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, amplitude=None):
 480             if amplitude is None:
 481                 amplitude = 1 / math.sqrt(d[-1])
 482             return nn.Parameter(amplitude * torch.randn(*d))
 483
 484         self.caterpillar_length = caterpillar_length
 485         self.caterpillar_height = caterpillar_height
 486         self.attention_dropout = attention_dropout
 487
 488         self.proba_gate_dropout = 0.0
 489
 490         self.w_G = randw(nb_heads, caterpillar_height, dim_model)
 491         self.b_G = nn.Parameter(
 492             torch.full(
 493                 (nb_heads, caterpillar_height), -math.log(caterpillar_height - 1)
 494             )
 495         )
 496
 497         self.w_K = randw(nb_heads, dim_qk, dim_model)
 498         self.w_V = randw(nb_heads, dim_v, dim_model)
 499         self.w_Q = randw(nb_heads, dim_qk, dim_model)
 500         self.w_O = randw(dim_v * nb_heads, dim_model)
 501
 502         self.init_K_rec = randw(
 503             caterpillar_height,
 504             caterpillar_length,
 505             dim_qk,
 506         )
 507         self.init_V_rec = randw(
 508             caterpillar_height,
 509             caterpillar_length,
 510             dim_v,
 511         )
 512
 513     def reset_inner_loss(self):
 514         self.acc_attention = 0
 515         self.acc_nb = 0
 516
 517     def get_inner_loss(self):
 518         # warnings.warn("l2 regularization", RuntimeWarning)
 519         # return (self.acc_attention / self.acc_nb).pow(2).sum()
 520         return torch.tensor([0], device=self.w_Q.device)
 521
 522     def forward(self, bs):
 523         # Dimensions to make the source a bit clearer, that's needed
 524
 525         X, t0, t1 = bs.slice(), bs.first, bs.first + bs.nb
 526
 527         N = bs.x.size(0)
 528         T = bs.x.size(1)
 529         H = self.w_V.size(0)
 530         DV = self.w_V.size(1)
 531         DK = self.w_K.size(1)
 532         DM = self.w_O.size(1)
 533         R = self.caterpillar_height
 534         L = self.caterpillar_length
 535
 536         assert (
 537             t0 >= L and (t1 - t0) % L == 0
 538         ), f"bs.first should be greater than caterpillar_length, and bs.nb should be a multiple of caterpillar_length"
 539
 540         # We cache values to deal efficiently with auto-regression
 541
 542         if bs.init_cache:
 543             self.rec_V = X.new_zeros(N, R, T, DV)
 544             self.rec_K = X.new_zeros(N, R, T, DK)
 545             # We start the recurrent sequences with optimizable
 546             # initial values. No idea if it helps.
 547             self.rec_V[:, :, t0 - L : t0] = self.init_V_rec[None, :, :, :]
 548             self.rec_K[:, :, t0 - L : t0] = self.init_K_rec[None, :, :, :]
 549
 550             self.cache_Y = X.new_zeros(N, T, DM)
 551
 552         V = torch.einsum("ntc,hdc->nhtd", X, self.w_V)
 553         K = torch.einsum("ntc,hdc->nhtd", X, self.w_K)
 554
 555         ######################################################################
 556         # Compute the recurrent state
 557
 558         # This is the Gating sequence that modulates the storing of
 559         # the new key and value in the R pairs of the current
 560         # stack. There are R independent gating values, which means
 561         # that the current K/V may be stored in multiple pairs of the
 562         # recurrent state, or not at all.
 563
 564         G = (
 565             torch.einsum("ntc,hrc->nhrt", X, self.w_G) + self.b_G[None, :, :, None]
 566         ).sigmoid()
 567
 568         ######################################################################
 569         # Roll the gating indexes
 570
 571         warnings.warn("rotating barrel", RuntimeWarning)
 572         n_barrel = torch.arange(N, device=G.device)[:, None, None, None]
 573         h_barrel = torch.arange(H, device=G.device)[None, :, None, None]
 574         r_barrel = torch.arange(R, device=G.device)[None, None, :, None]
 575         t_barrel = torch.arange(t1 - t0, device=G.device)[None, None, None, :]
 576         r_barrel = (r_barrel + t_barrel + t0) % R
 577
 578         # print(f"({N}, {H}, {R}, {t1-t0}) {G.size()=}")
 579
 580         G = G[n_barrel, h_barrel, r_barrel, t_barrel]
 581
 582         # print(G.sum())
 583
 584         ######################################################################
 585         # The "flashbacks"
 586
 587         if self.training and self.proba_gate_dropout > 0.0:
 588             # This is a better implementation of "flashbacks".
 589
 590             # G is NxHxExT where e is the caterpillar's row.
 591
 592             warnings.warn("gate dropout", RuntimeWarning)
 593             epsilon = 0.5
 594
 595             dropout_head = (
 596                 (torch.rand(N, H, 1, t1 - t0, device=G.device).sort(dim=3).indices == 0)
 597                 .expand_as(G)
 598                 .float()
 599             )
 600
 601             dropout_tail = dropout_head.cumsum(dim=3) - dropout_head
 602
 603             dropout_active = (
 604                 torch.rand(N, 1, 1, 1, device=G.device) < self.proba_gate_dropout
 605             ).long()
 606
 607             dropout_head *= dropout_active
 608             dropout_tail *= dropout_active
 609
 610             G = (
 611                 G
 612                 + dropout_head * (1 - epsilon - G.detach())
 613                 - dropout_tail * G.detach()
 614             )
 615
 616         ######################################################################
 617
 618         # We prepare the arguments for the parallel scan
 619
 620         # Clip the gating to avoid values greater than 1 when several
 621         # heads hit the same row
 622
 623         G = G / G.sum(1, keepdim=True).clamp(min=1)
 624
 625         A = 1 - G.sum(1)
 626
 627         # warnings.warn("harmonic recurrence", RuntimeWarning)
 628         # har = torch.arange(t0, t1, device = G.device).float() + 1
 629         # A = har / (har + 1)
 630         # G = G / har
 631
 632         gated_V = torch.einsum("nhrt,nhtd->nrtd", G, V)
 633         gated_K = torch.einsum("nhrt,nhtd->nrtd", G, K)
 634
 635         # We start from cached values, which matters in inference
 636
 637         init_rec_V = self.rec_V[:, :, t0 - L : t0]
 638         init_rec_K = self.rec_K[:, :, t0 - L : t0]
 639
 640         #################################################################
 641         # Associative scan
 642
 643         # Here there is a trick: Since the stack at position t is
 644         # computed by updating that at position t-L, the parallel
 645         # scan operates with a period of L. To do so we split the
 646         # sequence indexing in two axes, the second of size L, and
 647         # run the parallel scan using the first as the sequence index.
 648
 649         A = A.unflatten(2, (-1, L))
 650         gated_V = gated_V.unflatten(2, (-1, L))
 651         gated_K = gated_K.unflatten(2, (-1, L))
 652
 653         next_V = pscan_dim(A, gated_V, init_rec_V, dim=2)
 654         next_K = pscan_dim(A, gated_K, init_rec_K, dim=2)
 655
 656         self.rec_V[:, :, t0:t1] = next_V.flatten(2, 3)
 657         self.rec_K[:, :, t0:t1] = next_K.flatten(2, 3)
 658
 659         ######################################################################
 660         # compute the readout
 661
 662         Q = torch.einsum("ntc,hdc->nhtd", X, self.w_Q)
 663
 664         # We build tensors NxHxTxFxL where N is the sample index, H
 665         # the head, T the time, F the row in the caterpillar, and L
 666         # the column in the caterpillar
 667
 668         windowed_V = moving_window(
 669             self.rec_V[:, :, t0 - L + 1 : t1], dim=2, win_dim=3, win_size=L
 670         )
 671
 672         windowed_K = moving_window(
 673             self.rec_K[:, :, t0 - L + 1 : t1], dim=2, win_dim=3, win_size=L
 674         )
 675
 676         # We have an attention score for each of the RxL values
 677
 678         ar = torch.einsum(
 679             "nhtd,nftld->nhtfl",
 680             Q,
 681             windowed_K,
 682         ) / math.sqrt(DK)
 683
 684         # softmax can operate only on one dimension, hence the
 685         # flattening
 686
 687         ar = ar.flatten(3).softmax(dim=3).view(ar.size())
 688
 689         ar = F.dropout(ar, self.attention_dropout, self.training)
 690
 691         # Compute the output for each head, flatten to concatenate
 692
 693         Y = torch.einsum(
 694             "nhtfl,nftld->nthd",
 695             ar,
 696             windowed_V,
 697         ).flatten(2)
 698
 699         # Compute the final output
 700
 701         self.cache_Y[:, t0:t1] = Y @ self.w_O
 702
 703         return BracketedSequence(self.cache_Y, t0, t1 - t0, bs.init_cache)
 704
 705
 706 ##############################
 707
 708
 709 class QKVAttention(nn.Module):
 710     def __init__(
 711         self,
 712         dim_model,
 713         dim_qk,
 714         dim_v,
 715         nb_heads=1,
 716         causal=False,
 717         attention_dropout=0.0,
 718     ):
 719         super().__init__()
 720
 721         def randw(*d):
 722             return nn.Parameter(torch.randn(*d) / math.sqrt(d[-1]))
 723
 724         self.causal = causal
 725         self.attention_dropout = attention_dropout
 726         self.record_attention = False
 727
 728         self.w_q = randw(nb_heads, dim_qk, dim_model)
 729         self.w_k = randw(nb_heads, dim_qk, dim_model)
 730         self.w_v = randw(nb_heads, dim_v, dim_model)
 731         self.w_o = randw(dim_v * nb_heads, dim_model)
 732
 733     def forward(self, bs):
 734         x_q = bs.x
 735
 736         assert (
 737             self.causal or bs.complete()
 738         ), "Partial evaluation is only possible for causal models"
 739
 740         if bs.init_cache:
 741             self.cache_k = x_q.new_zeros(
 742                 x_q.size(0), self.w_k.size(0), x_q.size(1), self.w_k.size(1)
 743             )
 744             self.cache_v = x_q.new_zeros(
 745                 x_q.size(0), self.w_v.size(0), x_q.size(1), self.w_v.size(1)
 746             )
 747             self.cache_y = x_q.new_zeros(x_q.size(0), x_q.size(1), self.w_o.size(1))
 748
 749         q = torch.einsum("ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_q)
 750
 751         self.cache_k[:, :, bs.first : bs.first + bs.nb] = torch.einsum(
 752             "ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_k
 753         )
 754         self.cache_v[:, :, bs.first : bs.first + bs.nb] = torch.einsum(
 755             "ntc,hdc->nhtd", x_q[:, bs.first : bs.first + bs.nb], self.w_v
 756         )
 757
 758         a = torch.einsum(
 759             "nhtd,nhsd->nhts", q, self.cache_k[:, :, : bs.first + bs.nb]
 760         ) / math.sqrt(self.w_q.size(1))
 761
 762         if self.causal:
 763             if bs.init_cache:
 764                 self.cache_attzero = (
 765                     torch.arange(x_q.size(1), device=q.device)[None, None, :, None]
 766                     < torch.arange(x_q.size(1), device=q.device)[None, None, None, :]
 767                 )
 768             a = a.masked_fill(
 769                 self.cache_attzero[
 770                     :, :, bs.first : bs.first + bs.nb, : bs.first + bs.nb
 771                 ],
 772                 float("-inf"),
 773             )
 774
 775         a = a.softmax(dim=3)
 776
 777         if self.record_attention:
 778             self.a = a
 779
 780         a = F.dropout(a, self.attention_dropout, self.training)
 781
 782         y = torch.einsum(
 783             "nhts,nhsd->nthd", a, self.cache_v[:, :, : bs.first + bs.nb]
 784         ).flatten(2)
 785
 786         self.cache_y[:, bs.first : bs.first + bs.nb] = y @ self.w_o
 787
 788         return BracketedSequence(self.cache_y, bs.first, bs.nb, bs.init_cache)
 789
 790
 791 ##############################
 792
 793
 794 class MyGPT(nn.Module):
 795     def __init__(
 796         self,
 797         vocabulary_size,
 798         dim_model,
 799         dim_keys,
 800         dim_hidden,
 801         nb_heads,
 802         nb_blocks,
 803         nb_lines=None,
 804         caterpillar_height=None,
 805         causal=False,
 806         dropout=0.0,
 807         len_max=1e5,
 808         attention_layer="kvrec",
 809     ):
 810         super().__init__()
 811
 812         assert attention_layer in {
 813             "mha",
 814             "dumbrec",
 815             "kvrec",
 816             "caterpillar",
 817         }, f"Unknown attention operator {attention_layer}."
 818
 819         if attention_layer == "caterpillar":
 820             assert nb_lines % caterpillar_height == 0
 821             self.caterpillar_length = nb_lines // caterpillar_height
 822             self.caterpillar_height = caterpillar_height
 823         else:
 824             self.caterpillar_length = -1
 825             self.caterpillar_height = -1
 826
 827         assert dim_model % nb_heads == 0
 828
 829         self.embedding = nn.Sequential(
 830             CacheWrapper(nn.Embedding(vocabulary_size, dim_model), nn.Dropout(dropout)),
 831             AddPositionalEncoding(len_max),
 832         )
 833
 834         trunk_blocks = []
 835
 836         def attlayer():
 837             if attention_layer == "mha":
 838                 return QKVAttention(
 839                     dim_model=dim_model,
 840                     dim_qk=dim_keys,
 841                     dim_v=dim_model // nb_heads,
 842                     nb_heads=nb_heads,
 843                     causal=causal,
 844                     attention_dropout=dropout,
 845                 )
 846             elif attention_layer == "dumbrec":
 847                 return DumbRec(
 848                     dim_model=dim_model,
 849                     dim_qk=dim_keys,
 850                     dim_v=dim_model // nb_heads,
 851                     nb_heads=nb_heads,
 852                     nb_lines=nb_lines,
 853                     attention_dropout=dropout,
 854                 )
 855             elif attention_layer == "kvrec":
 856                 return KVRec(
 857                     dim_model=dim_model,
 858                     dim_qk=dim_keys,
 859                     dim_v=dim_model // nb_heads,
 860                     nb_heads=nb_heads,
 861                     nb_lines=nb_lines,
 862                     attention_dropout=dropout,
 863                 )
 864             elif attention_layer == "caterpillar":
 865                 return Caterpillar(
 866                     dim_model=dim_model,
 867                     dim_qk=dim_keys,
 868                     dim_v=dim_model // nb_heads,
 869                     nb_heads=nb_heads,
 870                     caterpillar_length=self.caterpillar_length,
 871                     caterpillar_height=self.caterpillar_height,
 872                     attention_dropout=dropout,
 873                 )
 874             else:
 875                 raise ValueError(f"Unknown attention type {attention_layer}.")
 876
 877         for b in range(nb_blocks):
 878             trunk_blocks += [
 879                 WithResidual(
 880                     CacheWrapper(nn.LayerNorm((dim_model,))),
 881                     attlayer(),
 882                 ),
 883                 WithResidual(
 884                     CacheWrapper(
 885                         nn.LayerNorm((dim_model,)),
 886                         nn.Linear(in_features=dim_model, out_features=dim_hidden),
 887                         nn.ReLU(),
 888                         nn.Linear(in_features=dim_hidden, out_features=dim_model),
 889                         nn.Dropout(dropout),
 890                     ),
 891                 ),
 892             ]
 893
 894         self.trunk = nn.Sequential(*trunk_blocks)
 895
 896         self.readout = CacheWrapper(
 897             nn.Linear(in_features=dim_model, out_features=vocabulary_size)
 898         )
 899
 900         with torch.no_grad():
 901             for m in self.modules():
 902                 if isinstance(m, nn.Embedding):
 903                     m.weight.normal_(mean=0, std=2e-2)
 904                 elif isinstance(m, nn.LayerNorm):
 905                     m.bias.zero_()
 906                     m.weight.fill_(1.0)
 907
 908         self.reset_inner_loss()
 909
 910     def forward(self, bs):
 911         bs = BracketedSequence(F.pad(bs.x, (1, -1)), bs.first, bs.nb, bs.init_cache)
 912
 913         # To make the code simpler in the Caterpillar layer, we pad
 914         # here. It's unclear if/how much it hurts computationaly by
 915         # increasing the sequence length for the other layers
 916
 917         if self.caterpillar_length > 0:
 918             original_nb = bs.nb
 919             if bs.nb % self.caterpillar_length > 0:
 920                 bs.nb += self.caterpillar_length - bs.nb % self.caterpillar_length
 921
 922             bs = BracketedSequence(
 923                 F.pad(bs.x, (self.caterpillar_length, self.caterpillar_length)),
 924                 bs.first + self.caterpillar_length,
 925                 bs.nb,
 926                 bs.init_cache,
 927             )
 928
 929         bs = self.embedding(bs)
 930         bs = self.trunk(bs)
 931         bs = self.readout(bs)
 932
 933         if self.caterpillar_length > 0:
 934             bs = BracketedSequence(
 935                 F.pad(bs.x, (0, 0, -self.caterpillar_length, -self.caterpillar_length)),
 936                 bs.first - self.caterpillar_length,
 937                 original_nb,
 938                 bs.init_cache,
 939             )
 940
 941         return bs
 942
 943     # ar_mask is a tensor with 0s and 1s, of same shape as input, with
 944     # 1s where tokens should be generated. The others are kept
 945     # unchanged.
 946
 947     def masked_inplace_autoregression(
 948         self,
 949         input_src,
 950         ar_mask_src,
 951         forbidden_tokens=None,
 952         deterministic_synthesis=False,
 953     ):
 954         input = input_src.to(self.readout.f.weight.device)
 955         ar_mask = ar_mask_src.to(self.readout.f.weight.device)
 956         to_generate = (ar_mask.sum(0) > 0).nonzero()
 957         if to_generate.min() > 0:
 958             self(
 959                 BracketedSequence(input, 0, to_generate.min(), True)
 960             )  # Needed to initialize the model's cache
 961         for s in range(to_generate.min(), to_generate.max() + 1):
 962             output = self(BracketedSequence(input, s, 1, s == 0)).x
 963             logits = output[:, s]
 964             if forbidden_tokens is not None:
 965                 logits = logits.masked_fill(forbidden_tokens, float("-inf"))
 966             if deterministic_synthesis:
 967                 t_next = logits.argmax(1)
 968             else:
 969                 dist = torch.distributions.categorical.Categorical(logits=logits)
 970                 t_next = dist.sample()
 971             input[:, s] = ar_mask[:, s] * t_next + (1 - ar_mask[:, s]) * input[:, s]
 972
 973         input_src.copy_(input)
 974
 975     def reset_inner_loss(self):
 976         for m in self.modules():
 977             if m is not self and hasattr(m, "reset_inner_loss"):
 978                 m.reset_inner_loss()
 979
 980     def get_inner_loss(self):
 981         l = torch.tensor([0.0], device=self.readout.f.weight.device)
 982         for m in self.modules():
 983             if m is not self and hasattr(m, "get_inner_loss"):
 984                 l += m.get_inner_loss()
 985         return l
 986
 987     def record_attention(self, v=True):
 988         for m in self.modules():
 989             if isinstance(m, QKVAttention):
 990                 m.record_attention = v
 991
 992     def retrieve_attention(self):
 993         a = []
 994         for m in self.modules():
 995             if isinstance(m, QKVAttention):
 996                 a.append(m.a)
 997         return a
 998
 999
1000 ######################################################################
1001
1002 if __name__ == "__main__":
1003     print("Basic check.")
1004
1005     m = Caterpillar(
1006         dim_model=4,
1007         dim_qk=3,
1008         dim_v=7,
1009         nb_heads=1,
1010         caterpillar_length=7,
1011         caterpillar_height=3,
1012         attention_dropout=0.0,
1013     )
1014
1015     m.reset_inner_loss()
1016     x = torch.randn(1, 21 + 2 * 7, 4)
1017     y1 = m(BracketedSequence(x, first=7, nb=21, init_cache=True)).x[:, 7:28]
1018     y2 = m(BracketedSequence(x, first=7, nb=21, init_cache=True)).x[:, 7:28]
1019     y3a = m(BracketedSequence(x, first=7, nb=14, init_cache=True)).x[:, 7:21]
1020     y3b = m(BracketedSequence(x, first=21, nb=7, init_cache=False)).x[:, 21:28]
1021     print((y1 - y2).abs().max())
1022     print((y1 - torch.cat([y3a, y3b], dim=1)).abs().max())
1023     exit(0)
1024
1025     device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
1026
1027     vocabulary_size = 128
1028     x = torch.randint(vocabulary_size, (6, 1024))
1029
1030     model = MyGPT(
1031         vocabulary_size=vocabulary_size,
1032         dim_model=512,
1033         dim_keys=64,
1034         dim_hidden=2048,
1035         nb_heads=8,
1036         nb_lines=128,
1037         nb_blocks=12,
1038         dropout=0.1,
1039         causal=True,
1040     )
1041
1042     x = x.to(device)
1043     model.to(device)
1044
1045     import time, sys
1046
1047     # import torchvision.models as models
1048     # from torch.profiler import profile, record_function, ProfilerActivity
1049
1050     # with profile(activities=[ProfilerActivity.CPU,  ProfilerActivity.CUDA], profile_memory=True, record_shapes=True) as prof:
1051     # with record_function("model_inference"):
1052
1053     model.eval()
1054     for i in range(3):
1055         start_time = time.perf_counter()
1056         for k in range(10):
1057             model(BracketedSequence(x))
1058         duration = time.perf_counter() - start_time
1059         print(duration)
1060         sys.stdout.flush()
1061
1062     # print(prof.key_averages().table(sort_by="cpu_time_total", row_limit=10))
1063     # print(prof.key_averages().table(sort_by="cuda_time_total", row_limit=10))
1064
1065     # print("##############################################################")
1066     # y2 = torch.randn_like(y1)
1067     # for s in range(x.size(1)):
1068     # z = model(BracketedSequence(x, s, 1))
1069     # y2[:, s : s + 1] = z.slice()
1070
1071     # print(f"error={((y1 - y2).norm() / (y1.norm() + y2.norm())).item()}")
1072
1073 ######################################################################