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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 fla.ops.linear_attn.utils import normalize_output |
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from fla.utils import autocast_custom_bwd, autocast_custom_fwd, contiguous |
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@triton.jit |
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def chunk_linear_attn_fwd_kernel_h( |
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k, |
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v, |
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h, |
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h0, |
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ht, |
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s_k_h, |
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s_k_t, |
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s_k_d, |
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s_v_h, |
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s_v_t, |
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s_v_d, |
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s_h_h, |
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s_h_t, |
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T: 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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NT: tl.constexpr, |
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USE_INITIAL_STATE: tl.constexpr, |
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STORE_FINAL_STATE: tl.constexpr |
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): |
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i_k, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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b_h = tl.zeros([BK, BV], dtype=tl.float32) |
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if USE_INITIAL_STATE: |
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p_h0 = tl.make_block_ptr(h0 + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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b_h = tl.load(p_h0, boundary_check=(0, 1)).to(tl.float32) |
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for i_t in range(NT): |
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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)) |
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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)) |
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p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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tl.store(p_h, b_h.to(p_h.dtype.element_ty), boundary_check=(0, 1)) |
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b_k = tl.load(p_k, boundary_check=(0, 1)) |
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b_v = tl.load(p_v, boundary_check=(0, 1)) |
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b_h += tl.dot(b_k, b_v, allow_tf32=False) |
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if STORE_FINAL_STATE: |
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p_ht = tl.make_block_ptr(ht + i_bh * K * V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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tl.store(p_ht, b_h.to(p_ht.dtype.element_ty), boundary_check=(0, 1)) |
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@triton.jit |
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def chunk_linear_attn_fwd_kernel_o( |
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q, |
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k, |
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v, |
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h, |
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o, |
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s_k_h, |
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s_k_t, |
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s_k_d, |
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s_v_h, |
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s_v_t, |
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s_v_d, |
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s_h_h, |
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s_h_t, |
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scale, |
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T: 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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): |
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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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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_s = tl.zeros([BT, BT], dtype=tl.float32) |
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for i_k in range(tl.cdiv(K, BK)): |
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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)) |
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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)) |
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p_h = tl.make_block_ptr(h + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 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_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, allow_tf32=False) |
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b_s += tl.dot(b_q, b_k, allow_tf32=False) |
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b_s = tl.where(m_s, b_s, 0) |
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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)) |
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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)) |
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b_v = tl.load(p_v, boundary_check=(0, 1)) |
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b_o = (b_o + tl.dot(b_s.to(b_v.dtype), b_v, allow_tf32=False)) * scale |
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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.jit |
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def chunk_linear_attn_bwd_kernel_dh( |
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q, |
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do, |
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dh, |
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s_k_h, |
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s_k_t, |
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s_k_d, |
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s_v_h, |
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s_v_t, |
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s_v_d, |
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s_h_h, |
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s_h_t, |
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scale, |
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T: 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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NT: tl.constexpr |
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): |
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i_k, i_v, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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b_dh = tl.zeros([BK, BV], dtype=tl.float32) |
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for i_t in range(NT - 1, -1, -1): |
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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)) |
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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)) |
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p_dh = tl.make_block_ptr(dh + i_bh * s_h_h + i_t * K * V, (K, V), (s_h_t, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1)) |
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b_q = tl.load(p_q, boundary_check=(0, 1)) |
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b_q = (b_q * scale).to(b_q.dtype) |
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b_do = tl.load(p_do, boundary_check=(0, 1)) |
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b_dh += tl.dot(b_q, b_do.to(b_q.dtype), allow_tf32=False) |
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@triton.jit |
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def chunk_linear_attn_bwd_kernel_dqkv( |
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q, |
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k, |
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v, |
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h, |
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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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s_k_h, |
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s_k_t, |
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s_k_d, |
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s_v_h, |
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s_v_t, |
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s_v_d, |
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s_h_h, |
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s_h_t, |
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scale, |
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T: 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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NT: tl.constexpr |
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): |
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i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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n_bh = tl.num_programs(2) |
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o_i = tl.arange(0, BT) |
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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)) |
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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)) |
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b_q = tl.load(p_q, boundary_check=(0, 1)) |
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b_k = tl.load(p_k, boundary_check=(0, 1)) |
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b_s = tl.dot(b_k, b_q, allow_tf32=False) * scale |
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b_s = tl.where(o_i[:, None] <= o_i[None, :], b_s, 0) |
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b_dq = tl.zeros([BT, BK], dtype=tl.float32) |
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b_dk = tl.zeros([BT, BK], dtype=tl.float32) |
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b_ds = tl.zeros([BT, BT], dtype=tl.float32) |
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for i_v in range(tl.cdiv(V, BV)): |
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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)) |
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p_h = tl.make_block_ptr(h + i_bh * s_h_h, (V, NT * K), (1, s_h_t), (i_v * BV, i_t * K + i_k * BK), (BV, BK), (0, 1)) |
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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)) |
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p_dh = tl.make_block_ptr(dh + i_bh * s_h_h, (NT * K, V), (s_h_t, 1), (i_t * K + i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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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)) |
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b_v = tl.load(p_v, boundary_check=(0, 1)) |
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b_do = tl.load(p_do, boundary_check=(0, 1)) |
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b_h = tl.load(p_h, boundary_check=(0, 1)) |
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b_dh = tl.load(p_dh, boundary_check=(0, 1)) |
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b_ds += tl.dot(b_do, tl.trans(b_v), allow_tf32=False) |
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b_dq += tl.dot(b_do, b_h, allow_tf32=False) * scale |
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b_dk += tl.dot(b_v, tl.trans(b_dh), allow_tf32=False) |
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b_dv = tl.dot(b_k, b_dh, allow_tf32=False) + tl.dot(b_s.to(b_q.dtype), b_do, allow_tf32=False) |
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tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) |
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b_ds = tl.where(o_i[:, None] >= o_i[None, :], b_ds * scale, 0).to(b_q.dtype) |
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b_dq += tl.dot(b_ds, b_k, allow_tf32=False) |
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b_dk += tl.trans(tl.dot(b_q, b_ds, allow_tf32=False)) |
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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)) |
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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)) |
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tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) |
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tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) |
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class ChunkLinearAttentionFunction(torch.autograd.Function): |
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@staticmethod |
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@contiguous |
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@autocast_custom_fwd |
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def forward(ctx, q, k, v, scale, initial_state, output_final_state): |
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B, H, T, K, V = *q.shape, v.shape[-1] |
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BT = 64 |
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BK, BV = min(64, triton.next_power_of_2(K)), min(64, triton.next_power_of_2(V)) |
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NT, NK, NV = triton.cdiv(T, BT), triton.cdiv(K, BK), triton.cdiv(V, BV) |
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num_stages = 1 |
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num_warps = 4 if BK == 64 else 2 |
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ctx.scale = scale |
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final_state = None |
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if output_final_state: |
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final_state = q.new_empty(B, H, K, V, dtype=torch.float32, requires_grad=False) |
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h = q.new_empty(B, H, NT * K, V) |
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grid = (NK, NV, B * H) |
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chunk_linear_attn_fwd_kernel_h[grid]( |
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k, v, h, initial_state, final_state, |
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q.stride(1), q.stride(2), q.stride(3), |
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v.stride(1), v.stride(2), v.stride(3), |
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h.stride(1), h.stride(2), |
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T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, |
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USE_INITIAL_STATE=initial_state is not None, |
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STORE_FINAL_STATE=output_final_state, |
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num_warps=num_warps, |
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num_stages=num_stages |
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) |
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grid = (NV, NT, B * H) |
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o = torch.empty_like(v) |
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chunk_linear_attn_fwd_kernel_o[grid]( |
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q, k, v, h, o, |
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q.stride(1), q.stride(2), q.stride(3), |
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v.stride(1), v.stride(2), v.stride(3), |
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h.stride(1), h.stride(2), |
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scale, |
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T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, |
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num_warps=num_warps, |
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num_stages=num_stages |
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) |
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ctx.save_for_backward(q, k, v, h) |
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return o.to(q.dtype), final_state |
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@staticmethod |
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@contiguous |
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@autocast_custom_bwd |
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def backward(ctx, do, dht=None): |
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q, k, v, h = ctx.saved_tensors |
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B, H, T, K, V = *q.shape, v.shape[-1] |
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BT = 64 |
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BK, BV = min(64, triton.next_power_of_2(K)), min(32 if q.dtype == torch.float32 else 64, triton.next_power_of_2(V)) |
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NT, NK, NV = triton.cdiv(T, BT), triton.cdiv(K, BK), triton.cdiv(V, BV) |
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num_stages = 1 |
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num_warps = 4 if BK == 64 else 2 |
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scale = ctx.scale |
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dh = q.new_empty(B, H, NT * K, V) |
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grid = (NK, NV, B * H) |
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chunk_linear_attn_bwd_kernel_dh[grid]( |
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q, do, dh, |
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q.stride(1), q.stride(2), q.stride(3), |
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v.stride(1), v.stride(2), v.stride(3), |
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dh.stride(1), dh.stride(2), |
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scale, |
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T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, |
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num_warps=num_warps, |
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num_stages=num_stages |
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) |
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grid = (NK, NT, B * H) |
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dq = torch.empty_like(q) |
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dk = torch.empty_like(k) |
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dv = v.new_empty(NK, *v.shape) |
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num_stages = 1 |
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num_warps = 4 if BK == 64 else 2 |
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chunk_linear_attn_bwd_kernel_dqkv[grid]( |
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q, k, v, h, do, dh, dq, dk, dv, |
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q.stride(1), q.stride(2), q.stride(3), |
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v.stride(1), v.stride(2), v.stride(3), |
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dh.stride(1), dh.stride(2), |
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scale, |
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T=T, K=K, V=V, BT=BT, BK=BK, BV=BV, NT=NT, |
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num_warps=num_warps, |
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num_stages=num_stages |
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) |
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dv = dv.sum(0) |
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return dq.to(q.dtype), dk.to(k.dtype), dv.to(v.dtype), None, None, None |
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def chunk_linear_attn( |
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q: torch.Tensor, |
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k: torch.Tensor, |
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v: torch.Tensor, |
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scale: Optional[float] = None, |
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initial_state: torch.Tensor = None, |
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output_final_state: bool = False, |
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normalize: bool = True, |
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head_first: bool = True |
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) -> Tuple[torch.Tensor, torch.Tensor]: |
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r""" |
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Args: |
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q (torch.Tensor): |
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queries of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]` |
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k (torch.Tensor): |
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keys of shape `[B, H, T, K]` if `head_first=True` else `[B, T, H, K]` |
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v (torch.Tensor): |
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values of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]` |
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scale (Optional[int]): |
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Scale factor for the linear attention scores. |
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If not provided, it will default to `1 / sqrt(K)`. Default: `None`. |
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initial_state (Optional[torch.Tensor]): |
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Initial state of shape `[B, H, K, V]`. Default: `None`. |
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output_final_state (Optional[bool]): |
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Whether to output the final state of shape `[B, H, K, V]`. Default: `False`. |
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normalize (bool): |
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Whether to normalize the output. Default: `True`. |
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head_first (Optional[bool]): |
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Whether the inputs are in the head-first format. Default: `True`. |
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Returns: |
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o (torch.Tensor): |
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Outputs of shape `[B, H, T, V]` if `head_first=True` else `[B, T, H, V]` |
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final_state (torch.Tensor): |
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Final state of shape `[B, H, K, V]` if `output_final_state=True` else `None` |
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""" |
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if scale is None: |
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scale = q.shape[-1] ** -0.5 |
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if not head_first: |
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q, k, v = map(lambda x: x.transpose(1, 2), (q, k, v)) |
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o, final_state = ChunkLinearAttentionFunction.apply(q, k, v, scale, initial_state, output_final_state) |
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if normalize: |
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o = normalize_output(q * scale, k, o) |
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if not head_first: |
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o = o.transpose(1, 2) |
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return o, final_state |
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