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from typing import Optional, Tuple |
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import torch |
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import torch.nn.functional as F |
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import triton |
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import triton.language as tl |
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from fla.modules.layernorm import group_norm |
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from fla.ops.common.utils import prepare_chunk_indices, prepare_chunk_offsets |
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from fla.utils import autocast_custom_bwd, autocast_custom_fwd, input_guard |
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@triton.heuristics({ |
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'USE_INITIAL_STATE': lambda args: args['h0'] is not None, |
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'USE_INITIAL_STATE_B': lambda args: args['hb0'] is not None, |
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'STORE_FINAL_STATE': lambda args: args['ht'] is not None, |
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'USE_OFFSETS': lambda args: args['offsets'] is not None, |
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}) |
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@triton.autotune( |
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configs=[ |
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triton.Config({}, num_warps=num_warps) |
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for num_warps in [1, 2, 4, 8] |
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], |
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key=['BT', 'BK', 'BV'] |
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) |
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@triton.jit(do_not_specialize=['T']) |
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def chunk_ttt_linear_fwd_kernel_h( |
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k, |
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v, |
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v_new, |
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eta, |
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w, |
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b, |
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eps, |
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h, |
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hb, |
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h0, |
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hb0, |
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ht, |
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hbt, |
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offsets, |
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chunk_offsets, |
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T, |
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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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NT: tl.constexpr, |
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USE_INITIAL_STATE: tl.constexpr, |
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USE_INITIAL_STATE_B: tl.constexpr, |
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STORE_FINAL_STATE: 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_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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i_n, i_h = i_nh // H, i_nh % H |
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if USE_OFFSETS: |
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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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boh = tl.load(chunk_offsets + i_n).to(tl.int32) |
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else: |
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bos, eos = i_n * T, i_n * T + T |
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NT = tl.cdiv(T, BT) |
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boh = i_n * NT |
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b_h = tl.zeros([BK, BV], dtype=tl.float32) |
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b_hb = tl.zeros([BV], dtype=tl.float32) |
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if USE_INITIAL_STATE: |
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p_h0 = tl.make_block_ptr(h0 + i_nh * 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), padding_option="zero").to(tl.float32) |
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if USE_INITIAL_STATE_B: |
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p_hb0 = tl.make_block_ptr(hb0 + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
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b_hb = tl.load(p_hb0, boundary_check=(0,), padding_option="zero").to(tl.float32) |
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offs = tl.arange(0, BV) |
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b_w = tl.load(w + i_h * V + offs, mask=offs < V, other=0.) |
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b_b = tl.load(b + i_h * V + offs, mask=offs < V, other=0.) |
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for i_t in range(NT): |
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if HEAD_FIRST: |
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p_h = tl.make_block_ptr(h + (i_nh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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p_hb = tl.make_block_ptr(hb + (i_nh * NT + i_t) * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
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else: |
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p_h = tl.make_block_ptr(h + ((boh + i_t) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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p_hb = tl.make_block_ptr(hb + ((boh + i_t) * H + i_h) * V, (V,), (1,), (i_v * BV,), (BV,), (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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tl.store(p_hb, b_hb.to(p_hb.dtype.element_ty), boundary_check=(0,)) |
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if HEAD_FIRST: |
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p_k = tl.make_block_ptr(k+i_nh*T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
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p_v = tl.make_block_ptr(v+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_v_new = tl.make_block_ptr(v_new+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_eta_last = eta+i_nh*T+T-1 if i_t == NT-1 else eta+i_nh*T+i_t*BT+BT-1 |
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else: |
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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_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)) |
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p_v_new = tl.make_block_ptr(v_new+(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_eta_last = eta+bos*H+i_h + (T-1)*H if i_t == NT-1 else eta+bos*H+i_h + (i_t*BT+BT-1)*H |
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b_k = tl.load(p_k, boundary_check=(0, 1), padding_option="zero") |
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b_v = tl.load(p_v, boundary_check=(0, 1), padding_option="zero") |
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b_kh = tl.dot(tl.trans(b_k), b_h.to(b_k.dtype), allow_tf32=False).to(tl.float32) + b_hb[None, :] |
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b_kh = tl.where((offs < V)[None, :], b_kh, 0.) |
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mean = tl.sum(b_kh, axis=1, keep_dims=True) / V |
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xbar = tl.where((offs < V)[None, :], b_kh - mean, 0.) |
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var = tl.sum(xbar * xbar, axis=1, keep_dims=True) / V |
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rstd = 1 / tl.sqrt(var.to(tl.float32) + eps) |
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b_kh_hat = (b_kh - mean) * rstd |
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b_v = b_kh_hat.to(b_k.dtype) * b_w[None, :].to(b_k.dtype) + \ |
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b_b[None, :].to(b_k.dtype) - b_v.to(b_k.dtype) + tl.trans(b_k) |
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b_v = tl.where((offs < V)[None, :], b_v * b_w[None, :].to(b_k.dtype), 0.) |
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b_v2 = rstd * (V * b_v - tl.sum(b_v, axis=1, keep_dims=True) - b_kh_hat.to(b_k.dtype) |
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* tl.sum(b_v * b_kh_hat.to(b_k.dtype), axis=1, keep_dims=True)) / V |
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tl.store(p_v_new, b_v2.to(p_v_new.dtype.element_ty), boundary_check=(0, 1)) |
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b_eta_last = tl.load(p_eta_last) |
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b_h = b_h - tl.dot(b_eta_last * b_k, b_v2.to(b_k.dtype), allow_tf32=False) |
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b_hb = b_hb - tl.sum(b_eta_last * b_v2.to(b_k.dtype), axis=0) |
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if STORE_FINAL_STATE: |
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p_ht = tl.make_block_ptr(ht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
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p_hbt = tl.make_block_ptr(hbt + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (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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tl.store(p_hbt, b_hb.to(p_hbt.dtype.element_ty), boundary_check=(0,)) |
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@triton.heuristics({ |
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'USE_OFFSETS': lambda args: args['offsets'] is not None, |
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}) |
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@triton.autotune( |
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configs=[ |
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triton.Config({}, num_warps=num_warps, num_stages=num_stages) |
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for num_warps in [2, 4, 8] |
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for num_stages in [2, 3] |
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], |
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key=['BT'], |
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) |
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@triton.jit(do_not_specialize=['T']) |
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def chunk_ttt_linear_fwd_kernel_o( |
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q, |
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k, |
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v, |
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eta, |
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h, |
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hb, |
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o, |
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offsets, |
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indices, |
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scale, |
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T, |
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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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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_b, i_h = i_bh // H, i_bh % H |
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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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q += (i_bh * T * K) if HEAD_FIRST else ((bos * H + i_h) * K) |
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k += (i_bh * T * K) if HEAD_FIRST else ((bos * H + i_h) * K) |
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v += (i_bh * T * V) if HEAD_FIRST else ((bos * H + i_h) * V) |
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eta += (i_bh * T) if HEAD_FIRST else (bos * H + i_h) |
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o += (i_bh * T * V) if HEAD_FIRST else ((bos * H + i_h) * V) |
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h += ((i_bh * NT + i_t) * K * V) if HEAD_FIRST else ((i_tg * H + i_h) * K * V) |
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hb += ((i_bh * NT + i_t) * V) if HEAD_FIRST else ((i_tg * H + i_h) * V) |
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stride_qk = K if HEAD_FIRST else H*K |
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stride_vo = V if HEAD_FIRST else H*V |
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stride_eta = 1 if HEAD_FIRST else H |
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p_q = tl.make_block_ptr(q, (T, K), (stride_qk, 1), (i_t * BT, 0), (BT, BK), (1, 0)) |
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p_k = tl.make_block_ptr(k, (K, T), (1, stride_qk), (0, i_t * BT), (BK, BT), (0, 1)) |
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p_eta = tl.make_block_ptr(eta, (T,), (stride_eta,), (i_t * BT,), (BT,), (0,)) |
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p_h = tl.make_block_ptr(h, (K, V), (V, 1), (0, i_v * BV), (BK, BV), (1, 0)) |
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p_hb = tl.make_block_ptr(hb, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
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b_q = tl.load(p_q, boundary_check=(0, 1), padding_option="zero") |
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b_k = tl.load(p_k, boundary_check=(0, 1), padding_option="zero") |
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b_eta = tl.load(p_eta, boundary_check=(0,), padding_option="zero") |
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b_h = tl.load(p_h, boundary_check=(0, 1), padding_option="zero") |
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b_hb = tl.load(p_hb, boundary_check=(0,), padding_option="zero") |
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b_o = tl.dot(b_q, b_h, allow_tf32=False) |
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b_A = tl.dot(b_q, b_k, allow_tf32=False) |
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o_i = tl.arange(0, BT) |
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m_A = o_i[:, None] >= o_i[None, :] |
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b_A = tl.where(m_A, b_A, 0) |
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b_Ae = tl.where(m_A, b_eta[:, None], 0.0) |
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p_v = tl.make_block_ptr(v, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_o = tl.make_block_ptr(o, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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b_v = tl.load(p_v, boundary_check=(0, 1), padding_option="zero") |
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b_o = (b_o - tl.dot(b_eta[:, None] * b_A.to(b_v.dtype), b_v, allow_tf32=False)) * scale |
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b_o += b_hb[None, :] - tl.dot(b_Ae.to(b_v.dtype), b_v, allow_tf32=False) |
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tl.store(p_o, b_o.to(p_o.dtype.element_ty), boundary_check=(0, 1)) |
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@triton.heuristics({ |
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'USE_INITIAL_STATE': lambda args: args['h0'] is not None, |
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'USE_INITIAL_STATE_B': lambda args: args['hb0'] is not None, |
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'USE_OFFSETS': lambda args: args['offsets'] is not None, |
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}) |
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@triton.autotune( |
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configs=[ |
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triton.Config({}, num_warps=num_warps) |
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for num_warps in [1, 2, 4, 8] |
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], |
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key=['BT', 'BK', 'BV'], |
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) |
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@triton.jit(do_not_specialize=['T']) |
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def chunk_ttt_linear_bwd_kernel_h( |
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k, |
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v, |
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v_new, |
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eta, |
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w, |
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b, |
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eps, |
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h, |
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h0, |
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hb0, |
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x, |
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y, |
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r, |
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offsets, |
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chunk_offsets, |
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T, |
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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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NT: tl.constexpr, |
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USE_INITIAL_STATE: tl.constexpr, |
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USE_INITIAL_STATE_B: 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_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
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i_n, i_h = i_nh // H, i_nh % H |
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if USE_OFFSETS: |
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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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boh = tl.load(chunk_offsets + i_n).to(tl.int32) |
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else: |
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bos, eos = i_n * T, i_n * T + T |
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NT = tl.cdiv(T, BT) |
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boh = i_n * NT |
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b_h = tl.zeros([BK, BV], dtype=tl.float32) |
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b_hb = tl.zeros([BV], dtype=tl.float32) |
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if USE_INITIAL_STATE: |
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p_h0 = tl.make_block_ptr(h0 + i_nh * 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), padding_option="zero").to(tl.float32) |
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if USE_INITIAL_STATE_B: |
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p_hb0 = tl.make_block_ptr(hb0 + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
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b_hb = tl.load(p_hb0, boundary_check=(0,), padding_option="zero").to(tl.float32) |
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offs = tl.arange(0, BV) |
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b_w = tl.load(w + i_h * V + offs, mask=offs < V, other=0.) |
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b_b = tl.load(b + i_h * V + offs, mask=offs < V, other=0.) |
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for i_t in range(NT): |
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if HEAD_FIRST: |
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p_h = tl.make_block_ptr(h + (i_nh * 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_h = tl.make_block_ptr(h + ((boh + i_t) * H + i_h) * K*V, (K, V), (V, 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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if HEAD_FIRST: |
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p_k = tl.make_block_ptr(k+i_nh*T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
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p_v = tl.make_block_ptr(v+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_v_new = tl.make_block_ptr(v_new+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_x = tl.make_block_ptr(x+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_y = tl.make_block_ptr(y+i_nh*T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
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p_r = tl.make_block_ptr(r+i_nh*T, (T, 1), (1, 1), (i_t * BT, 0), (BT, 1), (1, 0)) |
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p_eta_last = eta+i_nh*T+T-1 if i_t == NT-1 else eta+i_nh*T+i_t*BT+BT-1 |
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else: |
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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)) |
|
|
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_v_new = tl.make_block_ptr(v_new+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_x = tl.make_block_ptr(x+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_y = tl.make_block_ptr(y+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_r = tl.make_block_ptr(r+bos*H+i_h, (T, 1), (H, 1), (i_t*BT, 0), (BT, 1), (1, 0)) |
|
|
p_eta_last = eta+bos*H+i_h + (T-1)*H if i_t == NT-1 else eta+bos*H+i_h + (i_t*BT+BT-1)*H |
|
|
b_k = tl.load(p_k, boundary_check=(0, 1), padding_option="zero") |
|
|
b_v = tl.load(p_v, boundary_check=(0, 1), padding_option="zero") |
|
|
|
|
|
b_kh = tl.dot(tl.trans(b_k), b_h.to(b_k.dtype), allow_tf32=False).to(tl.float32) + b_hb[None, :] |
|
|
b_kh = tl.where((offs < V)[None, :], b_kh, 0.) |
|
|
mean = tl.sum(b_kh, axis=1, keep_dims=True) / V |
|
|
xbar = tl.where((offs < V)[None, :], b_kh - mean, 0.) |
|
|
var = tl.sum(xbar * xbar, axis=1, keep_dims=True) / V |
|
|
rstd = 1 / tl.sqrt(var.to(tl.float32) + eps) |
|
|
b_kh_hat = (b_kh - mean) * rstd |
|
|
|
|
|
b_v = b_kh_hat.to(b_k.dtype) * b_w[None, :].to(b_k.dtype) + \ |
|
|
b_b[None, :].to(b_k.dtype) - b_v.to(b_k.dtype) + tl.trans(b_k) |
|
|
b_v = tl.where((offs < V)[None, :], b_v * b_w[None, :].to(b_k.dtype), 0.) |
|
|
b_v2 = rstd * (V * b_v - tl.sum(b_v, axis=1, keep_dims=True) - b_kh_hat.to(b_k.dtype) |
|
|
* tl.sum(b_v * b_kh_hat.to(b_k.dtype), axis=1, keep_dims=True)) / V |
|
|
tl.store(p_x, b_kh_hat.to(p_x.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_y, b_v.to(p_y.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_r, rstd.to(p_r.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_v_new, b_v2.to(p_v_new.dtype.element_ty), boundary_check=(0, 1)) |
|
|
b_eta_last = tl.load(p_eta_last) |
|
|
b_h = b_h - tl.dot(b_eta_last * b_k, b_v2.to(b_k.dtype), allow_tf32=False) |
|
|
b_hb = b_hb - tl.sum(b_eta_last * b_v2.to(b_k.dtype), axis=0) |
|
|
|
|
|
|
|
|
@triton.heuristics({ |
|
|
'USE_OFFSETS': lambda args: args['offsets'] is not None, |
|
|
}) |
|
|
@triton.autotune( |
|
|
configs=[ |
|
|
triton.Config({}, num_warps=num_warps) |
|
|
for num_warps in [4] |
|
|
], |
|
|
key=['BT', 'BK', 'BV'], |
|
|
) |
|
|
@triton.jit(do_not_specialize=['T']) |
|
|
def chunk_ttt_linear_bwd_kernel_dv_local( |
|
|
q, |
|
|
k, |
|
|
eta, |
|
|
do, |
|
|
dv, |
|
|
offsets, |
|
|
indices, |
|
|
scale, |
|
|
T, |
|
|
H: tl.constexpr, |
|
|
K: tl.constexpr, |
|
|
V: tl.constexpr, |
|
|
BT: tl.constexpr, |
|
|
BK: tl.constexpr, |
|
|
BV: tl.constexpr, |
|
|
USE_OFFSETS: tl.constexpr, |
|
|
HEAD_FIRST: tl.constexpr, |
|
|
): |
|
|
i_t, i_bh = tl.program_id(0), tl.program_id(1) |
|
|
i_b, i_h = i_bh // H, i_bh % H |
|
|
if USE_OFFSETS: |
|
|
i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) |
|
|
bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
|
|
T = eos - bos |
|
|
else: |
|
|
bos, eos = i_b * T, i_b * T + T |
|
|
|
|
|
|
|
|
q += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
k += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
eta += (i_bh * T) if HEAD_FIRST else (bos * H + i_h) |
|
|
do += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V |
|
|
dv += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V |
|
|
stride_qk = K if HEAD_FIRST else H*K |
|
|
stride_vo = V if HEAD_FIRST else H*V |
|
|
stride_eta = 1 if HEAD_FIRST else H |
|
|
|
|
|
b_A = tl.zeros([BT, BT], dtype=tl.float32) |
|
|
for i_k in range(tl.cdiv(K, BK)): |
|
|
p_k = tl.make_block_ptr(k, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_q = tl.make_block_ptr(q, (K, T), (1, stride_qk), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
|
|
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_k, b_q) |
|
|
|
|
|
p_eta = tl.make_block_ptr(eta, (T,), (stride_eta,), (i_t * BT,), (BT,), (0,)) |
|
|
b_eta = tl.load(p_eta, boundary_check=(0,)) |
|
|
mask = (tl.arange(0, BT)[:, None] <= tl.arange(0, BT)[None, :]) |
|
|
b_A = - tl.where(mask, b_A * scale * b_eta[None, :], 0).to(do.dtype.element_ty) |
|
|
b_Ae = - tl.where(mask, b_eta[None, :], 0).to(do.dtype.element_ty) |
|
|
|
|
|
for i_v in range(tl.cdiv(V, BV)): |
|
|
p_do = tl.make_block_ptr(do, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dv = tl.make_block_ptr(dv, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
b_do = tl.load(p_do, boundary_check=(0, 1)) |
|
|
b_dv = tl.dot(b_A.to(b_do.dtype), b_do) + tl.dot(b_Ae.to(b_do.dtype), b_do) |
|
|
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) |
|
|
|
|
|
|
|
|
@triton.heuristics({ |
|
|
'USE_FINAL_STATE_GRADIENT': lambda args: args['dht'] is not None, |
|
|
'USE_FINAL_STATE_GRADIENT_B': lambda args: args['dhbt'] is not None, |
|
|
'USE_INITIAL_STATE': lambda args: args['dh0'] is not None, |
|
|
'USE_INITIAL_STATE_B': lambda args: args['dhb0'] is not None, |
|
|
'USE_OFFSETS': lambda args: args['offsets'] is not None, |
|
|
}) |
|
|
@triton.autotune( |
|
|
configs=[ |
|
|
triton.Config({}, num_warps=num_warps) |
|
|
for num_warps in [2, 4, 8, 16] |
|
|
], |
|
|
key=['BT', 'BK', 'BV'], |
|
|
) |
|
|
@triton.jit(do_not_specialize=['T']) |
|
|
def chunk_ttt_linear_bwd_kernel_norm( |
|
|
q, |
|
|
k, |
|
|
v, |
|
|
v_new, |
|
|
x, |
|
|
y, |
|
|
r, |
|
|
w, |
|
|
b, |
|
|
eta, |
|
|
h, |
|
|
dht, |
|
|
dhbt, |
|
|
dh0, |
|
|
dhb0, |
|
|
do, |
|
|
dh, |
|
|
dhb, |
|
|
dv, |
|
|
dv_new, |
|
|
dk, |
|
|
dw, |
|
|
db, |
|
|
offsets, |
|
|
chunk_offsets, |
|
|
scale, |
|
|
T, |
|
|
H: tl.constexpr, |
|
|
K: tl.constexpr, |
|
|
V: tl.constexpr, |
|
|
BT: tl.constexpr, |
|
|
BK: tl.constexpr, |
|
|
BV: tl.constexpr, |
|
|
USE_FINAL_STATE_GRADIENT: tl.constexpr, |
|
|
USE_FINAL_STATE_GRADIENT_B: tl.constexpr, |
|
|
USE_INITIAL_STATE: tl.constexpr, |
|
|
USE_INITIAL_STATE_B: tl.constexpr, |
|
|
USE_OFFSETS: tl.constexpr, |
|
|
HEAD_FIRST: tl.constexpr |
|
|
): |
|
|
i_k, i_v, i_nh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
|
|
i_n, i_h = i_nh // H, i_nh % H |
|
|
if USE_OFFSETS: |
|
|
bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
|
|
T = eos - bos |
|
|
NT = tl.cdiv(T, BT) |
|
|
boh = tl.load(chunk_offsets + i_n).to(tl.int32) |
|
|
else: |
|
|
bos, eos = i_n * T, i_n * T + T |
|
|
NT = tl.cdiv(T, BT) |
|
|
boh = i_n * NT |
|
|
|
|
|
|
|
|
b_dh = tl.zeros([BK, BV], dtype=tl.float32) |
|
|
|
|
|
b_dhb = tl.zeros([BV], dtype=tl.float32) |
|
|
if USE_FINAL_STATE_GRADIENT: |
|
|
p_dht = tl.make_block_ptr(dht + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
|
|
b_dh += tl.load(p_dht, boundary_check=(0, 1), padding_option="zero") |
|
|
if USE_FINAL_STATE_GRADIENT_B: |
|
|
p_dhbt = tl.make_block_ptr(dhbt + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
b_dhb += tl.load(p_dhbt, boundary_check=(0,), padding_option="zero") |
|
|
|
|
|
|
|
|
offs_v = tl.arange(0, BV) |
|
|
offs_t = tl.arange(0, BT) |
|
|
b_w = tl.load(w + i_h * V + offs_v, mask=offs_v < V, other=0.) |
|
|
b_b = tl.load(b + i_h * V + offs_v, mask=offs_v < V, other=0.) |
|
|
b_dw = tl.zeros([BV,], dtype=b_w.dtype) |
|
|
b_db = tl.zeros([BV,], dtype=b_b.dtype) |
|
|
p_dw = tl.make_block_ptr(dw + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
p_db = tl.make_block_ptr(db + i_nh * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
|
|
|
for i_t in range(NT - 1, -1, -1): |
|
|
if HEAD_FIRST: |
|
|
p_h = tl.make_block_ptr(h + (i_nh * NT + 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_nh * NT + i_t) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
|
|
p_dhb = tl.make_block_ptr(dhb + (i_nh * NT + i_t) * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
else: |
|
|
p_h = tl.make_block_ptr(h + ((boh+i_t) * 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 + ((boh+i_t) * H + i_h) * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
|
|
p_dhb = tl.make_block_ptr(dhb + ((boh+i_t) * H + i_h) * V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
tl.store(p_dh, b_dh.to(p_dh.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_dhb, b_dhb.to(p_dhb.dtype.element_ty), boundary_check=(0,)) |
|
|
if HEAD_FIRST: |
|
|
p_q = tl.make_block_ptr(q + i_nh * T*K, (K, T), (1, K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
|
|
p_k = tl.make_block_ptr(k + i_nh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_v = tl.make_block_ptr(v + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_v_new = tl.make_block_ptr(v_new + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_x = tl.make_block_ptr(x + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_y = tl.make_block_ptr(y + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dv_new = tl.make_block_ptr(dv_new + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dv = tl.make_block_ptr(dv + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dk = tl.make_block_ptr(dk + i_nh * T*K, (T, K), (K, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_do = tl.make_block_ptr(do + i_nh * T*V, (T, V), (V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_r = tl.make_block_ptr(r + i_nh * T, (T, 1), (1, 1), (i_t * BT, 0), (BT, 1), (1, 0)) |
|
|
p_eta_last = eta + i_nh*T + T - 1 if i_t == NT-1 else eta + i_nh*T + i_t*BT + BT - 1 |
|
|
else: |
|
|
p_q = tl.make_block_ptr(q+(bos*H+i_h)*K, (K, T), (1, H*K), (i_k * BK, i_t * BT), (BK, BT), (0, 1)) |
|
|
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_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_v_new = tl.make_block_ptr(v_new+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_x = tl.make_block_ptr(x+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_y = tl.make_block_ptr(y+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dv_new = tl.make_block_ptr(dv_new+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dv = tl.make_block_ptr(dv+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_dk = tl.make_block_ptr(dk+(bos*H+i_h)*K, (T, K), (H*K, 1), (i_t*BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_do = tl.make_block_ptr(do+(bos*H+i_h)*V, (T, V), (H*V, 1), (i_t*BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_r = tl.make_block_ptr(r+bos*H+i_h, (T, 1), (H, 1), (i_t*BT, 0), (BT, 1), (1, 0)) |
|
|
p_eta_last = eta+bos*H+i_h + (T-1)*H if i_t == NT-1 else eta+bos*H+i_h + (i_t*BT+BT-1)*H |
|
|
b_k = tl.load(p_k, boundary_check=(0, 1), padding_option="zero") |
|
|
b_dv_new = tl.load(p_dv_new, boundary_check=(0, 1), padding_option="zero").to(b_k.dtype) |
|
|
b_eta_last = tl.load(p_eta_last) |
|
|
b_dv_new -= tl.dot(b_eta_last * b_k, b_dh.to(b_k.dtype)) |
|
|
b_dv_new -= b_eta_last * b_dhb.to(b_k.dtype)[None, :] |
|
|
|
|
|
b_v_new = tl.load(p_v_new, boundary_check=(0, 1), padding_option="zero") |
|
|
b_x = tl.load(p_x, boundary_check=(0, 1), padding_option="zero").to(b_k.dtype) |
|
|
b_y = tl.load(p_y, boundary_check=(0, 1), padding_option="zero").to(b_k.dtype) |
|
|
b_rstd = tl.load(p_r, boundary_check=(0, 1), padding_option="zero").to(tl.float32) |
|
|
b_dy = b_rstd * (b_dv_new * V - tl.sum(b_dv_new, axis=1, keep_dims=True) - |
|
|
b_x * tl.sum(b_dv_new * b_x, axis=1, keep_dims=True)) / V |
|
|
b_dx = -b_rstd * (b_dv_new * tl.sum(b_x * b_y, axis=1, keep_dims=True) + |
|
|
b_y * tl.sum(b_dv_new * b_x, axis=1, keep_dims=True)) / V |
|
|
b_drstd = tl.sum(b_dv_new.to(b_rstd.dtype) * b_v_new.to(b_rstd.dtype) / b_rstd, axis=1, keep_dims=True) |
|
|
|
|
|
b_v = tl.load(p_v, boundary_check=(0, 1), padding_option="zero") |
|
|
b_w = b_w.to(b_k.dtype) |
|
|
b_b = b_b.to(b_k.dtype) |
|
|
b_dv = -b_w * b_dy.to(b_k.dtype) |
|
|
b_dk = b_w * b_dy.to(b_k.dtype) |
|
|
b_dw += tl.sum(2 * b_w * b_x * b_dy.to(b_k.dtype) + |
|
|
(b_b - b_v.to(b_k.dtype) + b_k) * b_dy.to(b_k.dtype), axis=0).to(b_dw.dtype) |
|
|
b_db += tl.sum(b_w * b_dy.to(b_k.dtype), axis=0).to(b_db.dtype) |
|
|
b_dx = b_dx.to(b_k.dtype) + b_w * b_w * b_dy.to(b_k.dtype) |
|
|
|
|
|
|
|
|
b_q = tl.load(p_q, boundary_check=(0, 1), padding_option="zero") |
|
|
b_h = tl.load(p_h, boundary_check=(0, 1), padding_option="zero") |
|
|
b_do = tl.load(p_do, boundary_check=(0, 1), padding_option="zero") |
|
|
b_q = (b_q * scale).to(b_q.dtype) |
|
|
b_dkh = b_rstd * (V * b_dx - tl.sum(b_dx, axis=1, keep_dims=True) - |
|
|
b_x * tl.sum(b_x * b_dx, axis=1, keep_dims=True)) / V |
|
|
b_dkh -= b_rstd * b_rstd * b_drstd * b_x / V |
|
|
b_dkh = tl.where((offs_v < V)[None, :] * (offs_t < T-i_t*BT)[:, None], b_dkh, 0.) |
|
|
b_dk += tl.dot(b_dkh, b_h.to(b_dkh.dtype)).to(b_k.dtype) |
|
|
b_dh += tl.dot(b_q, b_do.to(b_q.dtype)) + tl.dot(tl.trans(b_k).to(b_dkh.dtype), b_dkh) |
|
|
b_dhb += tl.sum(b_do + b_dkh, axis=0) |
|
|
b_dh = tl.where((offs_v < V)[None, :], b_dh, 0.) |
|
|
b_dhb = tl.where((offs_v < V), b_dhb, 0.) |
|
|
|
|
|
tl.store(p_dv, b_dv.to(p_dv.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_dw, b_dw.to(p_dw.dtype.element_ty), boundary_check=(0,)) |
|
|
tl.store(p_db, b_db.to(p_db.dtype.element_ty), boundary_check=(0,)) |
|
|
|
|
|
if USE_INITIAL_STATE: |
|
|
p_dh0 = tl.make_block_ptr(dh0 + i_nh * K*V, (K, V), (V, 1), (i_k * BK, i_v * BV), (BK, BV), (1, 0)) |
|
|
tl.store(p_dh0, b_dh.to(p_dh0.dtype.element_ty), boundary_check=(0, 1)) |
|
|
if USE_INITIAL_STATE_B: |
|
|
p_dhb0 = tl.make_block_ptr(dhb0+i_nh*V, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
tl.store(p_dhb0, b_dhb.to(p_dhb0.dtype.element_ty), boundary_check=(0,)) |
|
|
|
|
|
|
|
|
@triton.heuristics({ |
|
|
'USE_OFFSETS': lambda args: args['offsets'] is not None, |
|
|
}) |
|
|
@triton.autotune( |
|
|
configs=[ |
|
|
triton.Config({}, num_warps=num_warps, num_stages=num_stages) |
|
|
for num_warps in [2, 4, 8] |
|
|
for num_stages in [2, 3] |
|
|
], |
|
|
key=['BT', 'BK', 'BV'], |
|
|
) |
|
|
@triton.jit(do_not_specialize=['T']) |
|
|
def chunk_bwd_kernel_dqke( |
|
|
q, |
|
|
k, |
|
|
v, |
|
|
e, |
|
|
h, |
|
|
do, |
|
|
dh, |
|
|
dhb, |
|
|
dq, |
|
|
dk, |
|
|
de, |
|
|
offsets, |
|
|
indices, |
|
|
scale, |
|
|
T, |
|
|
B: tl.constexpr, |
|
|
H: tl.constexpr, |
|
|
K: tl.constexpr, |
|
|
V: tl.constexpr, |
|
|
BT: tl.constexpr, |
|
|
BK: tl.constexpr, |
|
|
BV: tl.constexpr, |
|
|
USE_OFFSETS: tl.constexpr, |
|
|
HEAD_FIRST: tl.constexpr, |
|
|
): |
|
|
i_k, i_t, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2) |
|
|
i_b, i_h = i_bh // H, i_bh % H |
|
|
if USE_OFFSETS: |
|
|
i_tg = i_t |
|
|
i_n, i_t = tl.load(indices + i_t * 2).to(tl.int32), tl.load(indices + i_t * 2 + 1).to(tl.int32) |
|
|
bos, eos = tl.load(offsets + i_n).to(tl.int32), tl.load(offsets + i_n + 1).to(tl.int32) |
|
|
T = eos - bos |
|
|
NT = tl.cdiv(T, BT) |
|
|
else: |
|
|
NT = tl.cdiv(T, BT) |
|
|
i_tg = i_b * NT + i_t |
|
|
bos, eos = i_b * T, i_b * T + T |
|
|
|
|
|
|
|
|
v += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V |
|
|
do += i_bh * T * V if HEAD_FIRST else (bos * H + i_h) * V |
|
|
h += (i_bh * NT + i_t) * K*V if HEAD_FIRST else (i_tg * H + i_h) * K * V |
|
|
dh += (i_bh * NT + i_t) * K*V if HEAD_FIRST else (i_tg * H + i_h) * K * V |
|
|
dhb += (i_bh * NT + i_t) * V if HEAD_FIRST else (i_tg * H + i_h) * V |
|
|
q += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
k += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
dq += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
dk += i_bh * T * K if HEAD_FIRST else (bos * H + i_h) * K |
|
|
e += i_bh * T if HEAD_FIRST else (bos * H + i_h) |
|
|
de += i_bh * T if HEAD_FIRST else (bos * H + i_h) |
|
|
stride_qk = K if HEAD_FIRST else H*K |
|
|
stride_vo = V if HEAD_FIRST else H*V |
|
|
stride_e = 1 if HEAD_FIRST else H |
|
|
|
|
|
b_dq = tl.zeros([BT, BK], dtype=tl.float32) |
|
|
b_dk = tl.zeros([BT, BK], dtype=tl.float32) |
|
|
b_ds = tl.zeros([BT, BT], dtype=tl.float32) |
|
|
b_de = tl.zeros([BT,], dtype=tl.float32) |
|
|
|
|
|
p_k = tl.make_block_ptr(k, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
b_k = tl.load(p_k, boundary_check=(0, 1)) |
|
|
p_e_last = (e + (i_t*BT+BT-1)*stride_e) if (i_t*BT+BT) <= T else (e + (T-1)*stride_e) |
|
|
i_last = (BT-1) if (i_t*BT+BT) <= T else (T % BT-1) |
|
|
mask = (tl.arange(0, BT) == i_last) |
|
|
b_e_last = tl.load(p_e_last) |
|
|
|
|
|
for i_v in range(tl.cdiv(V, BV)): |
|
|
p_v = tl.make_block_ptr(v, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_do = tl.make_block_ptr(do, (T, V), (stride_vo, 1), (i_t * BT, i_v * BV), (BT, BV), (1, 0)) |
|
|
p_h = tl.make_block_ptr(h, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) |
|
|
p_dh = tl.make_block_ptr(dh, (V, K), (1, V), (i_v * BV, i_k * BK), (BV, BK), (0, 1)) |
|
|
p_dhb = tl.make_block_ptr(dhb, (V,), (1,), (i_v * BV,), (BV,), (0,)) |
|
|
|
|
|
b_v = tl.load(p_v, boundary_check=(0, 1)) |
|
|
b_do = tl.load(p_do, boundary_check=(0, 1)) |
|
|
|
|
|
b_h = tl.load(p_h, boundary_check=(0, 1)) |
|
|
b_dh = tl.load(p_dh, boundary_check=(0, 1)) |
|
|
|
|
|
b_dhb = tl.load(p_dhb, boundary_check=(0,)) |
|
|
|
|
|
b_ds += tl.dot(b_do, tl.trans(b_v)) |
|
|
|
|
|
b_dq += tl.dot(b_do, b_h.to(b_do.dtype)) |
|
|
|
|
|
b_dk -= b_e_last * tl.dot(b_v, b_dh.to(b_v.dtype)) |
|
|
b_de -= mask * tl.sum(tl.trans(b_dh) * tl.dot(tl.trans(b_k), b_v.to(b_k.dtype))) |
|
|
b_de -= mask * tl.sum(b_dhb * tl.sum(b_v, axis=0).to(b_k.dtype)) |
|
|
|
|
|
o_i = tl.arange(0, BT) |
|
|
p_q = tl.make_block_ptr(q, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_e = tl.make_block_ptr(e, (T,), (stride_e,), (i_t * BT,), (BT,), (0,)) |
|
|
b_q = tl.load(p_q, boundary_check=(0, 1)) |
|
|
b_e = tl.load(p_e, boundary_check=(0,)) |
|
|
|
|
|
p_dq = tl.make_block_ptr(dq, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_dk = tl.make_block_ptr(dk, (T, K), (stride_qk, 1), (i_t * BT, i_k * BK), (BT, BK), (1, 0)) |
|
|
p_de = tl.make_block_ptr(de, (T,), (stride_e,), (i_t * BT,), (BT,), (0,)) |
|
|
|
|
|
b_ds = tl.where(o_i[:, None] >= o_i[None, :], b_ds, 0) |
|
|
b_ds = b_ds.to(b_k.dtype) |
|
|
b_dq -= tl.dot(b_ds, b_k) * b_e[:, None] |
|
|
b_dk -= tl.dot(tl.trans(b_ds), b_q * b_e[:, None]) * scale |
|
|
b_de -= tl.sum(scale * tl.dot(b_ds, b_k) * b_q, axis=1) |
|
|
b_de -= tl.sum(b_ds, axis=1) |
|
|
b_dq *= scale |
|
|
tl.store(p_dq, b_dq.to(p_dq.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_dk, b_dk.to(p_dk.dtype.element_ty), boundary_check=(0, 1)) |
|
|
tl.store(p_de, b_de.to(p_de.dtype.element_ty), boundary_check=(0,)) |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_fwd_h( |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
eps: float, |
|
|
initial_state: Optional[torch.Tensor] = None, |
|
|
initial_state_bias: 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 = 16, |
|
|
) -> Tuple[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 = chunk_size |
|
|
|
|
|
if offsets is None: |
|
|
N, NT, chunk_offsets = B, triton.cdiv(T, BT), None |
|
|
else: |
|
|
N, NT, chunk_offsets = len(offsets) - 1, len(indices), prepare_chunk_offsets(offsets, BT) |
|
|
BK = triton.next_power_of_2(K) |
|
|
BV = triton.next_power_of_2(V) |
|
|
assert max(BK, BV) <= 128, "current kernel does not support head dimension larger than 128." |
|
|
NK = triton.cdiv(K, BK) |
|
|
NV = triton.cdiv(V, BV) |
|
|
assert NK == 1, 'NK > 1 is not supported because it involves time-consuming synchronization' |
|
|
assert NV == 1, 'NV > 1 is not supported by TTT update rule.' |
|
|
|
|
|
if head_first: |
|
|
h = k.new_empty(B, H, NT, K, V) |
|
|
hb = k.new_empty(B, H, NT, 1, V) |
|
|
else: |
|
|
h = k.new_empty(B, NT, H, K, V) |
|
|
hb = k.new_empty(B, NT, H, 1, V) |
|
|
final_state = k.new_empty(N, H, K, V, dtype=torch.float32) if output_final_state else None |
|
|
final_state_bias = k.new_empty(N, H, 1, V, dtype=torch.float32) if output_final_state else None |
|
|
|
|
|
v_new = torch.empty_like(v) |
|
|
grid = (NK, NV, N * H) |
|
|
|
|
|
chunk_ttt_linear_fwd_kernel_h[grid]( |
|
|
k=k, |
|
|
v=v, |
|
|
v_new=v_new, |
|
|
eta=eta, |
|
|
w=w, |
|
|
b=b, |
|
|
eps=eps, |
|
|
h=h, |
|
|
hb=hb, |
|
|
h0=initial_state, |
|
|
hb0=initial_state_bias, |
|
|
ht=final_state, |
|
|
hbt=final_state_bias, |
|
|
offsets=offsets, |
|
|
chunk_offsets=chunk_offsets, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
NT=NT, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
return h, hb, v_new, final_state, final_state_bias |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_fwd_o( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
h: torch.Tensor, |
|
|
hb: torch.Tensor, |
|
|
scale: Optional[float] = None, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 64 |
|
|
) -> torch.Tensor: |
|
|
if head_first: |
|
|
B, H, T, K, V = *q.shape, v.shape[-1] |
|
|
else: |
|
|
B, T, H, K, V = *q.shape, v.shape[-1] |
|
|
if scale is None: |
|
|
scale = k.shape[-1] ** -0.5 |
|
|
BT = chunk_size |
|
|
NT = triton.cdiv(T, BT) if offsets is None else len(indices) |
|
|
BK = triton.next_power_of_2(K) |
|
|
BV = triton.next_power_of_2(V) |
|
|
NK = triton.cdiv(K, BK) |
|
|
NV = triton.cdiv(V, BV) |
|
|
assert NK == 1, 'NK > 1 is not supported because it involves time-consuming synchronization' |
|
|
assert NV == 1, 'NV > 1 is not supported by TTT update rule.' |
|
|
|
|
|
o = torch.empty_like(v) |
|
|
|
|
|
grid = (NV, NT, B * H) |
|
|
chunk_ttt_linear_fwd_kernel_o[grid]( |
|
|
q, |
|
|
k, |
|
|
v, |
|
|
eta, |
|
|
h, |
|
|
hb, |
|
|
o, |
|
|
offsets, |
|
|
indices, |
|
|
scale, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
return o |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd_h( |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
eps: float, |
|
|
initial_state: Optional[torch.Tensor] = None, |
|
|
initial_state_bias: Optional[torch.Tensor] = None, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 16, |
|
|
) -> Tuple[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 = chunk_size |
|
|
|
|
|
if offsets is None: |
|
|
N, NT, chunk_offsets = B, triton.cdiv(T, BT), None |
|
|
else: |
|
|
N, NT, chunk_offsets = len(offsets) - 1, len(indices), prepare_chunk_offsets(offsets, BT) |
|
|
BK = triton.next_power_of_2(K) |
|
|
BV = triton.next_power_of_2(V) |
|
|
assert max(BK, BV) <= 128, "current kernel does not support head dimension larger than 128." |
|
|
NK = triton.cdiv(K, BK) |
|
|
NV = triton.cdiv(V, BV) |
|
|
assert NK == 1, 'NK > 1 is not supported because it involves time-consuming synchronization' |
|
|
assert NV == 1, 'NV > 1 is not supported by TTT update rule.' |
|
|
|
|
|
if head_first: |
|
|
h = k.new_empty(B, H, NT, K, V) |
|
|
rstd = v.new_empty(B, H, T, 1, dtype=torch.float32) |
|
|
else: |
|
|
h = k.new_empty(B, NT, H, K, V) |
|
|
rstd = v.new_empty(B, T, H, 1, dtype=torch.float32) |
|
|
x = torch.empty_like(v) |
|
|
y = torch.empty_like(v) |
|
|
|
|
|
v_new = torch.empty_like(v) |
|
|
grid = (NK, NV, N * H) |
|
|
|
|
|
chunk_ttt_linear_bwd_kernel_h[grid]( |
|
|
k=k, |
|
|
v=v, |
|
|
v_new=v_new, |
|
|
eta=eta, |
|
|
w=w, |
|
|
b=b, |
|
|
eps=eps, |
|
|
h=h, |
|
|
h0=initial_state, |
|
|
hb0=initial_state_bias, |
|
|
x=x, |
|
|
y=y, |
|
|
r=rstd, |
|
|
offsets=offsets, |
|
|
chunk_offsets=chunk_offsets, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
NT=NT, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
return h, v_new, x, y, rstd |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd_dv_local( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
do: torch.Tensor, |
|
|
scale: float, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 16 |
|
|
) -> torch.Tensor: |
|
|
if head_first: |
|
|
B, H, T, K, V = *k.shape, do.shape[-1] |
|
|
else: |
|
|
B, T, H, K, V = *k.shape, do.shape[-1] |
|
|
BT = chunk_size |
|
|
NT = triton.cdiv(T, BT) if offsets is None else len(indices) |
|
|
BK = min(triton.next_power_of_2(K), 128) |
|
|
BV = min(triton.next_power_of_2(V), 128) |
|
|
|
|
|
dv = torch.empty_like(do) |
|
|
grid = (NT, B * H) |
|
|
chunk_ttt_linear_bwd_kernel_dv_local[grid]( |
|
|
q, |
|
|
k, |
|
|
eta, |
|
|
do, |
|
|
dv, |
|
|
offsets, |
|
|
indices, |
|
|
scale, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
return dv |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd_norm( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
v_new: torch.Tensor, |
|
|
x: torch.Tensor, |
|
|
y: torch.Tensor, |
|
|
rstd: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
h0: torch.Tensor, |
|
|
hb0: torch.Tensor, |
|
|
h: torch.Tensor, |
|
|
dht: Optional[torch.Tensor], |
|
|
dhbt: Optional[torch.Tensor], |
|
|
dv_new: Optional[torch.Tensor], |
|
|
do: torch.Tensor, |
|
|
scale: float, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 16 |
|
|
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]: |
|
|
|
|
|
assert offsets is None, "bwd of varlen is not implemented yet." |
|
|
if head_first: |
|
|
B, H, T, K, V = *q.shape, do.shape[-1] |
|
|
else: |
|
|
B, T, H, K, V = *q.shape, do.shape[-1] |
|
|
BT = chunk_size |
|
|
if offsets is None: |
|
|
N, NT, chunk_offsets = B, triton.cdiv(T, BT), None |
|
|
else: |
|
|
N, NT, chunk_offsets = len(offsets) - 1, len(indices), prepare_chunk_offsets(offsets, BT) |
|
|
|
|
|
BK = triton.next_power_of_2(K) |
|
|
BV = triton.next_power_of_2(V) |
|
|
NK = triton.cdiv(K, BK) |
|
|
NV = triton.cdiv(V, BV) |
|
|
assert NK == 1, 'NK > 1 is not supported by TTT.' |
|
|
assert NV == 1, 'NV > 1 is not supported by TTT.' |
|
|
|
|
|
if head_first: |
|
|
dh = q.new_empty(B, H, NT, K, V) |
|
|
dhb = q.new_empty(B, H, NT, 1, V) |
|
|
else: |
|
|
dh = q.new_empty(B, NT, H, K, V) |
|
|
dhb = q.new_empty(B, NT, H, 1, V) |
|
|
dh0 = torch.empty_like(h0, dtype=torch.float32) if h0 is not None else None |
|
|
dhb0 = torch.empty_like(hb0, dtype=torch.float32) if hb0 is not None else None |
|
|
dv = torch.empty_like(v) |
|
|
dk = torch.empty_like(k) |
|
|
dw = w.new_empty(B, H, V) |
|
|
db = b.new_empty(B, H, V) |
|
|
|
|
|
grid = (NK, NV, N * H) |
|
|
chunk_ttt_linear_bwd_kernel_norm[grid]( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v, |
|
|
v_new=v_new, |
|
|
x=x, |
|
|
y=y, |
|
|
r=rstd, |
|
|
w=w, |
|
|
b=b, |
|
|
eta=eta, |
|
|
h=h, |
|
|
dht=dht, |
|
|
dhbt=dhbt, |
|
|
dh0=dh0, |
|
|
dhb0=dhb0, |
|
|
do=do, |
|
|
dh=dh, |
|
|
dhb=dhb, |
|
|
dv=dv, |
|
|
dv_new=dv_new, |
|
|
dk=dk, |
|
|
dw=dw, |
|
|
db=db, |
|
|
offsets=offsets, |
|
|
chunk_offsets=chunk_offsets, |
|
|
scale=scale, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
dw = dw.sum(dim=0) |
|
|
db = db.sum(dim=0) |
|
|
return dh, dhb, dh0, dhb0, dv, dk, dw, db |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd_norm_ref( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
v_new: torch.Tensor, |
|
|
kh: torch.Tensor, |
|
|
y: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
h0: torch.Tensor, |
|
|
h: torch.Tensor, |
|
|
dht: Optional[torch.Tensor], |
|
|
dv_new: Optional[torch.Tensor], |
|
|
do: torch.Tensor, |
|
|
scale: float, |
|
|
eps: float, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 16 |
|
|
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]: |
|
|
|
|
|
assert offsets is None, "bwd of varlen is not implemented yet." |
|
|
if head_first: |
|
|
B, H, T, K, V = *q.shape, do.shape[-1] |
|
|
else: |
|
|
B, T, H, K, V = *q.shape, do.shape[-1] |
|
|
|
|
|
q, k, v, v_new, kh, y, h, eta, dv_new, do = [ |
|
|
x.transpose(1, 2) for x in |
|
|
[q, k, v, v_new, kh, y, h, eta, dv_new, do] |
|
|
] |
|
|
BT = chunk_size |
|
|
NT = triton.cdiv(T, BT) if offsets is None else len(indices) |
|
|
pad_len = (BT - (T % BT)) % BT |
|
|
if pad_len > 0: |
|
|
q, k, v, v_new, kh, y, eta, dv_new, do = [ |
|
|
F.pad(x, (0, 0, 0, pad_len)) for x in |
|
|
[q, k, v, v_new, kh, y, eta, dv_new, do] |
|
|
] |
|
|
eta[:, :, -1, :] = eta[:, :, -(pad_len+1), :] |
|
|
|
|
|
q, k, v, v_new, kh, y, eta, dv_new, do = [ |
|
|
x.reshape(B, H, NT, BT, -1).permute(2, 0, 1, 3, 4) for x in |
|
|
[q, k, v, v_new, kh, y, eta, dv_new, do] |
|
|
] |
|
|
h = h.permute(2, 0, 1, 3, 4) |
|
|
|
|
|
|
|
|
dh = q.new_zeros(NT, B, H, K, V) |
|
|
dv = torch.zeros_like(v) |
|
|
dk = torch.zeros_like(k) |
|
|
dw = torch.zeros_like(w) |
|
|
db = torch.zeros_like(b) |
|
|
|
|
|
b_dh = dht if dht is not None else torch.zeros_like(dh[0]) |
|
|
b_dh = b_dh.to(torch.float32) |
|
|
|
|
|
|
|
|
_w = w.reshape(H, 1, V).to(torch.float32) |
|
|
_b = b.reshape(H, 1, V).to(torch.float32) |
|
|
|
|
|
|
|
|
for i_t in range(NT - 1, -1, -1): |
|
|
dh[i_t] = b_dh.to(dh.dtype) |
|
|
|
|
|
_q, _k, _v, _v_new, _kh, _y, _h, _eta, _dv_new, _do = [ |
|
|
x[i_t].to(torch.float32) for x in |
|
|
(q, k, v, v_new, kh, y, h, eta, dv_new, do) |
|
|
] |
|
|
_dv_new -= (_eta[:, :, -1, :, None] * _k) @ b_dh |
|
|
|
|
|
mean = _kh.mean(dim=-1, keepdim=True) |
|
|
var = _kh.var(dim=-1, unbiased=False, keepdim=True).to(torch.float32) |
|
|
rstd = 1 / torch.sqrt(var + eps).to(torch.float32) |
|
|
x = (_kh - mean) * rstd |
|
|
|
|
|
dy = rstd * (_dv_new*V - _dv_new.sum(dim=-1, keepdim=True) - x*(x*_dv_new).sum(dim=-1, keepdim=True)) / V |
|
|
dx = -rstd * (_dv_new*(x*_y).sum(dim=-1, keepdim=True) + _y*(x*_dv_new).sum(dim=-1, keepdim=True)) / V |
|
|
d_rstd = (_dv_new * _v_new / rstd).sum(dim=-1, keepdim=True) |
|
|
|
|
|
dv[i_t] = (-_w*dy).to(dv.dtype) |
|
|
dk[i_t] += (_w*dy).to(dk.dtype) |
|
|
dw += (2*_w*x*dy+(_b-_v+_k)*dy).sum(dim=(0, 2)).to(dw.dtype) |
|
|
db += (_w*dy).sum(dim=(0, 2)).to(db.dtype) |
|
|
dx += _w*_w*dy |
|
|
|
|
|
|
|
|
dkh = rstd * (V * dx - dx.sum(dim=-1, keepdim=True) - x * (x * dx).sum(dim=-1, keepdim=True)) / V |
|
|
dkh -= rstd**2 * d_rstd * x / V |
|
|
dk[i_t] += (dkh @ _h.transpose(-2, -1)).to(dk.dtype) |
|
|
b_dh += (_q.transpose(-2, -1) * scale) @ _do + _k.transpose(-2, -1) @ dkh |
|
|
dh0 = b_dh.to(torch.float32) if h0 is not None else None |
|
|
|
|
|
|
|
|
dv = dv.permute(1, 2, 0, 3, 4).reshape(B, H, -1, V)[:, :, :T, :] |
|
|
dk = dk.permute(1, 2, 0, 3, 4).reshape(B, H, -1, K)[:, :, :T, :] |
|
|
|
|
|
dh = dh.permute(1, 2, 0, 3, 4) |
|
|
if not head_first: |
|
|
dv, dk, dh = [x.transpose(1, 2) for x in (dv, dk, dh)] |
|
|
dh, dv, dk, dw, db = [x.contiguous() for x in (dh, dv, dk, dw, db)] |
|
|
dh0 = dh0.contiguous() if h0 is not None else None |
|
|
return dh, dh0, dv, dk, dw, db |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd_dqke( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
h: torch.Tensor, |
|
|
do: torch.Tensor, |
|
|
dh: torch.Tensor, |
|
|
dhb: torch.Tensor, |
|
|
scale: float, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
chunk_size: int = 16, |
|
|
) -> Tuple[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 = chunk_size |
|
|
NT = triton.cdiv(T, BT) if offsets is None else len(indices) |
|
|
|
|
|
BK = triton.next_power_of_2(K) |
|
|
BV = min(triton.next_power_of_2(V), 64) |
|
|
NK = triton.cdiv(K, BK) |
|
|
assert NK == 1, "NK > 1 is not supported." |
|
|
|
|
|
dq = torch.empty_like(q) |
|
|
dk = torch.empty_like(k) |
|
|
de = torch.empty_like(eta) |
|
|
grid = (NK, NT, B * H) |
|
|
|
|
|
chunk_bwd_kernel_dqke[grid]( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v, |
|
|
e=eta, |
|
|
h=h, |
|
|
do=do, |
|
|
dh=dh, |
|
|
dhb=dhb, |
|
|
dq=dq, |
|
|
dk=dk, |
|
|
de=de, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
scale=scale, |
|
|
B=B, |
|
|
T=T, |
|
|
H=H, |
|
|
K=K, |
|
|
V=V, |
|
|
BT=BT, |
|
|
BK=BK, |
|
|
BV=BV, |
|
|
HEAD_FIRST=head_first |
|
|
) |
|
|
return dq, dk, de |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_fwd( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
scale: float, |
|
|
eps: float, |
|
|
initial_state: torch.Tensor, |
|
|
initial_state_bias: torch.Tensor, |
|
|
output_final_state: bool, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True, |
|
|
BT: int = 16 |
|
|
): |
|
|
h, hb, v_new, final_state, final_state_bias = chunk_ttt_linear_fwd_h( |
|
|
k=k, |
|
|
v=v, |
|
|
w=w, |
|
|
b=b, |
|
|
eta=eta, |
|
|
eps=eps, |
|
|
initial_state=initial_state, |
|
|
initial_state_bias=initial_state_bias, |
|
|
output_final_state=output_final_state, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
o = chunk_ttt_linear_fwd_o( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v_new, |
|
|
eta=eta, |
|
|
h=h, |
|
|
hb=hb, |
|
|
scale=scale, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
return o, final_state, final_state_bias |
|
|
|
|
|
|
|
|
def chunk_ttt_linear_bwd( |
|
|
q: torch.Tensor, |
|
|
k: torch.Tensor, |
|
|
v: torch.Tensor, |
|
|
w: torch.Tensor, |
|
|
b: torch.Tensor, |
|
|
eta: torch.Tensor, |
|
|
scale: float, |
|
|
eps: float, |
|
|
do: torch.Tensor, |
|
|
dht: torch.Tensor, |
|
|
dhbt: torch.Tensor, |
|
|
BT: int = 16, |
|
|
initial_state: torch.Tensor = None, |
|
|
initial_state_bias: torch.Tensor = None, |
|
|
offsets: Optional[torch.LongTensor] = None, |
|
|
indices: Optional[torch.LongTensor] = None, |
|
|
head_first: bool = True |
|
|
): |
|
|
h, v_new, x, y, rstd = chunk_ttt_linear_bwd_h( |
|
|
k=k, |
|
|
v=v, |
|
|
w=w, |
|
|
b=b, |
|
|
eta=eta, |
|
|
eps=eps, |
|
|
initial_state=initial_state, |
|
|
initial_state_bias=initial_state_bias, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
dv_new = chunk_ttt_linear_bwd_dv_local( |
|
|
q=q, |
|
|
k=k, |
|
|
eta=eta, |
|
|
do=do, |
|
|
scale=scale, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
dh, dhb, dh0, dhb0, dv, dk, dw, db = chunk_ttt_linear_bwd_norm( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v, |
|
|
v_new=v_new, |
|
|
x=x, |
|
|
y=y, |
|
|
rstd=rstd, |
|
|
w=w, |
|
|
b=b, |
|
|
eta=eta, |
|
|
h0=initial_state, |
|
|
hb0=initial_state_bias, |
|
|
h=h, |
|
|
dht=dht, |
|
|
dhbt=dhbt, |
|
|
dv_new=dv_new, |
|
|
do=do, |
|
|
scale=scale, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
dq, dk2, de = chunk_ttt_linear_bwd_dqke( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v_new, |
|
|
eta=eta, |
|
|
h=h, |
|
|
do=do, |
|
|
dh=dh, |
|
|
dhb=dhb, |
|
|
scale=scale, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
chunk_size=BT |
|
|
) |
|
|
dk.add_(dk2) |
|
|
return dq, dk, dv, de, dw, db, dh0, dhb0 |
|
|
|
|
|
|
|
|
class ChunkTTTLinearFunction(torch.autograd.Function): |
|
|
|
|
|
@staticmethod |
|
|
@input_guard |
|
|
@autocast_custom_fwd |
|
|
def forward(ctx, q, k, v, w, b, BT, eta, scale, eps, initial_state, |
|
|
initial_state_bias, output_final_state, offsets, head_first): |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
indices = prepare_chunk_indices(offsets, BT) if offsets is not None else None |
|
|
o, final_state, final_state_bias = chunk_ttt_linear_fwd( |
|
|
q=q, |
|
|
k=k, |
|
|
v=v, |
|
|
w=w, |
|
|
b=b, |
|
|
eta=eta, |
|
|
scale=scale, |
|
|
eps=eps, |
|
|
BT=BT, |
|
|
initial_state=initial_state, |
|
|
initial_state_bias=initial_state_bias, |
|
|
output_final_state=output_final_state, |
|
|
offsets=offsets, |
|
|
indices=indices, |
|
|
head_first=head_first, |
|
|
) |
|
|
ctx.save_for_backward(q, k, v, eta, w, b, initial_state, initial_state_bias) |
|
|
ctx.BT = BT |
|
|
ctx.scale = scale |
|
|
ctx.eps = eps |
|
|
ctx.offsets = offsets |
|
|
ctx.indices = indices |
|
|
ctx.head_first = head_first |
|
|
return o.to(q.dtype), final_state, final_state_bias |
|
|
|
|
|
@staticmethod |
|
|
@input_guard |
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@autocast_custom_bwd |
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def backward(ctx, do, dht, dhbt): |
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q, k, v, eta, w, b, initial_state, initial_state_bias = ctx.saved_tensors |
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dq, dk, dv, de, dw, db, dh0, dhb0 = chunk_ttt_linear_bwd( |
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q=q, |
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k=k, |
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v=v, |
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w=w, |
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b=b, |
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eta=eta, |
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scale=ctx.scale, |
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eps=ctx.eps, |
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do=do, |
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dht=dht, |
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dhbt=dhbt, |
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BT=ctx.BT, |
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initial_state=initial_state, |
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initial_state_bias=initial_state_bias, |
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offsets=ctx.offsets, |
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indices=ctx.indices, |
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head_first=ctx.head_first |
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) |
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return dq.to(q), dk.to(k), dv.to(v), dw.to(w), db.to(b), None, de.to(eta), None, None, dh0, dhb0, None, None, None |
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def norm_residual(x, weight, bias, eps, head_first): |
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if head_first: |
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B, H, T, D = x.shape |
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x = x.transpose(1, 2) |
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x += group_norm( |
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x.reshape(B, T, -1).clone(), |
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weight=weight.reshape(-1).clone(), |
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bias=bias.reshape(-1).clone(), |
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eps=eps, |
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num_groups=H, |
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).reshape(x.shape) |
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x = x.transpose(1, 2) |
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else: |
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B, T, H, D = x.shape |
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x += group_norm( |
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x.reshape(B, T, -1).clone(), |
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weight=weight.reshape(-1).clone(), |
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bias=bias.reshape(-1).clone(), |
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eps=eps, |
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num_groups=H, |
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).reshape(x.shape) |
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return x |
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def chunk_ttt_linear( |
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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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w: torch.Tensor, |
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b: torch.Tensor, |
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eta: torch.Tensor, |
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scale: float = None, |
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eps: float = 1e-6, |
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chunk_size: int = 16, |
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initial_state: torch.Tensor = None, |
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initial_state_bias: torch.Tensor = None, |
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output_final_state: bool = False, |
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cu_seqlens: Optional[torch.LongTensor] = None, |
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head_first: bool = True, |
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): |
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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)` |
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k (torch.Tensor): |
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keys of shape `(B, H, T, K)` |
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v (torch.Tensor): |
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values of shape `(B, H, T, V)` |
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w (torch.Tensor): |
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layer norm weight of shape `(H, V)` |
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b (torch.Tensor): |
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layer norm bias of shape `(H, V)` |
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eta (torch.Tensor): |
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Learning rate for hidden state, of shape `(B, H, T, 1)`. |
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scale (Optional[int]): |
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Scale factor for the RetNet attention scores. |
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If not provided, it will default to `1 / sqrt(K)`. Default: `None`. |
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chunk_size (int): |
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chunk size. Default: `16`. |
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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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initial_state_bias (Optional[torch.Tensor]): |
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Initial state bias of shape `(B, H, 1, 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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cu_seqlens (torch.LongTensor): |
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Cumulative sequence lengths of shape `[N+1]` used for variable-length training, |
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consistent with the FlashAttention API. |
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head_first (Optional[bool]): |
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Whether the inputs are in the head-first format, which is not supported for variable-length inputs. |
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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]` |
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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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assert q.dtype == k.dtype == v.dtype |
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assert k.shape[-1] == v.shape[-1], "DK must equal to DV." |
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if isinstance(eta, float): |
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eta = torch.full_like(q[:, :, :, :1], eta) |
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if cu_seqlens 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 `cu_seqlens`." |
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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.shape[0] != len(cu_seqlens) - 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(cu_seqlens) - 1} rather than {initial_state.shape[0]}.") |
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if scale is None: |
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scale = k.shape[-1] ** -0.5 |
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else: |
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assert scale > 0, "Scale must be positive." |
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o, final_state, final_state_bias = ChunkTTTLinearFunction.apply( |
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q, |
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k, |
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v, |
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w, |
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b, |
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chunk_size, |
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eta, |
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scale, |
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eps, |
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initial_state, |
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initial_state_bias, |
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output_final_state, |
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cu_seqlens, |
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head_first, |
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) |
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o = norm_residual(o, w, b, eps, head_first) |
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return o, final_state, final_state_bias |
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