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