mygpt.py

   1 #!/usr/bin/env python
   2
   3 # Any copyright is dedicated to the Public Domain.
   4 # https://creativecommons.org/publicdomain/zero/1.0/
   5
   6 # Written by Francois Fleuret <francois@fleuret.org>
   7
   8 # This is an implementation from scratch of a "GPT", that is a model
   9 # composed of several causal self-attention blocks. It is equipped
  10 # with a caching mechanism for keys and values to avoid a O(N^3) cost
  11 # for auto-regression.
  12
  13 import math, warnings
  14
  15 import torch, einops
  16
  17 from torch import nn
  18 from torch.nn import functional as F
  19
  20 import ffutils
  21
  22 # import memload
  23
  24 ######################################################################
  25
  26 # A BracketedSequence is a BxTx... tensor with a first and a nb time
  27 # steps to compute.
  28
  29 # Modules able to process it expect that they will have to process a
  30 # first bracket starting at t=0, followed by a succession of brackets
  31 # that move forward in time, do not overlap, and cover the axis T with
  32 # no holes.
  33 #
  34 # Although it is more general, for a classical prompt-conditioned
  35 # auto-regressive process it will be a first bracket starting at 0 and
  36 # of arbitrary length for the "prompt", followed by brackets of length
  37 # 1 for the successive tokens.
  38 #
  39 # Modules able to process brackets may implement a cache that is
  40 # resetted when the input bracket starts at t=0
  41
  42
  43 class BracketedSequence:
  44     def __init__(self, x, first=None, nb=None, init_cache=None):
  45         self.x = x
  46         assert (first is None and nb is None and init_cache is None) or (
  47             first is not None and nb is not None and init_cache is not None
  48         )
  49
  50         self.first = 0 if first is None else first
  51         self.nb = x.size(1) if nb is None else nb
  52         self.init_cache = True if init_cache is None else init_cache
  53
  54     def slice(self):
  55         return self.x[:, self.first : self.first + self.nb]
  56
  57     def complete(self):
  58         return self.first == 0 and self.nb == self.x.size(1)
  59
  60
  61 ######################################################################
  62
  63
  64 class CacheWrapper(nn.Module):
  65     def __init__(self, *f):
  66         super().__init__()
  67         self.f = f[0] if len(f) == 1 else nn.Sequential(*f)
  68
  69     def forward(self, bs):
  70         if bs.init_cache:
  71             y = self.f(bs.slice())
  72             self.cache_y = y.new(*((y.size(0), bs.x.size(1)) + y.size()[2:]))
  73             self.cache_y[:, bs.first : bs.first + bs.nb] = y
  74         else:
  75             assert tuple(bs.x.size()[:2]) == tuple(self.cache_y.size()[:2])
  76             assert bs.first + bs.nb <= self.cache_y.size(1)
  77             self.cache_y[:, bs.first : bs.first + bs.nb] = self.f(bs.slice())
  78
  79         return BracketedSequence(self.cache_y, bs.first, bs.nb, bs.init_cache)
  80
  81
  82 ##############################
  83
  84
  85 class WithResidual(nn.Module):
  86     def __init__(self, *f):
  87         super().__init__()
  88         self.f = f[0] if len(f) == 1 else nn.Sequential(*f)
  89
  90     def forward(self, bs):
  91         return BracketedSequence(bs.x + self.f(bs).x, bs.first, bs.nb, bs.init_cache)
  92
  93
  94 ##############################
  95
  96
  97 class AddPositionalEncoding(nn.Module):
  98     def __init__(self, len_max):
  99         super().__init__()
 100         self.len_max = len_max
 101
 102     # [Vaswani et al 2018] PE_{t,2i} = sin(t/(L^{2i/D})), PE_{t,2i+1} = cos(t/(L^{2i/D}))
 103
 104     def forward(self, bs):
 105         if bs.init_cache:
 106             t = torch.arange(bs.x.size(1), dtype=bs.x.dtype, device=bs.x.device)[
 107                 :, None
 108             ]
 109             j = torch.arange(bs.x.size(2), dtype=bs.x.dtype, device=bs.x.device)[
 110                 None, :
 111             ]
 112             k = j % 2
 113             self.pe = torch.sin(
 114                 t / (self.len_max ** ((j - k) / bs.x.size(2))) + math.pi / 2 * k
 115             )
 116             self.cache_y = bs.x.new(bs.x.size())
 117
 118         self.cache_y[:, bs.first : bs.first + bs.nb] = (
 119             bs.slice() + self.pe[bs.first : bs.first + bs.nb]
 120         )
 121
 122         return BracketedSequence(self.cache_y, bs.first, bs.nb, bs.init_cache)
 123
 124
 125 import pscan
 126
 127
 128 # X is /.../xTxD   A is /.../xT   Y_init is /.../xD
 129
 130
 131 def pscan_dim(A, X, Y_init, dim=-2):
 132     s = X.size()
 133     a, T, b = s[:dim].numel(), s[dim], s[dim + 1 :].numel()
 134
 135     A = A.reshape(a, T, *s[dim + 1 : -1])
 136     X = X.reshape(a, T, *s[dim + 1 : -1], -1)
 137
 138     if Y_init is None:
 139         Y_init = X.new_zeros(a, *s[dim + 1 : -1], X.size(-1))
 140     else:
 141         Y_init = Y_init.reshape(a, *s[dim + 1 : -1], -1)
 142
 143     Y = pscan.pscan(A, X, Y_init).reshape(s)
 144
 145     return Y
 146
 147
 148 def pscan_shape(A, X, Y_init):
 149     s = X.size()
 150     A = A.reshape(-1, s[-2])
 151     X = X.reshape(-1, s[-2], s[-1])
 152
 153     if Y_init is None:
 154         Y_init = X.new_zeros(X.size(0), s[-1])
 155     else:
 156         Y_init = Y_init.reshape(-1, s[-1])
 157
 158     Y = pscan.pscan(A, X, Y_init).reshape(s)
 159
 160     return Y
 161
 162
 163 def nsum_shape(X, Y_init):
 164     s = X.size()
 165     X = X.reshape(-1, s[-2], s[-1])  # ntd
 166
 167     Y = 0 if Y_init is None else Y_init.reshape(-1, s[-1])
 168     result = []
 169
 170     for k in range(X.size(1)):
 171         Y = Y + X[:, k]
 172         Y = Y / Y.norm(dim=-1, keepdim=True).clamp(min=1)
 173         result.append(Y)
 174
 175     return torch.cat(result, dim=1).reshape(s)
 176
 177
 178 ##############################
 179
 180
 181 class DumbRec(nn.Module):
 182     def __init__(
 183         self,
 184         dim_model,
 185         dim_qk,
 186         dim_v,
 187         nb_heads,
 188         nb_lines,
 189         attention_dropout=0.0,
 190         len_max=1e5,
 191     ):
 192         super().__init__()
 193
 194         def randw(*d):
 195             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 196
 197         self.nb_lines = nb_lines
 198         self.attention_dropout = attention_dropout
 199
 200         self.k_star = randw(nb_lines, dim_qk)
 201
 202         self.w_qw = randw(nb_heads, dim_qk, dim_model)
 203         self.w_qr = randw(nb_heads, dim_qk, dim_model)
 204         # self.w_k = randw(nb_heads, dim_qk, dim_model)
 205         self.w_v = randw(nb_heads, dim_v, dim_model)
 206         self.w_o = randw(dim_v * nb_heads, dim_model)
 207
 208     def reset_inner_loss(self):
 209         self.acc_attention = 0
 210         self.acc_nb = 0
 211
 212     def get_inner_loss(self):
 213         warnings.warn("l2 regularization", RuntimeWarning)
 214         return (self.acc_attention / self.acc_nb).pow(2).sum()
 215         # return torch.tensor([0], device=self.w_qw.device)
 216
 217     def forward(self, bs):
 218         x_q, t0, t1 = bs.x, bs.first, bs.first + bs.nb
 219
 220         if bs.init_cache:
 221             self.rec_v = x_q.new_zeros(
 222                 x_q.size(0), self.nb_lines, x_q.size(1), self.w_v.size(1)
 223             )
 224             # self.rec_k = x_q.new_zeros(
 225             # x_q.size(0), self.nb_lines, x_q.size(1), self.w_k.size(1)
 226             # )
 227             self.cache_y = x_q.new_zeros(x_q.size(0), x_q.size(1), self.w_o.size(1))
 228
 229         ######################################################################
 230         # Prepare the keys
 231
 232         k_star = self.k_star[:, None, :].expand(-1, t1 - t0, -1)
 233
 234         warnings.warn("rotating key barrel", RuntimeWarning)
 235         k_star = self.k_star[:, None, :].expand(-1, x_q.size(1), -1)
 236         t_barrel = torch.arange(t0, t1, device=k_star.device)
 237         t_barrel = t_barrel[None, :].expand(k_star.size(0), t1 - t0)
 238         l_barrel = (
 239             torch.arange(k_star.size(0), device=k_star.device)[:, None] + t_barrel
 240         ) % k_star.size(0)
 241         k_star = k_star[l_barrel, t_barrel]
 242
 243         ######################################################################
 244         # Compute the recurrent state
 245
 246         qw = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_qw)
 247
 248         v = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_v)
 249         # k = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_k)
 250
 251         aw = torch.einsum(
 252             "nhtd,ltd->nhlt",
 253             qw,
 254             k_star,
 255         ) / math.sqrt(self.w_qw.size(1))
 256
 257         aw = aw.softmax(dim=2)  # nhlt
 258
 259         if self.train:
 260             self.acc_attention += aw.sum(dim=(0, 1, 3))
 261             self.acc_nb += aw.size(0) * aw.size(1) * aw.size(3)
 262
 263         aw = F.dropout(aw, self.attention_dropout, self.training)
 264
 265         A = 1 - aw.sum(dim=1)  # nlt
 266
 267         V = torch.einsum("nhlt,nhtd->nltd", aw, v).contiguous()
 268         # K = torch.einsum("nhlt,nhtd->nltd", aw, k).contiguous()
 269
 270         if t0 == 0:
 271             V0 = None
 272             # K0 = None
 273         else:
 274             V0 = self.rec_v[:, :, t0 - 1]
 275             # K0 = self.rec_k[:, :, t0 - 1]
 276
 277         self.rec_v[:, :, t0:t1] = pscan_shape(A, V, V0)
 278         # self.rec_k[:, :, t0:t1] = pscan_shape(A, K, K0)
 279
 280         ######################################################################
 281         # compute the readout
 282
 283         qr = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_qr)
 284
 285         ar = torch.einsum(
 286             "nhtd,ld->nhlt",
 287             qr,
 288             # self.rec_k[:, :, t0:t1],
 289             self.k_star,
 290         ) / math.sqrt(self.w_qr.size(1))
 291
 292         ar = ar.softmax(dim=2)  # nhlt
 293
 294         ar = F.dropout(ar, self.attention_dropout, self.training)
 295
 296         y = torch.einsum(
 297             "nhlt,nltd->nthd",
 298             ar,
 299             self.rec_v[:, :, t0:t1],
 300         ).flatten(2)
 301
 302         self.cache_y[:, t0:t1] = y @ self.w_o
 303
 304         return BracketedSequence(self.cache_y, t0, t1 - t0, bs.init_cache)
 305
 306
 307 ##############################
 308
 309
 310 class KVRec(nn.Module):
 311     def __init__(
 312         self,
 313         dim_model,
 314         dim_qk,
 315         dim_v,
 316         nb_heads,
 317         nb_lines,
 318         attention_dropout=0.0,
 319         len_max=1e5,
 320     ):
 321         super().__init__()
 322
 323         def randw(*d):
 324             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 325
 326         self.nb_lines = nb_lines
 327         self.attention_dropout = attention_dropout
 328
 329         self.k_star = randw(nb_lines, dim_qk)
 330
 331         self.w_qw = randw(nb_heads, dim_qk, dim_model)
 332         self.w_qr = randw(nb_heads, dim_qk, dim_model)
 333         self.w_k = randw(nb_heads, dim_qk, dim_model)
 334         self.w_v = randw(nb_heads, dim_v, dim_model)
 335         self.w_o = randw(dim_v * nb_heads, dim_model)
 336
 337     def reset_inner_loss(self):
 338         self.acc_attention = 0
 339         self.acc_nb = 0
 340
 341     def get_inner_loss(self):
 342         warnings.warn("l2 regularization", RuntimeWarning)
 343         return (self.acc_attention / self.acc_nb).pow(2).sum()
 344         # return torch.tensor([0], device=self.w_qw.device)
 345         # warnings.warn("side regularization", RuntimeWarning)
 346         # return (
 347         # (0.5 / self.nb_lines - self.acc_attention / self.acc_nb).clamp(min=0).sum()
 348         # )
 349         # return torch.tensor([0], device=self.w_qw.device)
 350
 351     def forward(self, bs):
 352         x_q, t0, t1 = bs.x, bs.first, bs.first + bs.nb
 353
 354         if bs.init_cache:
 355             self.rec_v = x_q.new_zeros(
 356                 x_q.size(0), self.nb_lines, x_q.size(1), self.w_v.size(1)
 357             )
 358             self.rec_k = x_q.new_zeros(
 359                 x_q.size(0), self.nb_lines, x_q.size(1), self.w_k.size(1)
 360             )
 361             self.cache_y = x_q.new_zeros(x_q.size(0), x_q.size(1), self.w_o.size(1))
 362
 363         ######################################################################
 364         # Prepare the keys
 365
 366         k_star = self.k_star[:, None, :].expand(-1, t1 - t0, -1)
 367
 368         warnings.warn("rotating key barrel", RuntimeWarning)
 369         k_star = self.k_star[:, None, :].expand(-1, x_q.size(1), -1)
 370         t_barrel = torch.arange(t0, t1, device=k_star.device)
 371         t_barrel = t_barrel[None, :].expand(k_star.size(0), t1 - t0)
 372         l_barrel = (
 373             torch.arange(k_star.size(0), device=k_star.device)[:, None] + t_barrel
 374         ) % k_star.size(0)
 375         k_star = k_star[l_barrel, t_barrel]
 376
 377         ######################################################################
 378         # Compute the recurrent state
 379
 380         qw = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_qw)
 381
 382         v = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_v)
 383         k = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_k)
 384
 385         aw = torch.einsum(
 386             "nhtd,ltd->nhlt",
 387             qw,
 388             k_star,
 389         ) / math.sqrt(self.w_qw.size(1))
 390
 391         aw = aw.softmax(dim=2)  # nhlt
 392
 393         if self.train:
 394             # We want all the memory lines to be used similarly
 395             self.acc_attention += aw.sum(dim=(0, 1, 3))  # Sum accross NxHx_xT
 396             self.acc_nb += aw.size(0) * aw.size(1) * aw.size(3)
 397
 398         aw = F.dropout(aw, self.attention_dropout, self.training)
 399
 400         A = 1 - aw.sum(dim=1)  # nlt
 401
 402         V = torch.einsum("nhlt,nhtd->nltd", aw, v).contiguous()
 403         K = torch.einsum("nhlt,nhtd->nltd", aw, k).contiguous()
 404
 405         if t0 == 0:
 406             V0 = None
 407             K0 = None
 408         else:
 409             V0 = self.rec_v[:, :, t0 - 1]
 410             K0 = self.rec_k[:, :, t0 - 1]
 411
 412         self.rec_v[:, :, t0:t1] = pscan_shape(A, V, V0)
 413         self.rec_k[:, :, t0:t1] = pscan_shape(A, K, K0)
 414
 415         ######################################################################
 416         # compute the readout
 417
 418         qr = torch.einsum("ntc,hdc->nhtd", x_q[:, t0:t1], self.w_qr)
 419
 420         ar = torch.einsum(
 421             "nhtd,nltd->nhlt",
 422             qr,
 423             self.rec_k[:, :, t0:t1],
 424         ) / math.sqrt(self.w_qr.size(1))
 425
 426         ar = ar.softmax(dim=2)  # nhlt
 427
 428         ar = F.dropout(ar, self.attention_dropout, self.training)
 429
 430         y = torch.einsum(
 431             "nhlt,nltd->nthd",
 432             ar,
 433             self.rec_v[:, :, t0:t1],
 434         ).flatten(2)
 435
 436         self.cache_y[:, t0:t1] = y @ self.w_o
 437
 438         return BracketedSequence(self.cache_y, t0, t1 - t0, bs.init_cache)
 439
 440
 441 ##############################
 442
 443
 444 # Returns a tensor with an additional index at rank win_dim, that move
 445 # along the same dimension as dim, on a domain {0...win_size-1}, and
 446 # dim is restricted on a domain reduced by win_size-1 values.
 447
 448
 449 def moving_window(x, dim, win_dim, win_size):
 450     size, stride = x.size(), x.stride()
 451     size = size[:dim] + (size[dim] - win_size + 1,) + size[dim + 1 :]
 452     size = size[:win_dim] + (win_size,) + size[win_dim:]
 453     stride = stride[:win_dim] + (stride[dim],) + stride[win_dim:]
 454
 455     return x.as_strided(size=size, stride=stride)
 456
 457
 458 ##############################
 459
 460 # This is one order of magnitude more complicated than I expected
 461
 462
 463 def flash_back_time_src(N, H, t0, t1, CL, CH, proba, device):
 464     # starting flash backs
 465     fb_start = (torch.rand(N, CH, t1 - t0, device=device) <= proba).long()
 466     fb_start[:, :, -CL:] = 0
 467     fb_start[:, :, :CL] = 0
 468
 469     # Remove series longer than CL
 470     fb_body = fb_start.clone()
 471     fb_body[:, :, CL + 1 :] -= fb_start[:, :, : -(CL + 1)]
 472     fb_body = fb_body.cumsum(dim=2)
 473     fb_start = fb_start * (fb_body == 1)
 474
 475     # t_s = t0-(t0//L * R)*L
 476
 477     t = torch.arange(fb_start.size(2), device=fb_start.device)[None, None, :]
 478     src_time = fb_start * (
 479         t
 480         - CL
 481         * (
 482             1
 483             + (
 484                 torch.rand(fb_start.size(), device=fb_start.device) * (t // CL - 1)
 485             ).long()
 486         )
 487     )
 488     src_time[:, :, CL:] -= src_time.clone()[:, :, :-CL]
 489     src_time = src_time.cumsum(dim=2)
 490
 491     src_head = fb_start * torch.randint(H, fb_start.size(), device=fb_start.device)
 492     src_head[:, :, CL:] -= src_head.clone()[:, :, :-CL]
 493     src_head = src_head.cumsum(dim=2)
 494
 495     # combine
 496     src_delta = fb_start.clone()
 497     src_delta[:, :, CL:] -= fb_start[:, :, :-CL]
 498     src_delta = src_delta.cumsum(dim=2)
 499     src_delta[:, :, CL:] -= CL * fb_start[:, :, :-CL]
 500     src_time += src_delta.cumsum(dim=2) - 1
 501
 502     return src_time, src_head
 503
 504
 505 def insert_flash_back(rec_V, V, rec_K, K, t0, t1, CL, proba):
 506     N, H, CH = V.size(0), V.size(1), rec_V.size(1)
 507
 508     fbt, fbh = flash_back_time_src(N, H, t0, t1, CL, CH, proba, rec_V.device)
 509
 510     fbt_V = fbt[:, :, :, None].expand_as(rec_V[:, :, t0:t1])
 511     fbh_V = fbh[:, :, :, None].expand_as(rec_V[:, :, t0:t1])
 512     t = fbt_V.clamp(min=0)
 513     n = torch.arange(V.size(0), device=V.device)[:, None, None, None].expand_as(
 514         rec_V[:, :, t0:t1]
 515     )
 516     d = torch.arange(V.size(3), device=V.device)[None, None, None, :].expand_as(
 517         rec_V[:, :, t0:t1]
 518     )
 519     q = V[:, :, t0:t1][n, fbh_V, t, d]
 520     rec_V[:, :, t0:t1] = q * (fbt_V >= 0) + rec_V[:, :, t0:t1] * (fbt_V < 0)
 521
 522     fbt_K = fbt[:, :, :, None].expand_as(rec_K[:, :, t0:t1])
 523     fbh_K = fbh[:, :, :, None].expand_as(rec_K[:, :, t0:t1])
 524     t = fbt_K.clamp(min=0)
 525     n = torch.arange(K.size(0), device=K.device)[:, None, None, None].expand_as(
 526         rec_K[:, :, t0:t1]
 527     )
 528     d = torch.arange(K.size(3), device=K.device)[None, None, None, :].expand_as(
 529         rec_K[:, :, t0:t1]
 530     )
 531     q = K[:, :, t0:t1][n, fbh_K, t, d]
 532     rec_K[:, :, t0:t1] = q * (fbt_K >= 0) + rec_K[:, :, t0:t1] * (fbt_K < 0)
 533
 534     # print("SANITY", (fbt_K >=0).float().sum()/fbt_K.numel())
 535
 536
 537 ######################################################################
 538
 539
 540 class Caterpillar(nn.Module):
 541     def __init__(
 542         self,
 543         dim_model,
 544         dim_qk,
 545         dim_v,
 546         nb_heads,
 547         caterpillar_length,
 548         caterpillar_height,
 549         attention_dropout=0.0,
 550         len_max=1e5,
 551     ):
 552         super().__init__()
 553
 554         warnings.warn("Caterpillar", RuntimeWarning)
 555
 556         def randw(*d):
 557             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 558
 559         self.caterpillar_length = caterpillar_length
 560         self.caterpillar_height = caterpillar_height
 561         self.attention_dropout = attention_dropout
 562
 563         self.w_G = randw(nb_heads, caterpillar_height, dim_model)
 564         self.b_G = nn.Parameter(
 565             torch.full(
 566                 (nb_heads, caterpillar_height), -math.log(caterpillar_height - 1)
 567             )
 568         )
 569
 570         self.w_K = randw(nb_heads, dim_qk, dim_model)
 571         self.w_V = randw(nb_heads, dim_v, dim_model)
 572         self.w_Q = randw(nb_heads, dim_qk, dim_model)
 573         self.w_O = randw(dim_v * nb_heads, dim_model)
 574
 575         self.init_K_rec = randw(caterpillar_height, caterpillar_length, dim_qk)
 576         self.init_V_rec = randw(caterpillar_height, caterpillar_length, dim_v)
 577
 578     def reset_inner_loss(self):
 579         self.acc_attention = 0
 580         self.acc_nb = 0
 581
 582     def get_inner_loss(self):
 583         # warnings.warn("l2 regularization", RuntimeWarning)
 584         # return (self.acc_attention / self.acc_nb).pow(2).sum()
 585         return torch.tensor([0], device=self.w_Q.device)
 586
 587     def forward(self, bs):
 588         # Dimensions to make the source a bit clearer, that's needed
 589
 590         X, t0, t1 = bs.slice(), bs.first, bs.first + bs.nb
 591
 592         N = bs.x.size(0)
 593         T = bs.x.size(1)
 594         DV = self.w_V.size(1)
 595         DK = self.w_K.size(1)
 596         DM = self.w_O.size(1)
 597         CH = self.caterpillar_height
 598         CL = self.caterpillar_length
 599
 600         assert (
 601             t0 >= CL and (t1 - t0) % CL == 0
 602         ), f"bs.first should be greater than caterpillar_length, and bs.nb should be a multiple of caterpillar_length"
 603
 604         # We cache values to deal efficiently with auto-regression
 605
 606         if bs.init_cache:
 607             self.rec_V = X.new_zeros(N, CH, T, DV)
 608             self.rec_K = X.new_zeros(N, CH, T, DK)
 609             # We start the recurrent sequences with optimizable
 610             # initial values. No idea if it helps.
 611             self.rec_V[:, :, t0 - CL : t0] = self.init_V_rec[None, :, :, :]
 612             self.rec_K[:, :, t0 - CL : t0] = self.init_K_rec[None, :, :, :]
 613
 614             self.cache_Y = X.new_zeros(N, T, DM)
 615
 616         ######################################################################
 617         # Compute the recurrent state
 618
 619         # This is the Gating sequence that modulates the storing of
 620         # the new key and value in the CH pairs of the current
 621         # stack. The CH gating values are independent, which means
 622         # that the current K/V could be stored in multiple pairs of the
 623         # recurrent state, or not at all.
 624
 625         G = (
 626             torch.einsum("ntc,hec->nhet", X, self.w_G) + self.b_G[None, :, :, None]
 627         ).sigmoid()
 628
 629         # That bas a bad idea
 630         # G = F.dropout(G, self.attention_dropout, self.training)
 631
 632         V = torch.einsum("ntc,hdc->nhtd", X, self.w_V)
 633         K = torch.einsum("ntc,hdc->nhtd", X, self.w_K)
 634
 635         # We prepare the arguments for the parallel scan
 636
 637         A = 1 - G.sum(1)
 638         gated_V = torch.einsum("nhet,nhtd->netd", G, V)
 639         gated_K = torch.einsum("nhet,nhtd->netd", G, K)
 640
 641         init_rec_V = self.rec_V[:, :, t0 - CL : t0]
 642         init_rec_K = self.rec_K[:, :, t0 - CL : t0]
 643
 644         # Here there is a trick: Since the stack at time t is computed
 645         # by updating that at time t-L, the parallel scan operates
 646         # with a period of L. To do so we split the time indexing in
 647         # two axes, the second of size CL, and run the parallel scan
 648         # using the other as the sequence index.
 649
 650         A = A.unflatten(2, (-1, CL))
 651         gated_V = gated_V.unflatten(2, (-1, CL))
 652         gated_K = gated_K.unflatten(2, (-1, CL))
 653
 654         next_V = pscan_dim(A, gated_V, init_rec_V, dim=2)
 655         next_K = pscan_dim(A, gated_K, init_rec_K, dim=2)
 656
 657         # Put back the sequence index
 658
 659         self.rec_V[:, :, t0:t1] = next_V.flatten(2, 3)
 660         self.rec_K[:, :, t0:t1] = next_K.flatten(2, 3)
 661
 662         warnings.warn("flash back", RuntimeWarning)
 663         if self.training:
 664             insert_flash_back(self.rec_V, V, self.rec_K, K, t0, t1, CL, proba=1e-2 / CL)
 665
 666         ######################################################################
 667         # compute the readout
 668
 669         Q = torch.einsum("ntc,hdc->nhtd", X, self.w_Q)
 670
 671         # We build tensors NxHxTxFxL where N is the sample index, H
 672         # the head, T the time, F the row in the caterpillar, and L
 673         # the column in the caterpillar
 674
 675         windowed_V = moving_window(
 676             self.rec_V[:, :, t0 - CL + 1 : t1], dim=2, win_dim=3, win_size=CL
 677         )
 678
 679         windowed_K = moving_window(
 680             self.rec_K[:, :, t0 - CL + 1 : t1], dim=2, win_dim=3, win_size=CL
 681         )
 682
 683         # We have an attention score for each of the CHxCL values
 684
 685         ar = torch.einsum(
 686             "nhtd,nftld->nhtfl",
 687             Q,
 688             windowed_K,
 689         ) / math.sqrt(DK)
 690
 691         # softmax can operate only on one dimension, hence the
 692         # flattening
 693
 694         ar = ar.flatten(3).softmax(dim=3).view(ar.size())
 695
 696         ar = F.dropout(ar, self.attention_dropout, self.training)
 697
 698         # Compute the output for each head, flatten to concatenate
 699
 700         Y = torch.einsum(
 701             "nhtfl,nftld->nthd",
 702             ar,
 703             windowed_V,
 704         ).flatten(2)
 705
 706         # Compute the final output
 707
 708         self.cache_Y[:, t0:t1] = Y @ self.w_O
 709
 710         return BracketedSequence(self.cache_Y, t0, t1 - t0, bs.init_cache)
 711
 712
 713 ##############################
 714
 715
 716 class QKVAttention(nn.Module):
 717     def __init__(
 718         self,
 719         dim_model,
 720         dim_qk,
 721         dim_v,
 722         nb_heads=1,
 723         causal=False,
 724         attention_dropout=0.0,
 725     ):
 726         super().__init__()
 727
 728         def randw(*d):
 729             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 730
 731         self.causal = causal
 732         self.attention_dropout = attention_dropout
 733         self.record_attention = False
 734
 735         self.w_q = randw(nb_heads, dim_qk, dim_model)
 736         self.w_k = randw(nb_heads, dim_qk, dim_model)
 737         self.w_v = randw(nb_heads, dim_v, dim_model)
 738         self.w_o = randw(dim_v * nb_heads, dim_model)
 739
 740     def forward(self, bs):
 741         x_q = bs.x
 742
 743         assert (
 744             self.causal or bs.complete()
 745         ), "Partial evaluation is only possible for causal models"
 746
 747         if bs.init_cache:
 748             self.cache_k = x_q.new_zeros(
 749                 x_q.size(0), self.w_k.size(0), x_q.size(1), self.w_k.size(1)
 750             )
 751             self.cache_v = x_q.new_zeros(
 752                 x_q.size(0), self.w_v.size(0), x_q.size(1), self.w_v.size(1)
 753             )
 754             self.cache_y = x_q.new_zeros(x_q.size(0), x_q.size(1), self.w_o.size(1))
 755
 756         q = torch.einsum("ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_q)
 757
 758         self.cache_k[:, :, bs.first : bs.first + bs.nb] = torch.einsum(
 759             "ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_k
 760         )
 761         self.cache_v[:, :, bs.first : bs.first + bs.nb] = torch.einsum(
 762             "ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_v
 763         )
 764
 765         a = torch.einsum(
 766             "nhtd,nhsd->nhts", q, self.cache_k[:, :, : bs.first + bs.nb]
 767         ) / math.sqrt(self.w_q.size(1))
 768
 769         if self.causal:
 770             if bs.init_cache:
 771                 self.cache_attzero = (
 772                     torch.arange(x_q.size(1), device=q.device)[None, None, :, None]
 773                     < torch.arange(x_q.size(1), device=q.device)[None, None, None, :]
 774                 )
 775             a = a.masked_fill(
 776                 self.cache_attzero[
 777                     :, :, bs.first : bs.first + bs.nb, : bs.first + bs.nb
 778                 ],
 779                 float("-inf"),
 780             )
 781
 782         a = a.softmax(dim=3)
 783
 784         if self.record_attention:
 785             self.a = a
 786
 787         a = F.dropout(a, self.attention_dropout, self.training)
 788
 789         y = torch.einsum(
 790             "nhts,nhsd->nthd", a, self.cache_v[:, :, : bs.first + bs.nb]
 791         ).flatten(2)
 792
 793         self.cache_y[:, bs.first : bs.first + bs.nb] = y @ self.w_o
 794
 795         return BracketedSequence(self.cache_y, bs.first, bs.nb, bs.init_cache)
 796
 797
 798 ##############################
 799
 800
 801 class MyGPT(nn.Module):
 802     def __init__(
 803         self,
 804         vocabulary_size,
 805         dim_model,
 806         dim_keys,
 807         dim_hidden,
 808         nb_heads,
 809         nb_blocks,
 810         nb_lines=None,
 811         caterpillar_height=None,
 812         dim_rec_v=-1,
 813         causal=False,
 814         dropout=0.0,
 815         len_max=1e5,
 816         attention_layer="kvrec",
 817     ):
 818         super().__init__()
 819
 820         assert attention_layer in {"mha", "dumbrec", "kvrec", "caterpillar"}
 821
 822         if attention_layer == "caterpillar":
 823             assert nb_lines % caterpillar_height == 0
 824             self.caterpillar_length = nb_lines // caterpillar_height
 825             self.caterpillar_height = caterpillar_height
 826         else:
 827             self.caterpillar_length = -1
 828             self.caterpillar_height = -1
 829
 830         assert dim_model % nb_heads == 0
 831
 832         self.embedding = nn.Sequential(
 833             CacheWrapper(nn.Embedding(vocabulary_size, dim_model), nn.Dropout(dropout)),
 834             AddPositionalEncoding(len_max),
 835         )
 836
 837         trunk_blocks = []
 838
 839         def attlayer():
 840             if attention_layer == "mha":
 841                 return QKVAttention(
 842                     dim_model=dim_model,
 843                     dim_qk=dim_keys,
 844                     dim_v=dim_model // nb_heads,
 845                     nb_heads=nb_heads,
 846                     causal=causal,
 847                     attention_dropout=dropout,
 848                 )
 849             elif attention_layer == "dumbrec":
 850                 return DumbRec(
 851                     dim_model=dim_model,
 852                     dim_qk=dim_keys,
 853                     dim_v=dim_rec_v,
 854                     nb_heads=nb_heads,
 855                     nb_lines=nb_lines,
 856                     attention_dropout=dropout,
 857                 )
 858             elif attention_layer == "kvrec":
 859                 return KVRec(
 860                     dim_model=dim_model,
 861                     dim_qk=dim_keys,
 862                     dim_v=dim_rec_v,
 863                     nb_heads=nb_heads,
 864                     nb_lines=nb_lines,
 865                     attention_dropout=dropout,
 866                 )
 867             elif attention_layer == "caterpillar":
 868                 return Caterpillar(
 869                     dim_model=dim_model,
 870                     dim_qk=dim_keys,
 871                     dim_v=dim_rec_v,
 872                     nb_heads=nb_heads,
 873                     caterpillar_length=self.caterpillar_length,
 874                     caterpillar_height=self.caterpillar_height,
 875                     attention_dropout=dropout,
 876                 )
 877             else:
 878                 raise ValueError(f"Unknown attention type {attention_layer}.")
 879
 880         for b in range(nb_blocks):
 881             trunk_blocks += [
 882                 WithResidual(
 883                     CacheWrapper(nn.LayerNorm((dim_model,))),
 884                     attlayer(),
 885                 ),
 886                 WithResidual(
 887                     CacheWrapper(
 888                         nn.LayerNorm((dim_model,)),
 889                         nn.Linear(in_features=dim_model, out_features=dim_hidden),
 890                         nn.ReLU(),
 891                         nn.Linear(in_features=dim_hidden, out_features=dim_model),
 892                         nn.Dropout(dropout),
 893                     ),
 894                 ),
 895             ]
 896
 897         self.trunk = nn.Sequential(*trunk_blocks)
 898
 899         self.readout = CacheWrapper(
 900             nn.Linear(in_features=dim_model, out_features=vocabulary_size)
 901         )
 902
 903         with torch.no_grad():
 904             for m in self.modules():
 905                 if isinstance(m, nn.Embedding):
 906                     m.weight.normal_(mean=0, std=2e-2)
 907                 elif isinstance(m, nn.LayerNorm):
 908                     m.bias.zero_()
 909                     m.weight.fill_(1.0)
 910
 911         self.reset_inner_loss()
 912
 913     def forward(self, bs):
 914         bs = BracketedSequence(F.pad(bs.x, (1, -1)), bs.first, bs.nb, bs.init_cache)
 915
 916         # To make the code simpler in the Caterpillar layer, we pad
 917         # here. It's unclear if/how much it hurts computationaly by
 918         # increasing the sequence length for the other layers
 919
 920         if self.caterpillar_length > 0:
 921             original_nb = bs.nb
 922             if bs.nb % self.caterpillar_length > 0:
 923                 bs.nb += self.caterpillar_length - bs.nb % self.caterpillar_length
 924
 925             bs = BracketedSequence(
 926                 F.pad(bs.x, (self.caterpillar_length, self.caterpillar_length)),
 927                 bs.first + self.caterpillar_length,
 928                 bs.nb,
 929                 bs.init_cache,
 930             )
 931
 932         bs = self.embedding(bs)
 933         bs = self.trunk(bs)
 934         bs = self.readout(bs)
 935
 936         if self.caterpillar_length > 0:
 937             bs = BracketedSequence(
 938                 F.pad(bs.x, (0, 0, -self.caterpillar_length, -self.caterpillar_length)),
 939                 bs.first - self.caterpillar_length,
 940                 original_nb,
 941                 bs.init_cache,
 942             )
 943
 944         return bs
 945
 946     # ar_mask is a tensor with 0s and 1s, of same shape as input, with
 947     # 1s where tokens should be generated. The others are kept
 948     # unchanged.
 949
 950     def masked_inplace_autoregression(
 951         self,
 952         input_src,
 953         ar_mask_src,
 954         forbidden_tokens=None,
 955         deterministic_synthesis=False,
 956     ):
 957         input = input_src.to(self.readout.f.weight.device)
 958         ar_mask = ar_mask_src.to(self.readout.f.weight.device)
 959         to_generate = (ar_mask.sum(0) > 0).nonzero()
 960         if to_generate.min() > 0:
 961             self(
 962                 BracketedSequence(input, 0, to_generate.min(), True)
 963             )  # Needed to initialize the model's cache
 964         for s in range(to_generate.min(), to_generate.max() + 1):
 965             output = self(BracketedSequence(input, s, 1, s == 0)).x
 966             logits = output[:, s]
 967             if forbidden_tokens is not None:
 968                 logits = logits.masked_fill(forbidden_tokens, float("-inf"))
 969             if deterministic_synthesis:
 970                 t_next = logits.argmax(1)
 971             else:
 972                 dist = torch.distributions.categorical.Categorical(logits=logits)
 973                 t_next = dist.sample()
 974             input[:, s] = ar_mask[:, s] * t_next + (1 - ar_mask[:, s]) * input[:, s]
 975
 976         input_src.copy_(input)
 977
 978     def reset_inner_loss(self):
 979         for m in self.modules():
 980             if m is not self and hasattr(m, "reset_inner_loss"):
 981                 m.reset_inner_loss()
 982
 983     def get_inner_loss(self):
 984         l = torch.tensor([0.0], device=self.readout.f.weight.device)
 985         for m in self.modules():
 986             if m is not self and hasattr(m, "get_inner_loss"):
 987                 l += m.get_inner_loss()
 988         return l
 989
 990     def record_attention(self, v=True):
 991         for m in self.modules():
 992             if isinstance(m, QKVAttention):
 993                 m.record_attention = v
 994
 995     def retrieve_attention(self):
 996         a = []
 997         for m in self.modules():
 998             if isinstance(m, QKVAttention):
 999                 a.append(m.a)
1000         return a
1001
1002
1003 ######################################################################
1004
1005 if __name__ == "__main__":
1006     print("Basic check.")
1007
1008     m = Caterpillar(
1009         dim_model=4,
1010         dim_qk=3,
1011         dim_v=7,
1012         nb_heads=1,
1013         caterpillar_length=7,
1014         caterpillar_height=3,
1015         attention_dropout=0.0,
1016     )
1017
1018     m.reset_inner_loss()
1019     x = torch.randn(1, 21 + 2 * 7, 4)
1020     y1 = m(BracketedSequence(x, first=7, nb=21, init_cache=True)).x[:, 7:28]
1021     y2 = m(BracketedSequence(x, first=7, nb=21, init_cache=True)).x[:, 7:28]
1022     y3a = m(BracketedSequence(x, first=7, nb=14, init_cache=True)).x[:, 7:21]
1023     y3b = m(BracketedSequence(x, first=21, nb=7, init_cache=False)).x[:, 21:28]
1024     print((y1 - y2).abs().max())
1025     print((y1 - torch.cat([y3a, y3b], dim=1)).abs().max())
1026     exit(0)
1027
1028     device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
1029
1030     vocabulary_size = 128
1031     x = torch.randint(vocabulary_size, (6, 1024))
1032
1033     model = MyGPT(
1034         vocabulary_size=vocabulary_size,
1035         dim_model=512,
1036         dim_keys=64,
1037         dim_hidden=2048,
1038         nb_heads=8,
1039         nb_lines=128,
1040         nb_blocks=12,
1041         dropout=0.1,
1042         causal=True,
1043     )
1044
1045     x = x.to(device)
1046     model.to(device)
1047
1048     import time, sys
1049
1050     # import torchvision.models as models
1051     # from torch.profiler import profile, record_function, ProfilerActivity
1052
1053     # with profile(activities=[ProfilerActivity.CPU,  ProfilerActivity.CUDA], profile_memory=True, record_shapes=True) as prof:
1054     # with record_function("model_inference"):
1055
1056     model.eval()
1057     for i in range(3):
1058         start_time = time.perf_counter()
1059         for k in range(10):
1060             model(BracketedSequence(x))
1061         duration = time.perf_counter() - start_time
1062         print(duration)
1063         sys.stdout.flush()
1064
1065     # print(prof.key_averages().table(sort_by="cpu_time_total", row_limit=10))
1066     # print(prof.key_averages().table(sort_by="cuda_time_total", row_limit=10))
1067
1068     # print("##############################################################")
1069     # y2 = torch.randn_like(y1)
1070     # for s in range(x.size(1)):
1071     # z = model(BracketedSequence(x, s, 1))
1072     # y2[:, s : s + 1] = z.slice()
1073
1074     # print(f"error={((y1 - y2).norm() / (y1.norm() + y2.norm())).item()}")
1075
1076 ######################################################################