-
Notifications
You must be signed in to change notification settings - Fork 4
/
nn_models.py
742 lines (613 loc) · 47.1 KB
/
nn_models.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch_geometric.nn import global_add_pool
from torch_geometric.nn.conv import MessagePassing
from torch_geometric.nn.inits import reset
from torch_geometric.utils import remove_self_loops
import numpy as np
from torch.nn import Sequential as Seq, Linear, ReLU
from utils import neg_inf_to_zero, shift_func
import math
import time
from parameters import LN_ZERO
import json
# from bpnn_model import FactorGraphMsgPassingLayer_NoDoubleCounting
# from bpnn_model_partialRefactorNoBeliefRepeats import FactorGraphMsgPassingLayer_NoDoubleCounting
USE_OLD_CODE = False
if USE_OLD_CODE:
from bpnn_model_partialRefactorNoBeliefRepeats import FactorGraphMsgPassingLayer_NoDoubleCounting
# from bpnn_model_partialRefactor import FactorGraphMsgPassingLayer_NoDoubleCounting
from bpnn_model_clean import logsumexp_multipleDim
else:
from bpnn_model_clean import FactorGraphMsgPassingLayer_NoDoubleCounting, logsumexp_multipleDim
from parameters import alpha2
import time
class lbp_message_passing_network(nn.Module):
def __init__(self, max_factor_state_dimensions, msg_passing_iters, lne_mlp, use_MLP1, use_MLP2, use_MLP3, use_MLP4, use_MLP5, use_MLP6, use_MLP_EQUIVARIANT,
subtract_prv_messages, share_weights, bethe_MLP,
belief_repeats=None, var_cardinality=None, learn_bethe_residual_weight=False,
initialize_to_exact_bethe = True, alpha_damping_FtoV=None, alpha_damping_VtoF=None, use_old_bethe=None,
APPLY_BP_POST_BPNN=False, APPLY_BP_EVERY_ITER=False, BPNN_layers_per_shared_weight_layer=1,
USE_MLP_DAMPING_FtoV=False, USE_MLP_DAMPING_VtoF=False, learn_initial_messages=False):
'''
Inputs:
- max_factor_state_dimensions (int): the number of dimensions (variables) the largest factor have.
-> will have states space of size 2*max_factor_state_dimensions
- msg_passing_iters (int): the number of iterations of message passing to run (we have this many
message passing layers with their own learnable parameters)
- lne_mlp (bool): if True message passing mlps operate in standard space rather than log space
- use_MLP1 (bool): one of the original MLPs that operate on factor beliefs (problematic because they're not index invariant)
- use_MLP2 (bool): one of the original MLPs that operate on factor beliefs (problematic because they're not index invariant)
- use_MLP3 (bool): one of the new MLPs that operate on variable beliefs
- use_MLP4 (bool): one of the new MLPs that operate on variable beliefs
- use_MLP5/use_MLP6 (bool): new MLPs that adds to factor belief, should maintains belief consistency upon convergence
- use_MLP_EQUIVARIANT (bool): new MLP that adds to factor belief, should maintain belief consistency upon convergence, indexing equivariant for factors of cardinality 2
- subtract_prv_messages (bool): if true, subtract previously sent messages (to avoid 'double counting')
- share_weights (bool): if true, share the same weights across each message passing iteration
- bethe_MLP (string): ['shifted','standard','linear','none']
if 'none', then use the standard bethe approximation with no learning.
otherwise, use an MLP to learn a modified Bethe approximation where this argument
describes (potential) non linearities in the MLP
- learn_bethe_residual_weight (bool): if True, (and bethe_MLP is true) learn use the bethe_MLP
to predict the residual between then Bethe approximation and the exact partition function
- initialize_to_exact_bethe (bool): if True initialize the bethe_MLP to perform exact computation
of the bethe approximation (for beliefs from the last round of message passing). may make
training worse. should be False if learn_bethe_residual_weight=True
- APPLY_BP_POST_BPNN (bool): if True, apply standard BP message passing iterations (no learned MLPs) after BPNN layers
- APPLY_BP_EVERY_ITER (bool): if True, apply a standard BP message passing interation (no learned MLPS) after every shared weight BPNN layer
- BPNN_layers_per_shared_weight_layer (int): apply this many BP layers (with different weights) in every shared weight layer
- learn_initial_messages (bool): if true, make initial beliefs and messages learnable parameters (currently expects a fixed batch size, hard coded)
'''
super().__init__()
self.share_weights = share_weights
self.msg_passing_iters = msg_passing_iters
self.bethe_MLP = bethe_MLP
self.belief_repeats = belief_repeats
self.learn_bethe_residual_weight = learn_bethe_residual_weight
self.use_old_bethe = use_old_bethe
self.APPLY_BP_POST_BPNN = APPLY_BP_POST_BPNN
self.APPLY_BP_EVERY_ITER = APPLY_BP_EVERY_ITER
self.learn_initial_messages = learn_initial_messages
if learn_initial_messages:
self.prv_factor_beliefs = torch.nn.Parameter(torch.log(torch.rand([280, 1, 2, 2])))
self.prv_factorToVar_messages = torch.nn.Parameter(torch.log(torch.rand([460, 1, 2])))
self.prv_varToFactor_messages = torch.nn.Parameter(torch.log(torch.rand([460, 1, 2])))
print("self.prv_varToFactor_messages:", torch.exp(self.prv_varToFactor_messages))
# self.prv_factor_beliefs = torch.nn.Parameter(torch.zeros([280, 1, 2, 2]))
# self.prv_factorToVar_messages = torch.nn.Parameter(torch.zeros([460, 1, 2]))
# self.prv_varToFactor_messages = torch.nn.Parameter(torch.zeros([460, 1, 2]))
if learn_bethe_residual_weight:
self.alpha_betheMLP = torch.nn.Parameter(alpha2*torch.ones(1))
assert(initialize_to_exact_bethe == False), "Set initialize_to_exact_bethe=False when learn_bethe_residual_weight=True"
if USE_OLD_CODE:
if share_weights:
self.message_passing_layer = FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions)
else:
self.message_passing_layers = nn.ModuleList([FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions)\
for i in range(msg_passing_iters)])
else:
if share_weights:
# self.message_passing_layer = FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions,
# var_cardinality=var_cardinality, belief_repeats=belief_repeats, lne_mlp=lne_mlp, use_MLP1=use_MLP1, use_MLP2=use_MLP2,
# use_MLP3=use_MLP3, use_MLP4=use_MLP4, subtract_prv_messages=subtract_prv_messages, alpha_damping_FtoV=alpha_damping_FtoV, alpha_damping_VtoF=alpha_damping_VtoF)
self.message_passing_layers = nn.ModuleList([\
FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions,
var_cardinality=var_cardinality, belief_repeats=belief_repeats, lne_mlp=lne_mlp, use_MLP1=use_MLP1, use_MLP2=use_MLP2,
use_MLP3=use_MLP3, use_MLP4=use_MLP4, use_MLP5=use_MLP5, use_MLP6=use_MLP6, use_MLP_EQUIVARIANT=use_MLP_EQUIVARIANT,\
subtract_prv_messages=subtract_prv_messages, alpha_damping_FtoV=alpha_damping_FtoV, alpha_damping_VtoF=alpha_damping_VtoF,\
USE_MLP_DAMPING_FtoV=USE_MLP_DAMPING_FtoV, USE_MLP_DAMPING_VtoF=USE_MLP_DAMPING_VtoF)
for i in range(BPNN_layers_per_shared_weight_layer)])
self.fixed_BP_layer = FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions,
var_cardinality=var_cardinality, belief_repeats=belief_repeats, lne_mlp=lne_mlp, use_MLP1=False, use_MLP2=False,
use_MLP3=False, use_MLP4=False, use_MLP5=False, use_MLP6=False, use_MLP_EQUIVARIANT=False, subtract_prv_messages=True, alpha_damping_FtoV=alpha_damping_FtoV, alpha_damping_VtoF=alpha_damping_VtoF)
else:
self.message_passing_layers = nn.ModuleList([\
FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions,
var_cardinality=var_cardinality, belief_repeats=belief_repeats, lne_mlp=lne_mlp, use_MLP1=use_MLP1, use_MLP2=use_MLP2,
use_MLP3=use_MLP3, use_MLP4=use_MLP4, use_MLP5=use_MLP5, use_MLP6=use_MLP6, use_MLP_EQUIVARIANT=use_MLP_EQUIVARIANT, subtract_prv_messages=subtract_prv_messages, alpha_damping_FtoV=alpha_damping_FtoV, alpha_damping_VtoF=alpha_damping_VtoF)\
for i in range(msg_passing_iters)])
self.convergence_BPNN_layer = FactorGraphMsgPassingLayer_NoDoubleCounting(learn_BP=True, factor_state_space=2**max_factor_state_dimensions,
var_cardinality=var_cardinality, belief_repeats=belief_repeats, lne_mlp=lne_mlp, use_MLP1=False, use_MLP2=False,
use_MLP3=False, use_MLP4=False, use_MLP5=True, use_MLP6=True, use_MLP_EQUIVARIANT=False, subtract_prv_messages=True, alpha_damping_FtoV=alpha_damping_FtoV, alpha_damping_VtoF=alpha_damping_VtoF)
if bethe_MLP != 'none':
var_cardinality = var_cardinality #2 for binary variables
num_ones = belief_repeats*(2*(var_cardinality**max_factor_state_dimensions)+var_cardinality)
mlp_size = msg_passing_iters*num_ones
# self.final_mlp = Seq(Linear(mlp_size, mlp_size), ReLU(), Linear(mlp_size, 1))
self.linear1 = Linear(mlp_size, mlp_size)
self.linear2 = Linear(mlp_size, 1)
if initialize_to_exact_bethe:
# print("self.linear1.weight:", self.linear1.weight)
# print("self.linear1.bias:", self.linear1.bias)
# self.linear1.weight *= .001
# print("self.linear1.weight:", self.linear1.weight)
# sleep(alsfdjlksadjflks)
self.linear1.weight = torch.nn.Parameter(torch.eye(mlp_size))
self.linear1.bias = torch.nn.Parameter(torch.zeros(self.linear1.bias.shape))
weight_initialization = torch.zeros((1,mlp_size))
weight_initialization[0,-num_ones:] = 1.0/belief_repeats
# print("self.linear2.weight:", self.linear2.weight)
# print("self.linear2.weight.shape:", self.linear2.weight.shape)
# print("weight_initialization:", weight_initialization)
self.linear2.weight = torch.nn.Parameter(weight_initialization)
self.linear2.bias = torch.nn.Parameter(torch.zeros(self.linear2.bias.shape))
if bethe_MLP == 'shifted':
self.shifted_relu = shift_func(ReLU(), shift=-500)
self.final_mlp = Seq(self.linear1, self.shifted_relu, self.linear2, self.shifted_relu)
elif bethe_MLP == 'standard':
self.final_mlp = Seq(self.linear1, ReLU(), self.linear2, ReLU())
elif bethe_MLP == 'linear':
self.final_mlp = Seq(self.linear1, self.linear2)
else:
assert(False), "Error: invalid value given for bethe_MLP"
def forward(self, factor_graph, random_message_init_every_iter=False, PLOT_CONVERGENCE=False):
# prv_varToFactor_messages, prv_factorToVar_messages, prv_factor_beliefs, prv_var_beliefs = factor_graph.get_initial_beliefs_and_messages(device=self.device)
if self.learn_initial_messages:
prv_varToFactor_messages = self.prv_varToFactor_messages
prv_factorToVar_messages = self.prv_factorToVar_messages
prv_factor_beliefs_temp = self.prv_factor_beliefs
prv_factor_beliefs = prv_factor_beliefs_temp.clone()
prv_factor_beliefs[torch.where(factor_graph.factor_potential_masks==1)] = LN_ZERO
else:
if random_message_init_every_iter:
prv_varToFactor_messages = torch.log(torch.rand_like(factor_graph.prv_varToFactor_messages))
prv_factorToVar_messages = torch.log(torch.rand_like(factor_graph.prv_factorToVar_messages))
prv_factor_beliefs = torch.log(torch.rand_like(factor_graph.prv_factor_beliefs))
prv_factor_beliefs[torch.where(factor_graph.factor_potential_masks==1)] = LN_ZERO
# prv_varToFactor_messages = torch.clamp(prv_varToFactor_messages, min=np.exp(LN_ZERO))
# prv_factorToVar_messages = torch.clamp(prv_factorToVar_messages, min=np.exp(LN_ZERO))
# prv_factor_beliefs = torch.clamp(prv_factor_beliefs, min=np.exp(LN_ZERO))
else:
prv_varToFactor_messages = factor_graph.prv_varToFactor_messages
prv_factorToVar_messages = factor_graph.prv_factorToVar_messages
prv_factor_beliefs = factor_graph.prv_factor_beliefs
# print("prv_factor_beliefs.shape:", prv_factor_beliefs.shape)
# print("prv_factorToVar_messages.shape:", prv_factorToVar_messages.shape)
# print("prv_varToFactor_messages.shape:", prv_varToFactor_messages.shape)
# sleep(temp)
# print("factor_graph.facToVar_edge_idx.shape:", factor_graph.facToVar_edge_idx.shape)
pooled_states = []
if self.share_weights:
# for iter in range(self.msg_passing_iters):
random_msg_passing_iters = np.random.randint(5, 30)
# random_msg_passing_iters = np.random.randint(20, 50)
# random_msg_passing_iters = 200
# print()
# print("random_msg_passing_iters =", random_msg_passing_iters)
if PLOT_CONVERGENCE:
norm_per_isingmodel_vTOf_perIterList = []
norm_per_isingmodel_fTOv_perIterList = []
max_per_isingmodel_vTOf_perIterList = []
max_per_isingmodel_fTOv_perIterList = []
for iter in range(random_msg_passing_iters):
single_layer = False
if single_layer:
varToFactor_messages, factorToVar_messages, var_beliefs, factor_beliefs =\
self.message_passing_layer(factor_graph, prv_varToFactor_messages=prv_varToFactor_messages,
prv_factorToVar_messages=prv_factorToVar_messages, prv_factor_beliefs=prv_factor_beliefs,
iter=iter)
else:
tmp_varToFactor_messages = prv_varToFactor_messages
tmp_factorToVar_messages = prv_factorToVar_messages
tmp_factor_beliefs = prv_factor_beliefs
for message_passing_layer in self.message_passing_layers:
tmp_varToFactor_messages, tmp_factorToVar_messages, tmp_var_beliefs, tmp_factor_beliefs =\
message_passing_layer(factor_graph, prv_varToFactor_messages=tmp_varToFactor_messages,
prv_factorToVar_messages=tmp_factorToVar_messages, prv_factor_beliefs=tmp_factor_beliefs,
iter=iter)
varToFactor_messages = tmp_varToFactor_messages
factorToVar_messages = tmp_factorToVar_messages
var_beliefs = tmp_var_beliefs
factor_beliefs = tmp_factor_beliefs
prv_prv_varToFactor_messages = prv_varToFactor_messages
prv_prv_factorToVar_messages = prv_factorToVar_messages
prv_varToFactor_messages = varToFactor_messages
prv_factorToVar_messages = factorToVar_messages
prv_var_beliefs = var_beliefs
prv_factor_beliefs = factor_beliefs
if PLOT_CONVERGENCE:
message_count = 460#25 #10 # 10
batch_size=50
norm_per_isingmodel_vTOf = torch.norm((prv_prv_varToFactor_messages - prv_varToFactor_messages).view([batch_size, message_count*self.belief_repeats*2]), dim=1, p=2)
norm_per_isingmodel_fTOv = torch.norm((prv_prv_factorToVar_messages - prv_factorToVar_messages).view([batch_size, message_count*self.belief_repeats*2]), dim=1, p=2)
max_per_isingmodel_vTOf = torch.max(torch.abs(prv_prv_varToFactor_messages - prv_varToFactor_messages).view([batch_size, message_count*self.belief_repeats*2]), dim=1)[0]
max_per_isingmodel_fTOv = torch.max(torch.abs(prv_prv_factorToVar_messages - prv_factorToVar_messages).view([batch_size, message_count*self.belief_repeats*2]), dim=1)[0]
norm_per_isingmodel_vTOf_perIterList.append(norm_per_isingmodel_vTOf)
norm_per_isingmodel_fTOv_perIterList.append(norm_per_isingmodel_fTOv)
max_per_isingmodel_vTOf_perIterList.append(max_per_isingmodel_vTOf)
max_per_isingmodel_fTOv_perIterList.append(max_per_isingmodel_fTOv)
if self.APPLY_BP_EVERY_ITER:
# random_BP_iters = np.random.randint(0, 20)
# print("applying BP :)!!!!!!!")
random_BP_iters = 1
for BP_iter in range(random_BP_iters):
varToFactor_messages, factorToVar_messages, var_beliefs, factor_beliefs =\
self.fixed_BP_layer(factor_graph, prv_varToFactor_messages=prv_varToFactor_messages,
prv_factorToVar_messages=prv_factorToVar_messages, prv_factor_beliefs=prv_factor_beliefs, iter=-1)
prv_prv_varToFactor_messages = prv_varToFactor_messages
prv_prv_factorToVar_messages = prv_factorToVar_messages
prv_varToFactor_messages = varToFactor_messages
prv_factorToVar_messages = factorToVar_messages
prv_var_beliefs = var_beliefs
prv_factor_beliefs = factor_beliefs
if self.bethe_MLP != 'none':
cur_pooled_states = self.compute_bethe_free_energy_pooledStates_MLP(factor_beliefs=prv_factor_beliefs, var_beliefs=prv_var_beliefs, factor_graph=factor_graph)
pooled_states.append(cur_pooled_states)
if PLOT_CONVERGENCE:
norm_per_isingmodel_vTOf_perIterList = torch.stack(norm_per_isingmodel_vTOf_perIterList).permute(1,0).tolist()
norm_per_isingmodel_fTOv_perIterList = torch.stack(norm_per_isingmodel_fTOv_perIterList).permute(1,0).tolist()
max_per_isingmodel_vTOf_perIterList = torch.stack(max_per_isingmodel_vTOf_perIterList).permute(1,0).tolist()
max_per_isingmodel_fTOv_perIterList = torch.stack(max_per_isingmodel_fTOv_perIterList).permute(1,0).tolist()
data_to_save = (norm_per_isingmodel_vTOf_perIterList, norm_per_isingmodel_fTOv_perIterList, max_per_isingmodel_vTOf_perIterList, max_per_isingmodel_fTOv_perIterList)
# with open('./plot_convergence/BPNN_convergence_info.txt', 'w') as outfile:
with open('./plot_convergence/BP_convergence_info.txt', 'w') as outfile:
json.dump(data_to_save, outfile)
print("len(norm_per_isingmodel_vTOf_perIterList):", len(norm_per_isingmodel_vTOf_perIterList))
sleep(slkdfjlksdjfs)
if self.APPLY_BP_POST_BPNN:
#apply BP for a random number of iterations
#goal is to get consistency between variable and factor beleifs
# random_fixed_BP_iters = np.random.randint(1, 30)
random_fixed_BP_iters = 90
# random_msg_passing_iters = 5
for iter in range(random_fixed_BP_iters):
varToFactor_messages, factorToVar_messages, var_beliefs, factor_beliefs =\
self.fixed_BP_layer(factor_graph, prv_varToFactor_messages=prv_varToFactor_messages,
prv_factorToVar_messages=prv_factorToVar_messages, prv_factor_beliefs=prv_factor_beliefs, iter=-1)
prv_prv_varToFactor_messages = prv_varToFactor_messages
prv_prv_factorToVar_messages = prv_factorToVar_messages
prv_varToFactor_messages = varToFactor_messages
prv_factorToVar_messages = factorToVar_messages
prv_var_beliefs = var_beliefs
prv_factor_beliefs = factor_beliefs
# print('iter:', iter)
# print("from nn_models torch.max(prv_prv_factorToVar_messages - prv_factorToVar_messages):", torch.max(prv_prv_factorToVar_messages - prv_factorToVar_messages))
# print("from nn_models torch.max(prv_prv_varToFactor_messages - prv_varToFactor_messages):", torch.max(prv_prv_varToFactor_messages - prv_varToFactor_messages))
else:
for message_passing_layer in self.message_passing_layers:
# print("prv_varToFactor_messages:", prv_varToFactor_messages)
# print("prv_factorToVar_messages:", prv_factorToVar_messages)
# print("prv_factor_beliefs:", prv_factor_beliefs)
# print("prv_varToFactor_messages.shape:", prv_varToFactor_messages.shape)
# print("prv_factorToVar_messages.shape:", prv_factorToVar_messages.shape)
# print("prv_factor_beliefs.shape:", prv_factor_beliefs.shape)
# prv_factor_beliefs[torch.where(prv_factor_beliefs==-np.inf)] = 0
prv_prv_varToFactor_messages = prv_varToFactor_messages
prv_prv_factorToVar_messages = prv_factorToVar_messages
prv_varToFactor_messages, prv_factorToVar_messages, prv_var_beliefs, prv_factor_beliefs =\
message_passing_layer(factor_graph, prv_varToFactor_messages=prv_varToFactor_messages,
prv_factorToVar_messages=prv_factorToVar_messages, prv_factor_beliefs=prv_factor_beliefs, iter=-1)
# message_passing_layer(factor_graph, prv_varToFactor_messages=factor_graph.prv_varToFactor_messages,
# prv_factorToVar_messages=factor_graph.prv_factorToVar_messages, prv_factor_beliefs=factor_graph.prv_factor_beliefs)
if self.bethe_MLP != 'none':
cur_pooled_states = self.compute_bethe_free_energy_pooledStates_MLP(factor_beliefs=prv_factor_beliefs, var_beliefs=prv_var_beliefs, factor_graph=factor_graph)
# print("cur_pooled_states:", cur_pooled_states)
# print(check_pool)
# print("cur_pooled_states.shape:", cur_pooled_states.shape)
pooled_states.append(cur_pooled_states)
QUICK_TEST = False
if QUICK_TEST:
random_iters = np.random.randint(10, 30)
for iter in range(random_iters):
varToFactor_messages, factorToVar_messages, var_beliefs, factor_beliefs =\
self.convergence_BPNN_layer(factor_graph, prv_varToFactor_messages=prv_varToFactor_messages,
prv_factorToVar_messages=prv_factorToVar_messages, prv_factor_beliefs=prv_factor_beliefs, iter=-1)
prv_prv_varToFactor_messages = prv_varToFactor_messages
prv_prv_factorToVar_messages = prv_factorToVar_messages
prv_varToFactor_messages = varToFactor_messages
prv_factorToVar_messages = factorToVar_messages
prv_var_beliefs = var_beliefs
prv_factor_beliefs = factor_beliefs
if self.bethe_MLP != 'none':
# print("torch.min(pooled_states):", torch.min(torch.cat(pooled_states, dim=1)))
# print("torch.max(pooled_states):", torch.max(torch.cat(pooled_states, dim=1)))
# print("torch.mean(pooled_states):", torch.mean(torch.cat(pooled_states, dim=1)))
learned_estimated_ln_partition_function = self.final_mlp(torch.cat(pooled_states, dim=1))
if self.learn_bethe_residual_weight:
final_pooled_states = self.compute_bethe_free_energy_pooledStates_MLP(factor_beliefs=prv_factor_beliefs, var_beliefs=prv_var_beliefs, factor_graph=factor_graph)
bethe_estimated_ln_partition_function = torch.sum(final_pooled_states, dim=1)
final_estimate = (1-self.alpha_betheMLP)*learned_estimated_ln_partition_function.squeeze() +\
self.alpha_betheMLP*bethe_estimated_ln_partition_function.squeeze()
# print("bethe_estimated_ln_partition_function.shape:", bethe_estimated_ln_partition_function.shape)
# print("learned_estimated_ln_partition_function.shape:", learned_estimated_ln_partition_function.shape)
# print("final_estimate.shape:", final_estimate.shape)
return final_estimate
else:
return learned_estimated_ln_partition_function
else:
if self.use_old_bethe:
# print("prv_factor_beliefs.shape:", prv_factor_beliefs.shape)
# print("prv_var_beliefs.shape:", prv_var_beliefs.shape)
# print("factor_graph.factor_potentials.shape:", factor_graph.factor_potentials.shape)
# sleep(asdlfkjsdlkf)
#broken for batch_size > 1
bethe_free_energy = compute_bethe_free_energy(factor_beliefs=prv_factor_beliefs.squeeze(), var_beliefs=prv_var_beliefs.squeeze(), factor_graph=factor_graph)
estimated_ln_partition_function = -bethe_free_energy
# print("prv_factor_beliefs.squeeze():", prv_factor_beliefs.squeeze())
# print("prv_var_beliefs.squeeze():", prv_var_beliefs.squeeze())
# print("factor_graph.factor_potentials.squeeze():", factor_graph.factor_potentials.squeeze())
# print("factor_graph.numVars:", factor_graph.numVars)
# print("factor_graph.var_degrees:", factor_graph.var_degrees)
# print("estimated_ln_partition_function:", estimated_ln_partition_function)
# sleep(nn_models_debug_alsfj)
debug=False
if debug:
final_pooled_states = self.compute_bethe_free_energy_pooledStates_MLP(factor_beliefs=prv_factor_beliefs, var_beliefs=prv_var_beliefs, factor_graph=factor_graph)
check_estimated_ln_partition_function = torch.sum(final_pooled_states)
# print("check_estimated_ln_partition_function:", check_estimated_ln_partition_function)
# print("estimated_ln_partition_function:", estimated_ln_partition_function)
# sleep(debug_bethe)
assert(torch.allclose(check_estimated_ln_partition_function, estimated_ln_partition_function)), (check_estimated_ln_partition_function, estimated_ln_partition_function)
return estimated_ln_partition_function
#corrected for batch_size > 1
# print(prv_factor_beliefs.shape)
final_pooled_states = self.compute_bethe_free_energy_pooledStates_MLP(factor_beliefs=prv_factor_beliefs, var_beliefs=prv_var_beliefs, factor_graph=factor_graph)
# print(final_pooled_states.shape)
# sleep(asldkfj)
estimated_ln_partition_function = torch.sum(final_pooled_states, dim=1)/self.belief_repeats
return estimated_ln_partition_function, prv_prv_varToFactor_messages, prv_prv_factorToVar_messages, prv_varToFactor_messages, prv_factorToVar_messages
# return estimated_ln_partition_function
def compute_bethe_average_energy_MLP(self, factor_beliefs, factor_potentials, batch_factors, debug=False):
'''
Equation (37) in:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
assert(factor_potentials.shape == factor_beliefs.shape), (factor_potentials.shape, factor_beliefs.shape)
if debug:
print()
print('!!!!!!!')
print("debugging compute_bethe_average_energy")
print("torch.exp(factor_beliefs):", torch.exp(factor_beliefs))
print("neg_inf_to_zero(factor_potentials):", neg_inf_to_zero(factor_potentials))
pooled_fac_beleifPotentials = global_add_pool(torch.exp(factor_beliefs)*neg_inf_to_zero(factor_potentials), batch_factors)
#keep 1st dimension for # of factors, but flatten remaining dimensions for belief_repeats and each factor
pooled_fac_beleifPotentials = pooled_fac_beleifPotentials.view(pooled_fac_beleifPotentials.shape[0], -1)
if debug:
factor_beliefs_shape = factor_beliefs.shape
pooled_fac_beleifPotentials_orig = torch.sum((torch.exp(factor_beliefs)*neg_inf_to_zero(factor_potentials)).view(factor_beliefs_shape[0], -1), dim=0)
print("original pooled_fac_beleifPotentials_orig:", pooled_fac_beleifPotentials_orig)
print("pooled_fac_beleifPotentials:", pooled_fac_beleifPotentials)
print("factor_beliefs.shape:", factor_beliefs.shape)
print("pooled_fac_beleifPotentials_orig.shape:", pooled_fac_beleifPotentials_orig.shape)
print("pooled_fac_beleifPotentials.shape:", pooled_fac_beleifPotentials.shape)
print("(torch.exp(factor_beliefs)*neg_inf_to_zero(factor_potentials)).view(factor_beliefs_shape[0], -1).shape:", (torch.exp(factor_beliefs)*neg_inf_to_zero(factor_potentials)).view(factor_beliefs_shape[0], -1).shape)
return pooled_fac_beleifPotentials #negate and sum to get average bethe energy
def compute_bethe_entropy_MLP(self, factor_beliefs, var_beliefs, numVars, var_degrees, batch_factors, batch_vars, debug=False):
'''
Equation (38) in:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
pooled_fac_beliefs = -global_add_pool(torch.exp(factor_beliefs)*neg_inf_to_zero(factor_beliefs), batch_factors)
#keep 1st dimension for # of factors, but flatten remaining dimensions for belief_repeats and each factor
pooled_fac_beliefs = pooled_fac_beliefs.view(pooled_fac_beliefs.shape[0], -1)
if debug:
factor_beliefs_shape = factor_beliefs.shape
pooled_fac_beliefs_orig = -torch.sum((torch.exp(factor_beliefs)*neg_inf_to_zero(factor_beliefs)).view(factor_beliefs_shape[0], -1), dim=0)
print("pooled_fac_beliefs_orig:", pooled_fac_beliefs_orig)
print("pooled_fac_beliefs:", pooled_fac_beliefs)
var_beliefs_shape = var_beliefs.shape
assert(var_beliefs_shape[0] == var_degrees.shape[0])
pooled_var_beliefs = global_add_pool(torch.exp(var_beliefs)*neg_inf_to_zero(var_beliefs)*(var_degrees.float() - 1).view(var_degrees.shape[0], 1, 1), batch_vars)
#keep 1st dimension for # of factors, but flatten remaining dimensions for belief_repeats and variable states
pooled_var_beliefs = pooled_var_beliefs.view(pooled_var_beliefs.shape[0], -1)
if debug:
pooled_var_beliefs_orig = torch.sum(torch.exp(var_beliefs)*neg_inf_to_zero(var_beliefs)*(var_degrees.float() - 1).view(var_beliefs_shape[0], -1), dim=0)
print("pooled_var_beliefs_orig:", pooled_var_beliefs_orig)
print("pooled_var_beliefs:", pooled_var_beliefs)
# sleep(SHAPECHECK)
return pooled_fac_beliefs, pooled_var_beliefs
def compute_bethe_free_energy_pooledStates_MLP(self, factor_beliefs, var_beliefs, factor_graph):
'''
Compute the Bethe approximation of the free energy.
- free energy = -ln(Z)
where Z is the partition function
- (Bethe approximation of the free energy) = (Bethe average energy) - (Bethe entropy)
For more details, see page 11 of:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
# print("var_beliefs.shape:", var_beliefs.shape)
# print("factor_beliefs.shape:", factor_beliefs.shape)
#switch to Temp=False/remove me after generalized to handle repeated beliefs!
TEMP=False
if TEMP:
var_beliefs = torch.mean(var_beliefs, dim=1) #remove me after generalized to handle repeated beliefs!
factor_beliefs = torch.mean(factor_beliefs, dim=1) #remove me after generalized to handle repeated beliefs!
normalized_var_beliefs = var_beliefs - logsumexp_multipleDim(var_beliefs, dim_to_keep=[0])#normalize variable beliefs
# print("normalized_var_beliefs.shape:", normalized_var_beliefs.shape)
check_normalization = torch.sum(torch.exp(normalized_var_beliefs), dim=[i for i in range(1,len(var_beliefs.shape))])
# print("check_normalization.shape:", check_normalization.shape)
# print("check_normalization:", check_normalization)
assert(torch.max(torch.abs(check_normalization-1)) < .001), (torch.sum(torch.abs(check_normalization-1)), torch.max(torch.abs(check_normalization-1)), check_normalization)
normalized_factor_beliefs = factor_beliefs - logsumexp_multipleDim(factor_beliefs, dim_to_keep=[0])#normalize factor beliefs
check_normalization = torch.sum(torch.exp(normalized_factor_beliefs), dim=[i for i in range(1,len(factor_beliefs.shape))])
# print("normalized_factor_beliefs.shape:", normalized_factor_beliefs.shape)
# print("check_normalization.shape:", check_normalization.shape)
# print("check_normalization:", check_normalization)
# print()
assert(torch.max(torch.abs(check_normalization-1)) < .00001), (torch.sum(torch.abs(check_normalization-1)), torch.max(torch.abs(check_normalization-1)), check_normalization)
else:
normalized_var_beliefs = var_beliefs - logsumexp_multipleDim(var_beliefs, dim_to_keep=[0,1])#normalize variable beliefs
# print("normalized_var_beliefs.shape:", normalized_var_beliefs.shape)
check_normalization = torch.sum(torch.exp(normalized_var_beliefs), dim=[i for i in range(2,len(var_beliefs.shape))])
# print("check_normalization.shape:", check_normalization.shape)
# print("check_normalization:", check_normalization)
# print("var_beliefs[torch.where(torch.abs(check_normalization-1)) >= .00001)]:", var_beliefs[torch.where(torch.abs(check_normalization-1) >= .00001)])
assert(torch.max(torch.abs(check_normalization-1)) < .01), (torch.sum(torch.abs(check_normalization-1)), torch.max(torch.abs(check_normalization-1)), check_normalization, var_beliefs)
# print("factor_beliefs.shape:", factor_beliefs.shape)
normalized_factor_beliefs = factor_beliefs - logsumexp_multipleDim(factor_beliefs, dim_to_keep=[0,1])#normalize factor beliefs
check_normalization = torch.sum(torch.exp(normalized_factor_beliefs), dim=[i for i in range(2,len(factor_beliefs.shape))])
CHECK_CONSISTENCY = False
if CHECK_CONSISTENCY:
print("normalized_factor_beliefs:", normalized_factor_beliefs)
print("unary factor beliefs:", normalized_factor_beliefs[:10,:,:,0])
print("normalized_var_beliefs:", normalized_var_beliefs[:10,::])
print("normalized_factor_beliefs.shape:", normalized_factor_beliefs.shape)
print("normalized_var_beliefs.shape:", normalized_var_beliefs.shape)
# sleep(temp)
# assert(normalized_var_beliefs)
# print("normalized_factor_beliefs.shape:", normalized_factor_beliefs.shape)
# print("check_normalization.shape:", check_normalization.shape)
# print("check_normalization:", check_normalization)
# print()
assert(torch.max(torch.abs(check_normalization-1)) < .01), (torch.sum(torch.abs(check_normalization-1)), torch.max(torch.abs(check_normalization-1)), check_normalization)
# print("normalized_var_beliefs.shape:", normalized_var_beliefs.shape)
# print("factor_beliefs.shape:", factor_beliefs.shape)
# sleep(salfjlsdkj)
# print("self.compute_bethe_average_energy():", self.compute_bethe_average_energy())
# print("self.compute_bethe_entropy():", self.compute_bethe_entropy())
if torch.isnan(normalized_factor_beliefs).any():
print("values, some should be nan:")
for val in normalized_factor_beliefs.flatten():
print(val)
assert(not torch.isnan(normalized_factor_beliefs).any()), (normalized_factor_beliefs, torch.where(normalized_factor_beliefs == torch.tensor(float('nan'))), torch.where(normalized_var_beliefs == torch.tensor(float('nan'))))
assert(not torch.isnan(normalized_var_beliefs).any()), normalized_var_beliefs
if TEMP:
#quick option for not dealing with repeated beliefs
factor_potentials_quick = factor_graph.factor_potentials[:, 0, ::]
factor_potentials_check = torch.mean(factor_graph.factor_potentials, dim=1, keepdim=False)
assert(torch.max(torch.abs(factor_potentials_quick - factor_potentials_check)) < .00001), (factor_potentials_quick, factor_potentials_check, torch.max(torch.abs(factor_potentials_quick - factor_potentials_check)))
else:
factor_potentials_quick = factor_graph.factor_potentials
pooled_fac_beleifPotentials = self.compute_bethe_average_energy_MLP(factor_beliefs=normalized_factor_beliefs,\
factor_potentials=factor_potentials_quick, batch_factors=factor_graph.batch_factors)
pooled_fac_beliefs, pooled_var_beliefs = self.compute_bethe_entropy_MLP(factor_beliefs=normalized_factor_beliefs, var_beliefs=normalized_var_beliefs, numVars=torch.sum(factor_graph.numVars), var_degrees=factor_graph.var_degrees, batch_factors=factor_graph.batch_factors, batch_vars=factor_graph.batch_vars)
# print("pooled_fac_beleifPotentials.shape:", pooled_fac_beleifPotentials.shape)
# print("pooled_fac_beliefs.shape:", pooled_fac_beliefs.shape)
# print("pooled_var_beliefs.shape:", pooled_var_beliefs.shape)
# print("factor_graph.factor_potentials.shape:", factor_graph.factor_potentials.shape)
# sleep(laskdjfowin)
if len(pooled_fac_beleifPotentials.shape) > 1:
cat_dim = 1
else:
cat_dim = 0
return torch.cat([pooled_fac_beleifPotentials, pooled_fac_beliefs, pooled_var_beliefs], dim=cat_dim)
def compute_bethe_average_energy(factor_beliefs, factor_potentials, debug=False):
'''
Equation (37) in:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
assert(factor_potentials.shape == factor_beliefs.shape)
if debug:
print()
print('!!!!!!!')
print("debugging compute_bethe_average_energy")
print("torch.exp(factor_beliefs):", torch.exp(factor_beliefs))
print("neg_inf_to_zero(factor_potentials):", neg_inf_to_zero(factor_potentials))
bethe_average_energy = -torch.sum(torch.exp(factor_beliefs)*neg_inf_to_zero(factor_potentials)) #elementwise multiplication, then sum
# print("bethe_average_energy:", bethe_average_energy)
return bethe_average_energy
def compute_bethe_entropy(factor_beliefs, var_beliefs, numVars, var_degrees):
'''
Equation (38) in:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
bethe_entropy = -torch.sum(torch.exp(factor_beliefs)*neg_inf_to_zero(factor_beliefs)) #elementwise multiplication, then sum
# print("numVars:", numVars)
assert(var_beliefs.shape == torch.Size([numVars, 2])), (var_beliefs.shape, [numVars, 2])
# sum_{x_i} b_i(x_i)*ln(b_i(x_i))
inner_sum = torch.einsum('ij,ij->i', [torch.exp(var_beliefs), neg_inf_to_zero(var_beliefs)])
# sum_{i=1}^N (d_i - 1)*inner_sum
outer_sum = torch.sum((var_degrees.float() - 1) * inner_sum)
# outer_sum = torch.einsum('i,i->', [var_degrees - 1, inner_sum])
bethe_entropy += outer_sum
# print("bethe_entropy:", bethe_entropy)
return bethe_entropy
def compute_bethe_free_energy(factor_beliefs, var_beliefs, factor_graph):
'''
BROKEN FOR BATCH SIZE > 1
Compute the Bethe approximation of the free energy.
- free energy = -ln(Z)
where Z is the partition function
- (Bethe approximation of the free energy) = (Bethe average energy) - (Bethe entropy)
For more details, see page 11 of:
https://www.cs.princeton.edu/courses/archive/spring06/cos598C/papers/YedidaFreemanWeiss2004.pdf
'''
# print("self.compute_bethe_average_energy():", self.compute_bethe_average_energy())
# print("self.compute_bethe_entropy():", self.compute_bethe_entropy())
if torch.isnan(factor_beliefs).any():
print("values, some should be nan:")
for val in factor_beliefs.flatten():
print(val)
assert(not torch.isnan(factor_beliefs).any()), (factor_beliefs, torch.where(factor_beliefs == torch.tensor(float('nan'))), torch.where(var_beliefs == torch.tensor(float('nan'))))
assert(not torch.isnan(var_beliefs).any()), var_beliefs
return (compute_bethe_average_energy(factor_beliefs=factor_beliefs, factor_potentials=factor_graph.factor_potentials.squeeze())\
- compute_bethe_entropy(factor_beliefs=factor_beliefs, var_beliefs=var_beliefs, numVars=torch.sum(factor_graph.numVars), var_degrees=factor_graph.var_degrees))
class GIN_Network_withEdgeFeatures(nn.Module):
def __init__(self, input_state_size=1, edge_attr_size=1, hidden_size=4, msg_passing_iters=5, feat_all_layers=True, edgedevice=None):
'''
Inputs:
- msg_passing_iters (int): the number of iterations of message passing to run (we have this many
message passing layers with their own learnable parameters)
- feat_all_layers (bool): if True, use concatenation of sum of all node features after every layer as input to final MLP
'''
super().__init__()
layers = [GINConv_withEdgeFeatures(nn1=Seq(Linear(hidden_size, hidden_size), ReLU(), Linear(hidden_size, hidden_size)),
nn2=Seq(Linear(input_state_size + edge_attr_size, hidden_size), ReLU(), Linear(hidden_size, hidden_size)))] + \
[GINConv_withEdgeFeatures(nn1=Seq(Linear(hidden_size, hidden_size), ReLU(), Linear(hidden_size, hidden_size)),
nn2=Seq(Linear(hidden_size + edge_attr_size, hidden_size), ReLU(), Linear(hidden_size, hidden_size)))\
for i in range(msg_passing_iters - 1)]
self.message_passing_layers = nn.ModuleList(layers)
self.feat_all_layers = feat_all_layers
if self.feat_all_layers:
self.final_mlp = Seq(Linear(msg_passing_iters*hidden_size, msg_passing_iters*hidden_size), ReLU(), Linear(msg_passing_iters*hidden_size, 1))
else:
self.final_mlp = Seq(Linear(hidden_size, hidden_size), ReLU(), Linear(hidden_size, 1))
def forward(self, x, edge_index, edge_attr, batch):
if self.feat_all_layers:
summed_node_features_all_layers = []
for message_passing_layer in self.message_passing_layers:
x = message_passing_layer(x=x, edge_index=edge_index, edge_attr=edge_attr)
summed_node_features_all_layers.append(global_add_pool(x, batch))
# print("torch.cat(summed_node_features_all_layers, dim=0).shape:", torch.cat(summed_node_features_all_layers, dim=1).shape)
# print("global_add_pool(x, batch).shape:", global_add_pool(x, batch).shape)
return self.final_mlp(torch.cat(summed_node_features_all_layers, dim=1))
else:
for message_passing_layer in self.message_passing_layers:
x = message_passing_layer(x=x, edge_index=edge_index, edge_attr=edge_attr)
return self.final_mlp(global_add_pool(x, batch))
class GINConv_withEdgeFeatures(MessagePassing):
r"""Modification of the graph isomorphism operator from the `"How Powerful are
Graph Neural Networks?" <https://arxiv.org/abs/1810.00826>`_ paper, which uses
edge features.
.. math::
\mathbf{x}^{\prime}_i = \text{MLP}_1 \left( (1 + \epsilon) \cdot
\mathbf{x}_i + \sum_{j \in \mathcal{N}(i)} \text{MLP}_2 \left( \mathbf{x}_j, \mathbf{e}_{i,j} \right) \right),
Args:
nn1 (torch.nn.Module): A neural network :math:`h_{\mathbf{\Theta}}` that
maps node features :obj:`x` of shape :obj:`[-1, in_channels]` to
shape :obj:`[-1, out_channels]`, *e.g.*, defined by
:class:`torch.nn.Sequential`.
nn2 (torch.nn.Module): A neural network mapping shape [-1, in_channels + edge_features]
to [-1, in_channels]
eps (float, optional): (Initial) :math:`\epsilon` value.
(default: :obj:`0`)
train_eps (bool, optional): If set to :obj:`True`, :math:`\epsilon`
will be a trainable parameter. (default: :obj:`False`)
**kwargs (optional): Additional arguments of
:class:`torch_geometric.nn.conv.MessagePassing`.
"""
def __init__(self, nn1, nn2, eps=0, train_eps=False, **kwargs):
super(GINConv_withEdgeFeatures, self).__init__(aggr='add', **kwargs)
self.nn1 = nn1
self.nn2 = nn2
self.initial_eps = eps
if train_eps:
self.eps = torch.nn.Parameter(torch.Tensor([eps]))
else:
self.register_buffer('eps', torch.Tensor([eps]))
self.reset_parameters()
def reset_parameters(self):
reset(self.nn1)
self.eps.data.fill_(self.initial_eps)
def forward(self, x, edge_index, edge_attr):
""""""
x = x.unsqueeze(-1) if x.dim() == 1 else x
edge_index, _ = remove_self_loops(edge_index)
out = self.nn1((1 + self.eps) * x + self.propagate(edge_index, x=x, edge_attr=edge_attr))
return out
def message(self, x_j, edge_attr):
# x_i has shape [E, in_channels]
# edge_attr has shape [E, edge_features]
tmp = torch.cat([x_j, edge_attr], dim=1) # tmp has shape [E, in_channels + edge_features]
return self.nn2(tmp)