282 lines
9.6 KiB
Python
282 lines
9.6 KiB
Python
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# -*- coding: utf-8 -*-
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# Copyright (c) 2023, Yu Zhang, Songlin Yang
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from typing import 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.utils import contiguous
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# on-the-fly computation without materializing hidden statets into HBMs
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@triton.jit
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def fused_recurrent_retention_fwd_kernel(
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# B: batch_size, H: n_heads, T: seq_len, D: d_head
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q, # query [B, H, L, D_head_K]
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k, # key [B, H, L, D_head_V]
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v, # value [B, H, L, D_head_V]
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o, # output [B, H, L, D_head_V]
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initial_state,
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final_state, # final hidden state [B, H, D_head_K, D_head_V]
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s_qk_h, # stride size: L * D_head_K
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s_qk_t, # stride size: D_head_K
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s_qk_d, # stride size: 1
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s_vo_h, # stride size: L * D_head_V
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s_vo_t, # stride size: D_head_V
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s_vo_d, # stride size: 1
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B, # batch size
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H, # n_heads
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T, # seq_len
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scale, # D_head_K ** -0.5
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BK: tl.constexpr, # BLOCK SIZE along the K dimension
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BV: tl.constexpr, # BLOCK SIZE along the V dimension
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DK: tl.constexpr, # D_head_K
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DV: tl.constexpr, # D_head_V
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USE_INITIAL_STATE: tl.constexpr, # whether to use initial state
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STORE_FINAL_STATE: tl.constexpr, # whether to store final state
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):
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# indices
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i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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i_h = i_bh % H
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# decay rate given the head index
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b_b = (1 - tl.math.pow(2, -5 - i_h * 1.0))
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p_q = q + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK)
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p_k = k + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK)
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p_v = v + i_bh * s_vo_h + i_v * BV + tl.arange(0, BV)
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p_o = o + (i_bh + i_k * B * H) * s_vo_h + i_v * BV + tl.arange(0, BV)
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mask_bk = (i_k * BK + tl.arange(0, BK)) < DK
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mask_bv = (i_v * BV + tl.arange(0, BV)) < DV
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mask_kv = mask_bk[None, :] & mask_bv[:, None]
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h = tl.zeros([BV, BK], dtype=tl.float32)
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if USE_INITIAL_STATE:
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p_init_s = initial_state + i_bh * DK * DV + \
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(i_k * BK + tl.arange(0, BK)[None, :]) * \
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DV + (i_v * BV + tl.arange(0, BV)[:, None])
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h += tl.load(p_init_s, mask=mask_kv, other=0).to(tl.float32)
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for _ in range(0, T):
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_k = tl.load(p_k, mask=mask_bk, other=0).to(tl.float32)
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_v = tl.load(p_v, mask=mask_bv, other=0).to(tl.float32)
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_q = tl.load(p_q, mask=mask_bk, other=0).to(tl.float32) * scale
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h = b_b * h + _k[None, :] * _v[:, None]
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_o = h * _q[None, :]
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_o = tl.sum(_o, axis=1)
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tl.store(p_o, _o.to(p_o.dtype.element_ty), mask=mask_bv)
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p_q += DK
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p_k += DK
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p_o += DV
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p_v += DV
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if STORE_FINAL_STATE:
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p_final_s = final_state + i_bh * DK * DV + \
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(i_k * BK + tl.arange(0, BK)[None, :]) * \
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DV + (i_v * BV + tl.arange(0, BV)[:, None])
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tl.store(p_final_s, h.to(p_final_s.dtype.element_ty), mask=mask_kv)
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# Similar to Algorithm1 of https://arxiv.org/abs/2006.16236
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@triton.jit
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def fused_recurrent_retention_bwd_kernel(
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# B: batch_size, H: n_heads, T: seq_len, D: d_head
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# NV: number of split in the V dimension. NK: number of split in the K dimension
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q, # query [B, H, L, D_head_K]
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k, # key [B, H, L, D_head_V]
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v, # value [B, H, L, D_head_V]
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do, # gradient of output [B, H, L, D_head_V]
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dq, # gradient of query [NV, B, H, L, D_head_K]
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dk, # gradient of key [NV, B, H, L, D_head_K]
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dv, # gradient of value [NK, B, H, L, D_head_V]
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# initial hidden state initialization [B, H, D_head_K, D_head_V]
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initial_state,
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s_qk_h, # stride size: L * D_head_K
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s_qk_t, # stride size: D_head_K
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s_qk_d, # stride size: 1
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s_vo_h, # stride size: L * D_head_V
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s_vo_t, # stride size: D_head_V
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s_vo_d, # stride size: 1
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B, # batch_size
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H, # n_heads
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T, # seq_len
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scale, # D_head_K ** -0.5
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BK: tl.constexpr, # BLOCK SIZE along the K dimension
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BV: tl.constexpr, # BLOCK SIZE along the V dimension
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DK: tl.constexpr, # D_head_K
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DV: tl.constexpr, # D_head_V
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USE_INITIAL_STATE: tl.constexpr, # whether to use initial state
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):
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i_v, i_k, i_bh = tl.program_id(0), tl.program_id(1), tl.program_id(2)
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i_h = i_bh % H
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b_b = 1 - tl.math.pow(2, -5 - i_h * 1.0)
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p_q = q + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK)
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p_k = k + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK)
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p_v = v + i_bh * s_vo_h + i_v * BV + tl.arange(0, BV)
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p_do = do + i_bh * s_vo_h + i_v * BV + tl.arange(0, BV)
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p_dq = dq + (i_bh + i_v * B * H) * s_qk_h + i_k * BK + tl.arange(0, BK)
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mask_bk = i_k * BK + tl.arange(0, BK) < DK
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mask_bv = i_v * BV + tl.arange(0, BV) < DV
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h = tl.zeros([BK, BV], dtype=tl.float32)
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if USE_INITIAL_STATE:
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mask_kv = mask_bk[:, None] & mask_bv[None, :]
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p_init_s = initial_state + i_bh * DK * DV + \
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(i_k * BK + tl.arange(0, BK)[:, None]) * \
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DV + (i_v * BV + tl.arange(0, BV)[None, :])
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h += tl.load(p_init_s, mask=mask_kv, other=0).to(tl.float32)
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for i in range(0, T):
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_k = tl.load(p_k, mask=mask_bk, other=0).to(tl.float32)
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_v = tl.load(p_v, mask=mask_bv, other=0).to(tl.float32)
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_do = tl.load(p_do, mask=mask_bv, other=0).to(tl.float32)
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h = b_b * h + _k[:, None] * _v[None, :]
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_d_q = h * _do[None, :]
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d_q = tl.sum(_d_q, axis=1) * scale
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tl.store(p_dq, d_q.to(p_dq.dtype.element_ty), mask=mask_bk)
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p_k += DK
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p_do += DV
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p_v += DV
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p_dq += DK
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# sync threads
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tl.debug_barrier()
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p_q = q + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (T - 1) * DK
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p_k = k + i_bh * s_qk_h + i_k * BK + tl.arange(0, BK) + (T - 1) * DK
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p_do = do + i_bh * s_vo_h + i_v * BV + tl.arange(0, BV) + (T - 1) * DV
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p_v = v + i_bh * s_vo_h + i_v * BV + tl.arange(0, BV) + (T - 1) * DV
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p_dk = dk + (i_bh + i_v * B * H) * s_qk_h + i_k * \
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BK + tl.arange(0, BK) + (T - 1) * DK
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p_dv = dv + (i_bh + i_k * B * H) * s_vo_h + i_v * \
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BV + tl.arange(0, BV) + (T - 1) * DV
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d_h = tl.zeros([BK, BV], dtype=tl.float32)
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for _ in range(T):
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_do = tl.load(p_do, mask=mask_bv, other=0).to(tl.float32)
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_q = tl.load(p_q, mask=mask_bk, other=0).to(tl.float32) * scale
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_k = tl.load(p_k, mask=mask_bk, other=0).to(tl.float32)
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_v = tl.load(p_v, mask=mask_bv, other=0).to(tl.float32)
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d_h += _q[:, None] * _do[None, :]
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d_k = tl.sum(d_h * _v[None, :], axis=1)
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d_v = tl.sum(d_h * _k[:, None], axis=0)
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d_h *= b_b
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tl.store(p_dk, d_k.to(p_dk.dtype.element_ty), mask=mask_bk)
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tl.store(p_dv, d_v.to(p_dv.dtype.element_ty), mask=mask_bv)
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p_do -= DV
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p_q -= DK
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p_k -= DK
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p_v -= DV
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p_dk -= DK
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p_dv -= DV
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class FusedRecurrentRetentionFunction(torch.autograd.Function):
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@staticmethod
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@contiguous
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def forward(ctx, q, k, v, initial_state=None, output_final_state=False):
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batch_size, n_heads, seq_len, d_head_qk = q.shape
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d_head_v = v.shape[-1]
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scale = d_head_qk ** -0.5
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BK, BV = min(d_head_qk, 32), min(d_head_v, 32)
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NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
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num_stages = 1
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num_warps = 1
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o = q.new_empty(NK, batch_size, n_heads, seq_len, d_head_v)
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if output_final_state:
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final_state = q.new_empty(batch_size, n_heads, d_head_qk, d_head_v)
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else:
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final_state = None
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grid = (NV, NK, batch_size * n_heads)
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fused_recurrent_retention_fwd_kernel[grid](
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q, k, v, o, 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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batch_size, n_heads, seq_len, scale,
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DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
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num_warps=num_warps,
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num_stages=num_stages,
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USE_INITIAL_STATE=initial_state is not None,
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STORE_FINAL_STATE=final_state is not None
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)
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o = o.sum(0)
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ctx.save_for_backward(q, k, v, initial_state)
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return o, final_state
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@staticmethod
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@contiguous
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def backward(ctx, do, d_final_state=None):
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q, k, v, initial_state = ctx.saved_tensors
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batch_size, n_heads, seq_len, d_head_qk = q.shape
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d_head_v = v.shape[-1]
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scale = d_head_qk ** -0.5
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BK, BV = min(d_head_qk, 32), min(d_head_v, 32)
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NK, NV = triton.cdiv(d_head_qk, BK), triton.cdiv(d_head_v, BV)
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num_stages = 1
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num_warps = 1
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dq = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
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dk = q.new_empty(NV, batch_size, n_heads, seq_len, d_head_qk)
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dv = q.new_empty(NK, batch_size, n_heads, seq_len, d_head_v)
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grid = (NV, NK, batch_size * n_heads)
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fused_recurrent_retention_bwd_kernel[grid](
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q, k, v, do, dq, dk, dv, initial_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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batch_size, n_heads, seq_len, scale,
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DK=d_head_qk, DV=d_head_v, BK=BK, BV=BV,
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num_warps=num_warps,
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num_stages=num_stages,
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USE_INITIAL_STATE=initial_state is not None
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)
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dq = dq.sum(0)
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dk = dk.sum(0)
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dv = dv.sum(0)
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return dq, dk, dv, None, None
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# fused_recurrent_retention = FusedRecurrentRetentionFunction.apply
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def fused_recurrent_retention(
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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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initial_state: torch.Tensor = None,
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output_final_state: bool = False
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) -> Tuple[torch.Tensor, torch.Tensor]:
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if initial_state is not None:
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initial_state = initial_state.detach()
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o, final_state = FusedRecurrentRetentionFunction.apply(q, k, v, initial_state, output_final_state)
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return o, final_state
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