: tl.constexpr, |
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NG: tl.constexpr, |
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USE_OFFSETS: tl.constexpr, |
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HEAD_FIRST: tl.constexpr |
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): |
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i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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i_bg = i_bh // NG |
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i_b, i_hq = i_bh // HQ, i_bh % HQ |
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i_h = i_hq // NG |
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i_t, i_i, i_j = i_c // (NC * NC), (i_c % (NC * NC)) // NC, (i_c % (NC * NC)) % NC |
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if USE_OFFSETS: |
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i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) |
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bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
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all = T |
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T = eos - bos |
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else: |
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bos, eos = i_b * T, i_b * T + T |
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all = B * T |
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o_v = i_v * BV + tl.arange(0, BV) |
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m_v = o_v < V |
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if i_t * BT + i_i * BC > T: |
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return |
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if HEAD_FIRST: |
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p_dA = tl.make_block_ptr(dA+(i_v*B*H+i_bh)*T*BT, (T, BT), (BT, 1), (i_t * BT + i_i * BC, i_j * BC), (BC, BC), (1, 0)) |
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else: |
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p_dA = tl.make_block_ptr(dA+((i_v*all+bos)*HQ+i_hq)*BT, (T, BT), (HQ*BT, 1), (i_t*BT+i_i*BC, i_j*BC), (BC, BC), (1, 0)) |
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b_dA = tl.zeros([BC, BC], dtype=tl.float32) |
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if i_i > i_j: |
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if HEAD_FIRST: |
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p_v = tl.make_block_ptr(v + i_bg * T*V, (V, T), (1, V), (i_v * BV, i_t * BT + i_j * BC), (BV, BC), (0, 1)) |
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p_gv = tl.make_block_ptr(g + i_bg * T*V, (V, T), (1, V), (i_v * BV, i_t * BT + i_j * BC), (BV, BC), (0, 1)) |
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p_gn = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (i_t * BT + i_i * BC) * V + o_v, BV), BV) |
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p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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else: |
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p_v = tl.make_block_ptr(v + (bos*H+i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t*BT + i_j*BC), (BV, BC), (0, 1)) |
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p_gv = tl.make_block_ptr(g + (bos*H+i_h) * V, (V, T), (1, H*V), (i_v * BV, i_t*BT + i_j*BC), (BV, BC), (0, 1)) |
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p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + i_t*BT + i_i*BC) * H*V + i_h * V + o_v, BV), BV) |
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p_g = tl.make_block_ptr(g + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
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p_do = tl.make_block_ptr(do + (bos*HQ+i_hq) * V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
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b_gn = tl.load(p_gn, mask=m_v, other=0.) |
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b_g = tl.load(p_g, boundary_check=(0, 1)) |
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b_do = tl.load(p_do, boundary_check=(0, 1)) |
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b_do = (b_do * tl.exp(b_g - b_gn[None, :]) * scale).to(b_do.dtype) |
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b_v = tl.load(p_v, boundary_check=(0, 1)) |
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b_gv = tl.load(p_gv, boundary_check=(0, 1)) |
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b_vg = (b_v * tl.exp(b_gn[:, None] - b_gv)).to(b_v.dtype) |
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b_dA = tl.dot(b_do, b_vg) |
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elif i_i == i_j: |
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if HEAD_FIRST: |
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p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
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p_v = tl.max_contiguous(tl.multiple_of(v + i_bg * T*V + (i_t * BT + i_j * BC) * V + o_v, BV), BV) |
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p_gv = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (i_t * BT + i_j * BC) * V + o_v, BV), BV) |
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else: |
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p_g = tl.make_block_ptr(g + (bos*H + i_h) * V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
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p_do = tl.make_block_ptr(do + (bos*HQ + i_hq) * V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
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p_v = tl.max_contiguous(tl.multiple_of(v + (bos + i_t*BT + i_j*BC) * H*V + i_h * V + o_v, BV), BV) |
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p_gv = tl.max_contiguous(tl.multiple_of(g + (bos + i_t*BT + i_j*BC) * H*V + i_h * V + o_v, BV), BV) |
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b_g = tl.load(p_g, boundary_check=(0, 1)) |
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b_do = tl.load(p_do, boundary_check=(0, 1)) * scale |
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m_v = o_v < V |
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o_i = tl.arange(0, BC) |
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m_dA = o_i[:, None] >= o_i[None, :] |
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for j in range(0, min(BC, T - i_t * BT - i_j * BC)): |
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b_v = tl.load(p_v, mask=m_v, other=0).to(tl.float32) |
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b_gv = tl.load(p_gv, mask=m_v, other=0).to(tl.float32) |
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b_dAj = tl.sum(b_do * b_v[None, :] * tl.exp(b_g - b_gv[None, :]), 1) |
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b_dA = tl.where((o_i == j)[None, :], b_dAj[:, None], b_dA) |
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p_v += (1 if HEAD_FIRST else H) * V |
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p_gv += (1 if HEAD_FIRST else H) * V |
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b_dA = tl.where(m_dA, b_dA, 0.) |
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tl.store(p_dA, b_dA.to(dA.dtype.element_ty), boundary_check=(0, 1)) |
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@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) |
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@triton.jit |
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def chunk_gsa_bwd_k_kernel_dqkvg( |
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q, |
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k, |
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v, |
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h, |
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g, |
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A, |
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do, |
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dh, |
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dq, |
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dk, |
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dv, |
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dg, |
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dgv, |
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dA, |
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offsets, |
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indices, |
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scale, |
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B: tl.constexpr, |
|
T: tl.constexpr, |
|
HQ: tl.constexpr, |
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H: tl.constexpr, |
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K: tl.constexpr, |
|
V: tl.constexpr, |
|
BT: tl.constexpr, |
|
BK: tl.constexpr, |
|
BV: tl.constexpr, |
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NG: tl.constexpr, |
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USE_OFFSETS: tl.constexpr, |
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HEAD_FIRST: tl.constexpr |
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): |
|
i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
|
i_bg = i_bh // NG |
|
i_b, i_hq = i_bh // HQ, i_bh % HQ |
|
i_h = i_hq // NG |
|
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) |
|
all = T |
|
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 |
|
all = B * T |
|
|
|
o_i = tl.arange(0, BT) |
|
o_t = min(i_t * BT + BT, T) |
|
m_s = o_i[:, None] >= o_i[None, :] |
|
|
|
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_bg * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
p_A = tl.make_block_ptr(A + (i_k*B*H+i_bh) * T*BT, (T, BT), (BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) |
|
else: |
|
p_q = tl.make_block_ptr(q + (bos*HQ+i_hq) * K, (T, K), (HQ*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_A = tl.make_block_ptr(A + ((i_k*all+bos)*HQ+i_hq)*BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) |
|
|
|
|
|
b_q = tl.load(p_q, boundary_check=(0, 1)) |
|
b_k = tl.load(p_k, boundary_check=(0, 1)) |
|
|
|
b_A = tl.dot((b_q * scale).to(b_q.dtype), tl.trans(b_k)) |
|
b_A = tl.where(m_s, b_A, 0.) |
|
tl.store(p_A, b_A.to(p_A.dtype.element_ty), boundary_check=(0, 1)) |
|
|
|
b_dq = tl.zeros([BT, BK], dtype=tl.float32) |
|
b_dk = tl.zeros([BT, BK], dtype=tl.float32) |
|
for i_v in range(tl.cdiv(V, BV)): |
|
o_v = i_v * BV + tl.arange(0, BV) |
|
if HEAD_FIRST: |
|
p_v = tl.make_block_ptr(v + i_bg * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_gn = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (o_t - 1) * V + o_v, BV), BV) |
|
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_k*B*H+i_bh) * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_dg = tl.make_block_ptr(dg + i_bh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_dgv = tl.make_block_ptr(dgv + (i_k*B*H+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_bg * 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, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (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_g = tl.make_block_ptr(g + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + o_t - 1) * H*V + i_h * V + o_v, BV), BV) |
|
p_do = tl.make_block_ptr(do + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_dv = tl.make_block_ptr(dv + ((i_k*all+bos)*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_dg = tl.make_block_ptr(dg + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
p_dgv = tl.make_block_ptr(dgv+((i_k*all+bos)*HQ+i_hq)*V, (T, V), (HQ*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 * HQ + i_hq) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
|
m_v = o_v < V |
|
|
|
|
|
b_gn = tl.load(p_gn, mask=m_v, other=0) |
|
|
|
b_v = tl.load(p_v, boundary_check=(0, 1)) |
|
b_g = tl.load(p_g, boundary_check=(0, 1)) |
|
b_gv = tl.exp(b_gn[None, :] - b_g) |
|
|
|
b_h = tl.load(p_h, boundary_check=(0, 1)) |
|
|
|
b_do = tl.load(p_do, boundary_check=(0, 1)) |
|
b_do = (b_do * tl.exp(b_g) * scale).to(b_do.dtype) |
|
|
|
b_dh = tl.load(p_dh, boundary_check=(0, 1)) |
|
|
|
b_dg = tl.sum(tl.trans(b_h) * b_dh, 0) * tl.exp(b_gn) |
|
|
|
b_dh = b_dh.to(b_k.dtype) |
|
|
|
b_dq += tl.dot(b_do, b_h.to(b_k.dtype)) |
|
b_dk += tl.dot((b_v * b_gv).to(b_v.dtype), tl.trans(b_dh)) |
|
|
|
b_dv = tl.dot(b_k, b_dh) * b_gv |
|
|
|
b_dg += tl.sum(b_dv * b_v, 0) |
|
|
|
if i_k == 0: |
|
b_dgv = tl.load(p_dg, boundary_check=(0, 1)) + b_dg[None, :] |
|
else: |
|
b_dgv = tl.zeros([BT, BV], dtype=tl.float32) + b_dg[None, :] |
|
|
|
tl.store(p_dgv, b_dgv.to(p_dgv.dtype.element_ty), boundary_check=(0, 1)) |
|
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) |
|
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)) |
|
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_dA = tl.make_block_ptr(dA + (bos*HQ + i_hq) * BT, (T, BT), (HQ*BT, 1), (i_t * BT, 0), (BT, BT), (1, 0)) |
|
p_dq = tl.make_block_ptr(dq + (bos*HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
p_dk = tl.make_block_ptr(dk + (bos*HQ + i_hq) * K, (T, K), (HQ*K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
|
b_dA = tl.load(p_dA, boundary_check=(0, 1)) |
|
|
|
b_dq += tl.dot(b_dA, b_k) |
|
b_dk += tl.dot(tl.trans(b_dA).to(b_k.dtype), b_q) |
|
|
|
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)) |
|
|
|
|
|
@triton.heuristics({'USE_OFFSETS': lambda args: args['offsets'] is not None}) |
|
@triton.jit |
|
def chunk_gsa_bwd_k_kernel_intra_dvg( |
|
v, |
|
g, |
|
o, |
|
A, |
|
do, |
|
dv, |
|
dg, |
|
offsets, |
|
indices, |
|
T: tl.constexpr, |
|
HQ: tl.constexpr, |
|
H: tl.constexpr, |
|
V: tl.constexpr, |
|
BT: tl.constexpr, |
|
BC: tl.constexpr, |
|
BV: tl.constexpr, |
|
NC: tl.constexpr, |
|
NG: tl.constexpr, |
|
USE_OFFSETS: tl.constexpr, |
|
HEAD_FIRST: tl.constexpr |
|
): |
|
i_v, i_c, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
|
i_bg = i_bh // NG |
|
i_b, i_hq = i_bh // HQ, i_bh % HQ |
|
i_h = i_hq // NG |
|
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) |
|
T = eos - bos |
|
else: |
|
bos, eos = i_b * T, i_b * T + T |
|
|
|
o_v = i_v * BV + tl.arange(0, BV) |
|
m_v = o_v < V |
|
|
|
if i_t * BT + i_i * BC > T: |
|
return |
|
|
|
if HEAD_FIRST: |
|
p_gv = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_gn = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (min(i_t * BT + i_i * BC + BC, T) - 1) * V + o_v, BV), BV) |
|
else: |
|
p_gv = tl.make_block_ptr(g + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_gn = tl.max_contiguous(tl.multiple_of(g + (bos + min(i_t * BT + i_i * BC + BC, T)-1)*H*V + i_h*V + o_v, BV), BV) |
|
|
|
b_gn = tl.load(p_gn, mask=m_v, other=0) |
|
|
|
b_gv = tl.load(p_gv, boundary_check=(0, 1)) |
|
b_dv = tl.zeros([BC, BV], dtype=tl.float32) |
|
for i_j in range(i_i + 1, NC): |
|
if HEAD_FIRST: |
|
p_g = tl.make_block_ptr(g + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_A = tl.make_block_ptr(A + i_bh * T*BT, (BT, T), (1, BT), (i_i * BC, i_t * BT + i_j * BC), (BC, BC), (0, 1)) |
|
p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
|
else: |
|
p_g = tl.make_block_ptr(g + (bos*H+i_h) * V, (T, V), (H*V, 1), (i_t * BT + i_j * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_A = tl.make_block_ptr(A + (bos*HQ+i_hq) * BT, (BT, T), (1, HQ*BT), (i_i*BC, i_t*BT + i_j*BC), (BC, BC), (0, 1)) |
|
p_do = tl.make_block_ptr(do + (bos*HQ+i_hq) * V, (T, V), (HQ*V, 1), (i_t*BT + i_j*BC, i_v*BV), (BC, BV), (1, 0)) |
|
|
|
b_g = tl.load(p_g, boundary_check=(0, 1)) |
|
b_do = tl.load(p_do, boundary_check=(0, 1)) |
|
b_do = (b_do * tl.exp(b_g - b_gn[None, :])).to(b_do.dtype) |
|
|
|
b_A = tl.load(p_A, boundary_check=(0, 1)) |
|
b_dv += tl.dot(b_A, b_do) |
|
b_dv *= tl.exp(b_gn[None, :] - b_gv) |
|
|
|
o_i = tl.arange(0, BC) |
|
o_c = i_i * BC + tl.arange(0, BC) |
|
|
|
if HEAD_FIRST: |
|
p_g = tl.max_contiguous(tl.multiple_of(g + i_bg * T*V + (i_t * BT + i_i * BC) * V + o_v, BV), BV) |
|
p_A = tl.max_contiguous(tl.multiple_of(A + i_bh * T*BT + (i_t * BT + i_i * BC) * BT + o_c, BC), BC) |
|
p_do = tl.max_contiguous(tl.multiple_of(do + i_bh * T*V + (i_t * BT + i_i * BC) * V + o_v, BV), BV) |
|
else: |
|
p_g = tl.max_contiguous(tl.multiple_of(g + (bos + i_t * BT + i_i * BC) * H*V + i_h * V + o_v, BV), BV) |
|
p_A = tl.max_contiguous(tl.multiple_of(A + (bos + i_t*BT + i_i*BC) * HQ*BT + i_hq * BT + o_c, BC), BC) |
|
p_do = tl.max_contiguous(tl.multiple_of(do + (bos + i_t*BT + i_i*BC) * HQ*V + i_hq * V + o_v, BV), BV) |
|
|
|
for j in range(0, min(BC, T - i_t * BT - i_i * BC)): |
|
|
|
b_A = tl.load(p_A) |
|
|
|
b_g = tl.load(p_g, mask=m_v, other=0) |
|
b_do = tl.load(p_do, mask=m_v, other=0) |
|
|
|
m_i = o_i[:, None] <= j |
|
b_dv += tl.where(m_i, tl.exp(b_g[None, :] - b_gv) * b_A[:, None] * b_do[None, :], 0.) |
|
|
|
p_g += (1 if HEAD_FIRST else H) * V |
|
p_A += (1 if HEAD_FIRST else HQ) * BT |
|
p_do += (1 if HEAD_FIRST else HQ) * V |
|
if HEAD_FIRST: |
|
p_o = tl.make_block_ptr(o + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_v = tl.make_block_ptr(v + i_bg * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_do = tl.make_block_ptr(do + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_dv = tl.make_block_ptr(dv + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
p_dg = tl.make_block_ptr(dg + i_bh * T*V, (T, V), (V, 1), (i_t * BT + i_i * BC, i_v * BV), (BC, BV), (1, 0)) |
|
else: |
|
p_o = tl.make_block_ptr(o + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
|
p_v = tl.make_block_ptr(v + (bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
|
p_do = tl.make_block_ptr(do + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
|
p_dv = tl.make_block_ptr(dv + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
|
p_dg = tl.make_block_ptr(dg + (bos*HQ+i_hq)*V, (T, V), (HQ*V, 1), (i_t*BT + i_i*BC, i_v*BV), (BC, BV), (1, 0)) |
|
|
|
b_o = tl.load(p_o, boundary_check=(0, 1)).to(tl.float32) |
|
b_v = tl.load(p_v, boundary_check=(0, 1)).to(tl.float32) |
|
b_do = tl.load(p_do, boundary_check=(0, 1)).to(tl.float32) |
|
b_dv = b_dv + tl.load(p_dv, boundary_check=(0, 1)).to(tl.float32) |
|
b_dg = b_o * b_do - b_v * b_dv |
|
tl.store(p_dv, b_dv.to(p_dv.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_gsa_fwd_v( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
g: torch.Tensor, |
|
scale: float = 1., |
|
initial_state: Optional[torch.Tensor] = None, |
|
output_final_state: bool = False, |
|
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, torch.Tensor]: |
|
_, A, h, ht, o = chunk_gla_fwd( |
|
q=q, |
|
k=k, |
|
v=v, |
|
g=None, |
|
g_cumsum=g, |
|
scale=scale, |
|
initial_state=initial_state, |
|
output_final_state=output_final_state, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
return A, h, ht, o |
|
|
|
|
|
def chunk_gsa_fwd_k( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
g: torch.Tensor, |
|
h0: Optional[torch.Tensor] = None, |
|
output_final_state: bool = False, |
|
scale: float = 1., |
|
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, torch.Tensor]: |
|
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], BT).tolist()]) |
|
indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) |
|
NT = len(indices) |
|
BC = min(16, BT) |
|
BK = min(64, triton.next_power_of_2(K)) |
|
BV = min(64, triton.next_power_of_2(V)) |
|
HQ = q.shape[1] if head_first else q.shape[2] |
|
NV = triton.cdiv(V, BV) |
|
NC = triton.cdiv(BT, BC) |
|
NG = HQ // H |
|
num_warps = 4 if BK == 64 else 2 |
|
num_stages = 1 |
|
|
|
h, ht = chunk_fwd_h( |
|
k=k, |
|
v=v, |
|
g=None, |
|
gk=None, |
|
gv=g, |
|
h0=h0, |
|
output_final_state=output_final_state, |
|
states_in_fp32=False, |
|
offsets=offsets, |
|
head_first=head_first, |
|
chunk_size=BT |
|
) |
|
o = v.new_empty(B, *((HQ, T) if head_first else (T, HQ)), V) |
|
A = q.new_empty(B, *((HQ, T) if head_first else (T, HQ)), BT) |
|
grid = (NV, NT, B * HQ) |
|
chunk_gsa_fwd_k_kernel_inter[grid]( |
|
q, |
|
k, |
|
h, |
|
g, |
|
o, |
|
A, |
|
offsets=offsets, |
|
indices=indices, |
|
scale=scale, |
|
T=T, |
|
HQ=HQ, |
|
H=H, |
|
K=K, |
|
V=V, |
|
BT=BT, |
|
BK=BK, |
|
BV=BV, |
|
NG=NG, |
|
HEAD_FIRST=head_first, |
|
num_warps=num_warps, |
|
num_stages=num_stages |
|
) |
|
grid = (NV, NT * NC, B * HQ) |
|
chunk_gsa_fwd_k_kernel_intra[grid]( |
|
v, |
|
g, |
|
o, |
|
A, |
|
offsets=offsets, |
|
indices=indices, |
|
T=T, |
|
HQ=HQ, |
|
H=H, |
|
V=V, |
|
BT=BT, |
|
BC=BC, |
|
BV=BV, |
|
NC=NC, |
|
NG=NG, |
|
HEAD_FIRST=head_first, |
|
num_warps=num_warps, |
|
num_stages=num_stages |
|
) |
|
return A, h, ht, o |
|
|
|
|
|
def chunk_gsa_bwd_v( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
g: torch.Tensor, |
|
h0: torch.Tensor, |
|
h: torch.Tensor, |
|
A: torch.Tensor, |
|
do: torch.Tensor, |
|
dht: torch.Tensor, |
|
dg: torch.Tensor, |
|
scale: float = 1., |
|
offsets: Optional[torch.LongTensor] = None, |
|
indices: Optional[torch.LongTensor] = None, |
|
head_first: bool = True, |
|
chunk_size: int = 64 |
|
): |
|
dq, dk, dv, dg, dh0 = chunk_gla_bwd( |
|
q=q, |
|
k=k, |
|
v=v, |
|
g=None, |
|
g_cumsum=g, |
|
scale=scale, |
|
initial_state=h0, |
|
h=h, |
|
A=A, |
|
do=do, |
|
dht=dht, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
return dq, dk, dv, dg, dh0 |
|
|
|
|
|
def chunk_gsa_bwd_k( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
g: torch.Tensor, |
|
h: torch.Tensor, |
|
h0: torch.Tensor, |
|
o: torch.Tensor, |
|
do: torch.Tensor, |
|
dht: torch.Tensor, |
|
dg: torch.Tensor, |
|
scale: float = 1., |
|
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], BT).tolist()]) |
|
indices = torch.stack([indices.eq(0).cumsum(0) - 1, indices], 1).to(offsets) |
|
NT = len(indices) |
|
BC = min(16, BT) |
|
BK = min(64, triton.next_power_of_2(K)) |
|
BV = min(64, triton.next_power_of_2(V)) |
|
HQ = q.shape[1] if head_first else q.shape[2] |
|
NC = triton.cdiv(BT, BC) |
|
NK = triton.cdiv(K, BK) |
|
NV = triton.cdiv(V, BV) |
|
NG = HQ // H |
|
num_warps = 4 if BK == 64 else 2 |
|
num_stages = 1 |
|
|
|
if h is None: |
|
h, _ = chunk_fwd_h( |
|
k=k, |
|
v=v, |
|
g=None, |
|
gk=None, |
|
gv=g, |
|
h0=h0, |
|
output_final_state=False, |
|
states_in_fp32=False, |
|
offsets=offsets, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
dh, dh0 = chunk_bwd_dh( |
|
q=q, |
|
k=k, |
|
v=v, |
|
g=None, |
|
gk=None, |
|
gv=g, |
|
do=do, |
|
h0=h0, |
|
dht=dht, |
|
scale=scale, |
|
states_in_fp32=True, |
|
offsets=offsets, |
|
head_first=head_first, |
|
chunk_size=BT |
|
) |
|
dA = q.new_empty(NV, B, *((HQ, T) if head_first else (T, HQ)), BT) |
|
grid = (NV, NT * NC * NC, B * HQ) |
|
chunk_gsa_bwd_k_kernel_dA[grid]( |
|
v, |
|
g, |
|
do, |
|
dA, |
|
offsets=offsets, |
|
indices=indices, |
|
scale=scale, |
|
B=B, |
|
T=T, |
|
HQ=HQ, |
|
H=H, |
|
V=V, |
|
BT=BT, |
|
BC=BC, |
|
BV=BV, |
|
NC=NC, |
|
NG=NG, |
|
HEAD_FIRST=head_first, |
|
num_warps=num_warps, |
|
num_stages=num_stages |
|
) |
|
dA = dA.sum(0, dtype=dA.dtype) |
|
|
|
A = do.new_empty(NK, B, *((HQ, T) if head_first else (T, HQ)), BT) |
|
dq = torch.empty_like(q) |
|
dk = k.new_empty(B, *((HQ, T) if head_first else (T, HQ)), K) |
|
dv = v.new_empty(NK, B, *((HQ, T) if head_first else (T, HQ)), V) |
|
dgv = g.new_empty(NK, B, *((HQ, T) if head_first else (T, HQ)), V, dtype=torch.float) |
|
grid = (NK, NT, B * HQ) |
|
chunk_gsa_bwd_k_kernel_dqkvg[grid]( |
|
q, |
|
k, |
|
v, |
|
h, |
|
g, |
|
A, |
|
do, |
|
dh, |
|
dq, |
|
dk, |
|
dv, |
|
dg, |
|
dgv, |
|
dA, |
|
offsets=offsets, |
|
indices=indices, |
|
scale=scale, |
|
B=B, |
|
T=T, |
|
HQ=HQ, |
|
H=H, |
|
K=K, |
|
V=V, |
|
BT=BT, |
|
BK=BK, |
|
BV=BV, |
|
NG=NG, |
|
HEAD_FIRST=head_first, |
|
num_warps=num_warps, |
|
num_stages=num_stages |
|
) |
|
A = A.sum(0, dtype=A.dtype) |
|
dv = dv.sum(0, dtype=dv.dtype) |
|
dgv = dgv.sum(0, dtype=dgv.dtype) |
|
|
|
grid = (NV, NT * NC, B * HQ) |
|
chunk_gsa_bwd_k_kernel_intra_dvg[grid]( |
|
v, |
|
g, |
|
o, |
|
A, |
|
do, |
|
dv, |
|
dg, |
|
offsets=offsets, |
|
indices=indices, |
|
T=T, |
|
HQ=HQ, |
|
H=H, |
|
V=V, |
|
BT=BT, |
|
BC=BC, |
|
BV=BV, |
|
NC=NC, |
|
NG=NG, |
|
HEAD_FIRST=head_first, |
|
num_warps=num_warps, |
|
num_stages=num_stages |
|
) |
|
dg = dgv.add_(chunk_local_cumsum(dg, chunk_size=BT, reverse=True, offsets=offsets, indices=indices, head_first=head_first)) |
|
|
|
return dq, dk, dv, dg, dh0 |
|
|
|
|
|
def chunk_gsa_fwd( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
s: torch.Tensor, |
|
g: torch.Tensor, |
|
initial_state: Optional[Tuple[torch.Tensor, torch.Tensor]] = None, |
|
output_final_state: bool = False, |
|
scale: float = 1., |
|
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, torch.Tensor]: |
|
hk0, hv0 = None, None |
|
if initial_state is not None: |
|
hk0, hv0 = initial_state |
|
Ak, hk, hkt, ok = chunk_gsa_fwd_k( |
|
q=q, |
|
k=k, |
|
v=s, |
|
g=g, |
|
h0=hk0, |
|
output_final_state=output_final_state, |
|
scale=scale, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
|
|
|
|
p = softmax_fwd(ok, dtype=torch.float) |
|
|
|
qv = p.to(q.dtype) |
|
Av, hv, hvt, ov = chunk_gsa_fwd_v( |
|
q=qv, |
|
k=s, |
|
v=v, |
|
g=g, |
|
scale=1., |
|
initial_state=hv0, |
|
output_final_state=output_final_state, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
return Ak, hk, hkt, ok, p, Av, hv, hvt, ov |
|
|
|
|
|
def chunk_gsa_bwd( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
s: torch.Tensor, |
|
g: torch.Tensor, |
|
ok: torch.Tensor, |
|
p: torch.Tensor, |
|
A: Tuple[torch.Tensor, torch.Tensor], |
|
h: Tuple[torch.Tensor, torch.Tensor], |
|
initial_state: Optional[Tuple[torch.Tensor, torch.Tensor]], |
|
scale: float, |
|
do: torch.Tensor, |
|
dht: Tuple[torch.Tensor, torch.Tensor], |
|
offsets: Optional[torch.LongTensor] = None, |
|
indices: Optional[torch.LongTensor] = None, |
|
head_first: bool = True, |
|
chunk_size: int = 64 |
|
): |
|
hk0, hv0 = None, None |
|
if initial_state is not None: |
|
hk0, hv0 = initial_state |
|
|
|
_, Av = A |
|
hk, hv = h |
|
dhkt, dhvt = dht |
|
|
|
qv = p.to(q.dtype) |
|
dqv, dsv, dv, dg, dhv0 = chunk_gsa_bwd_v( |
|
q=qv, |
|
k=s, |
|
v=v, |
|
g=g, |
|
h0=hv0, |
|
h=hv, |
|
A=Av, |
|
do=do, |
|
dht=dhvt, |
|
dg=None, |
|
scale=1., |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
|
|
|
|
|
|
dok = softmax_bwd(p, dqv, dtype=ok.dtype) |
|
|
|
dq, dk, dsk, dg, dhk0 = chunk_gsa_bwd_k( |
|
q=q, |
|
k=k, |
|
v=s, |
|
g=g, |
|
h0=hk0, |
|
h=hk, |
|
o=ok, |
|
do=dok, |
|
dht=dhkt, |
|
dg=dg, |
|
scale=scale, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
|
|
ds = dsv.add_(dsk) |
|
if q.shape[1] != k.shape[1]: |
|
dk, dv, ds, dg = map(lambda x: reduce(x, 'b (h g) ... -> b h ...', 'sum', h=k.shape[1]), (dk, dv, ds, dg)) |
|
dg = dg.to(s.dtype) |
|
return dq, dk, dv, ds, dg, dhk0, dhv0 |
|
|
|
|
|
class ChunkGSAFunction(torch.autograd.Function): |
|
|
|
@staticmethod |
|
@contiguous |
|
def forward( |
|
ctx, |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
s: torch.Tensor, |
|
g: torch.Tensor, |
|
scale: float, |
|
hk0: Optional[torch.Tensor], |
|
hv0: Optional[torch.Tensor], |
|
output_final_state: bool, |
|
checkpoint_level: int, |
|
offsets: Optional[torch.LongTensor], |
|
head_first: bool = True |
|
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]: |
|
T = q.shape[2] if head_first else q.shape[1] |
|
chunk_size = min(64, triton.next_power_of_2(T)) |
|
|
|
|
|
|
|
|
|
|
|
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_org, g = g, chunk_local_cumsum(g, chunk_size, offsets=offsets, indices=indices, head_first=head_first) |
|
Ak, hk, hkt, ok, p, Av, hv, hvt, ov = chunk_gsa_fwd( |
|
q=q, |
|
k=k, |
|
v=v, |
|
s=s, |
|
g=g, |
|
initial_state=(hk0, hv0), |
|
output_final_state=output_final_state, |
|
scale=scale, |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
|
|
if checkpoint_level >= 1: |
|
del g |
|
g = g_org |
|
if checkpoint_level > 1: |
|
del hk |
|
del hv |
|
hk, hv = None, None |
|
else: |
|
hk0, hv0 = None, None |
|
|
|
ctx.save_for_backward(q, k, v, s, g, ok, p, Av, hk0, hv0, hk, hv) |
|
ctx.checkpoint_level = checkpoint_level |
|
ctx.scale = scale |
|
ctx.offsets = offsets |
|
ctx.indices = indices |
|
ctx.head_first = head_first |
|
ctx.chunk_size = chunk_size |
|
return ov, hkt, hvt |
|
|
|
@staticmethod |
|
@contiguous |
|
def backward(ctx, dov, dhkt=None, dhvt=None): |
|
q, k, v, s, g, ok, p, Av, hk0, hv0, hk, hv = ctx.saved_tensors |
|
scale = ctx.scale |
|
offsets = ctx.offsets |
|
indices = ctx.indices |
|
head_first = ctx.head_first |
|
chunk_size = ctx.chunk_size |
|
|
|
if ctx.checkpoint_level >= 1: |
|
g = chunk_local_cumsum(g, chunk_size, offsets=offsets, indices=indices, head_first=head_first) |
|
dq, dk, dv, ds, dg, dhk0, dhv0 = chunk_gsa_bwd( |
|
q=q, |
|
k=k, |
|
v=v, |
|
s=s, |
|
g=g, |
|
ok=ok, |
|
p=p, |
|
A=(None, Av), |
|
h=(hk, hv), |
|
initial_state=(hk0, hv0), |
|
scale=scale, |
|
do=dov, |
|
dht=(dhkt, dhvt), |
|
offsets=offsets, |
|
indices=indices, |
|
head_first=head_first, |
|
chunk_size=chunk_size |
|
) |
|
return dq, dk, dv, ds, dg, None, dhk0, dhv0, None, None, None, None |
|
|
|
|
|
def chunk_gsa( |
|
q: torch.Tensor, |
|
k: torch.Tensor, |
|
v: torch.Tensor, |
|
s: torch.Tensor, |
|
g: Optional[torch.Tensor] = None, |
|
scale: Optional[int] = None, |
|
initial_state: Optional[Tuple[torch.Tensor]] = None, |
|
output_final_state: Optional[bool] = False, |
|
checkpoint_level: Optional[int] = 2, |
|
offsets: Optional[torch.LongTensor] = None, |
|
head_first: Optional[bool] = True |
|
) -> Tuple[torch.Tensor, torch.Tensor]: |
|
r""" |
|
Args: |
|
q (torch.Tensor): |
|
queries of shape `[B, HQ, T, K]` if `head_first=True` else `[B, T, HQ, K]`. |
|
k (torch.Tensor): |
|
keys of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]`. |
|
GQA is performed if `H` is not equal to `HQ`. |
|
v (torch.Tensor): |
|
values of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]`. |
|
s (torch.Tensor): |
|
slot representations of shape `[B, H, T, M]` if `head_first=True` else `[B, T, H, M]`. |
|
g (torch.Tensor): |
|
Forget gates of shape `[B, H, T, M]` applied to keys. |
|
If not provided, this function is equivalent to vanilla ABC. |
|
scale (Optional[int]): |
|
Scale factor for attention scores. |
|
If not provided, it will default to `1 / sqrt(K)`. Default: `None`. |
|
initial_state (Optional[Tuple[torch.Tensor]]): |
|
Initial state tuple having tensors of shape `[N, H, K, M]` and `[N, H, M, 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 tuple, having tensors of shape `[N, H, K, M]` and `[N, H, M, V]`. |
|
Default: `False`. |
|
checkpoint_level (Optional[int]): |
|
Checkpointing level; higher values will save more memories and do more recomputations during backward. |
|
Default: `2`: |
|
- 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. |
|
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 (Tuple[torch.Tensor]): |
|
Final state tuple having tensors of shape `[N, H, K, M]` and `[N, H, M, V]` if `output_final_state=True`. |
|
`None` otherwise. |
|
|
|
Examples:: |
|
>>> import torch |
|
>>> import torch.nn.functional as F |
|
>>> from einops import rearrange |
|
>>> from fla.ops.gsa import fused_recurrent_gsa |
|
# inputs with equal lengths |
|
>>> B, T, H, K, V, M = 4, 2048, 4, 512, 512, 64 |
|
>>> 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') |
|
>>> s = torch.randn(B, T, H, M, device='cuda') |
|
>>> g = F.logsigmoid(torch.randn(B, T, H, M, device='cuda')) |
|
>>> h0 = (torch.randn(B, H, K, M, device='cuda'), torch.randn(B, H, M, V, device='cuda')) |
|
>>> o, (hk, hv) = chunk_gsa(q, k, v, s, 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, s, g = map(lambda x: rearrange(x, 'b t h d -> 1 (b t) h d'), (q, k, v, s, g)) |
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# for a batch with 4 sequences, offsets with 5 start/end positions are expected |
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>>> offsets = q.new_tensor([0, 2048, 4096, 6144, 8192], dtype=torch.long) |
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>>> o_var, (hk_var, hv_var) = chunk_gsa(q, k, v, s, g, |
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initial_state=h0, |
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output_final_state=True, |
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offsets=offsets, |
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head_first=False) |
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>>> assert o.allclose(o_var.view(o.shape)) |
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>>> assert hk.allclose(hk_var) |
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>>> assert hv.allclose(hv_var) |
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""" |
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if offsets is not None: |
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if q.shape[0] != 1: |
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raise ValueError(f"The batch size is expected to be 1 rather than {q.shape[0]} when using `offsets`." |
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f"Please flatten variable-length inputs before processing.") |
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if head_first: |
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raise RuntimeError("Sequences with variable lengths are not supported for head-first mode") |
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if initial_state is not None and initial_state[0].shape[0] != len(offsets) - 1: |
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raise ValueError(f"The number of initial states is expected to be equal to the number of input sequences, " |
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f"i.e., {len(offsets) - 1} rather than {initial_state[0].shape[0]}.") |
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assert checkpoint_level in [0, 1, 2] |
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if g is None: |
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|
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z = s.float().logcumsumexp(2) |
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g = torch.cat((z[:, :, :1], z[:, :, :-1]), 2) - z |
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s = torch.exp(s - z).to(k.dtype) |
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if scale is None: |
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scale = q.shape[-1] ** -0.5 |
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|
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hk0, hv0 = None, None |
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if initial_state is not None: |
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hk0, hv0 = initial_state |
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o, *final_state = ChunkGSAFunction.apply( |
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q, |
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k, |
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v, |
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s, |
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g, |
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scale, |
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hk0, |
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hv0, |
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output_final_state, |
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checkpoint_level, |
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offsets, |
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head_first |
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) |
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return o, final_state |
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|
