-
Notifications
You must be signed in to change notification settings - Fork 0
/
analyzer.ipynb.orig
1704 lines (1704 loc) · 61.3 KB
/
analyzer.ipynb.orig
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
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import sys\n",
"sys.path.insert(0, '../ELINA/python_interface/')\n",
"\n",
"import numpy as np\n",
"import re\n",
"import csv\n",
"from elina_box import *\n",
"from elina_interval import *\n",
"from elina_abstract0 import *\n",
"from elina_manager import *\n",
"from elina_dimension import *\n",
"from elina_scalar import *\n",
"from elina_interval import *\n",
"from elina_linexpr0 import *\n",
"from elina_lincons0 import *\n",
"import ctypes\n",
"from ctypes.util import find_library\n",
"from gurobipy import *\n",
"import time\n",
"from pprint import pprint\n",
"import copy\n",
"import warnings\n",
"\n",
"libc = CDLL(find_library('c'))\n",
"cstdout = c_void_p.in_dll(libc, 'stdout')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Import for debugging in jupyter notebook\n",
"from IPython.core.debugger import set_trace #TODO remove at end."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"class layers:\n",
" def __init__(self):\n",
" self.layertypes = []\n",
" self.weights = []\n",
" self.biases = []\n",
" self.numlayer = 0\n",
" self.ffn_counter = 0\n",
" self.rank = []\n",
" self.use_LP = []"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"def parse_bias(text):\n",
" if len(text) < 1 or text[0] != '[':\n",
" raise Exception(\"expected '['\")\n",
" if text[-1] != ']':\n",
" raise Exception(\"expected ']'\")\n",
" v = np.array([*map(lambda x: np.double(x.strip()), text[1:-1].split(','))])\n",
" #return v.reshape((v.size,1))\n",
" return v\n",
"\n",
"def parse_vector(text):\n",
" if len(text) < 1 or text[0] != '[':\n",
" raise Exception(\"expected '['\")\n",
" if text[-1] != ']':\n",
" raise Exception(\"expected ']'\")\n",
" v = np.array([*map(lambda x: np.double(x.strip()), text[1:-1].split(','))])\n",
" return v.reshape((v.size,1))\n",
" #return v\n",
" \n",
"def balanced_split(text):\n",
" i = 0\n",
" bal = 0\n",
" start = 0\n",
" result = []\n",
" while i < len(text):\n",
" if text[i] == '[':\n",
" bal += 1\n",
" elif text[i] == ']':\n",
" bal -= 1\n",
" elif text[i] == ',' and bal == 0:\n",
" result.append(text[start:i])\n",
" start = i+1\n",
" i += 1\n",
" if start < i:\n",
" result.append(text[start:i])\n",
" return result\n",
"\n",
"def parse_matrix(text):\n",
" i = 0\n",
" if len(text) < 1 or text[0] != '[':\n",
" raise Exception(\"expected '['\")\n",
" if text[-1] != ']':\n",
" raise Exception(\"expected ']'\")\n",
" return np.array([*map(lambda x: parse_vector(x.strip()).flatten(), balanced_split(text[1:-1]))])\n",
"\n",
"def parse_net(text):\n",
" lines = [*filter(lambda x: len(x) != 0, text.split('\\n'))]\n",
" i = 0\n",
" res = layers()\n",
" while i < len(lines):\n",
" if lines[i] in ['ReLU', 'Affine']:\n",
" W = parse_matrix(lines[i+1])\n",
" b = parse_bias(lines[i+2])\n",
" res.layertypes.append(lines[i])\n",
" res.weights.append(W)\n",
" res.biases.append(b)\n",
" res.numlayer+= 1\n",
" res.rank.append(np.zeros((W.shape[0],1)))\n",
" res.use_LP.append(np.full((W.shape[0],1), False))\n",
" i += 3\n",
" else:\n",
" raise Exception('parse error: '+lines[i])\n",
" return res\n",
"\n",
"def parse_spec(text):\n",
" text = text.replace(\"[\", \"\")\n",
" text = text.replace(\"]\", \"\")\n",
" with open('dummy', 'w') as my_file:\n",
" my_file.write(text)\n",
" data = np.genfromtxt('dummy', delimiter=',',dtype=np.double)\n",
" low = copy.deepcopy(data[:,0])\n",
" high = copy.deepcopy(data[:,1])\n",
" return low,high"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def get_perturbed_image(x, epsilon):\n",
" image = x[1:len(x)]\n",
" num_pixels = len(image)\n",
" LB_N0 = image - epsilon\n",
" UB_N0 = image + epsilon\n",
" \n",
" for i in range(num_pixels):\n",
" if(LB_N0[i] < 0):\n",
" LB_N0[i] = 0\n",
" if(UB_N0[i] > 1):\n",
" UB_N0[i] = 1\n",
" return LB_N0, UB_N0"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def generate_linexpr0(weights, bias, size):\n",
" linexpr0 = elina_linexpr0_alloc(ElinaLinexprDiscr.ELINA_LINEXPR_DENSE, size)\n",
" cst = pointer(linexpr0.contents.cst)\n",
" elina_scalar_set_double(cst.contents.val.scalar, bias)\n",
" for i in range(size):\n",
" elina_linexpr0_set_coeff_scalar_double(linexpr0,i,weights[i])\n",
" return linexpr0"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def analyze(nn, LB_N0, UB_N0, label): \n",
" num_pixels = len(LB_N0)\n",
" nn.ffn_counter = 0\n",
" numlayer = nn.numlayer \n",
" man = elina_box_manager_alloc()\n",
" itv = elina_interval_array_alloc(num_pixels)\n",
" for i in range(num_pixels):\n",
" elina_interval_set_double(itv[i],LB_N0[i],UB_N0[i])\n",
"\n",
" ## construct input abstraction\n",
" element = elina_abstract0_of_box(man, 0, num_pixels, itv)\n",
" elina_interval_array_free(itv,num_pixels)\n",
" for layerno in range(numlayer):\n",
" if(nn.layertypes[layerno] in ['ReLU', 'Affine']):\n",
" weights = nn.weights[nn.ffn_counter]\n",
" biases = nn.biases[nn.ffn_counter]\n",
" dims = elina_abstract0_dimension(man,element)\n",
" num_in_pixels = dims.intdim + dims.realdim\n",
" num_out_pixels = len(weights)\n",
"\n",
" dimadd = elina_dimchange_alloc(0,num_out_pixels) \n",
" for i in range(num_out_pixels):\n",
" dimadd.contents.dim[i] = num_in_pixels\n",
" elina_abstract0_add_dimensions(man, True, element, dimadd, False)\n",
" elina_dimchange_free(dimadd)\n",
" np.ascontiguousarray(weights, dtype=np.double)\n",
" np.ascontiguousarray(biases, dtype=np.double)\n",
" var = num_in_pixels\n",
" # handle affine layer\n",
" for i in range(num_out_pixels):\n",
" tdim= ElinaDim(var)\n",
" linexpr0 = generate_linexpr0(weights[i],biases[i],num_in_pixels)\n",
" element = elina_abstract0_assign_linexpr_array(man, True, element, tdim, linexpr0, 1, None)\n",
" var+=1\n",
" dimrem = elina_dimchange_alloc(0,num_in_pixels)\n",
" for i in range(num_in_pixels):\n",
" dimrem.contents.dim[i] = i\n",
" elina_abstract0_remove_dimensions(man, True, element, dimrem)\n",
" elina_dimchange_free(dimrem)\n",
" # handle ReLU layer \n",
" if(nn.layertypes[layerno]=='ReLU'):\n",
" element = relu_box_layerwise(man,True,element,0, num_out_pixels)\n",
" nn.ffn_counter+=1 \n",
"\n",
" else:\n",
" print(' net type not supported')\n",
" \n",
" dims = elina_abstract0_dimension(man,element)\n",
" output_size = dims.intdim + dims.realdim\n",
" # get bounds for each output neuron\n",
" bounds = elina_abstract0_to_box(man,element)\n",
"\n",
" \n",
" # if epsilon is zero, try to classify else verify robustness \n",
" \n",
" verified_flag = True\n",
" predicted_label = 0\n",
" if(LB_N0[0]==UB_N0[0]):\n",
" for i in range(output_size):\n",
" inf = bounds[i].contents.inf.contents.val.dbl\n",
" flag = True\n",
" for j in range(output_size):\n",
" if(j!=i):\n",
" sup = bounds[j].contents.sup.contents.val.dbl\n",
" if(inf<=sup):\n",
" flag = False\n",
" break\n",
" if(flag):\n",
" predicted_label = i\n",
" break \n",
" else:\n",
" inf = bounds[label].contents.inf.contents.val.dbl\n",
" for j in range(output_size):\n",
" if(j!=label):\n",
" sup = bounds[j].contents.sup.contents.val.dbl\n",
" if(inf<=sup):\n",
" predicted_label = label\n",
" verified_flag = False\n",
" break\n",
"\n",
" elina_interval_array_free(bounds,output_size)\n",
" elina_abstract0_free(man,element)\n",
" elina_manager_free(man) \n",
" return predicted_label, verified_flag"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define operations on abstract domain using linear approximations"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def add_hidden_constraint(model, layerno, z, z_hat, weights, biases):\n",
" \"\"\"\n",
" This function computes “which side” of the ReLU the pre-ReLU activations lies on.\n",
" INPUT:\n",
" - model: gurobi model\n",
" - layerno: layer number from which z_hat belong\n",
" - z: gurobi variables for hidden layer input\n",
" - z_hat: gurobi variables for hidden layer output\n",
" - weights: weights for the hidden layer\n",
" - bias: bias in the hidden layer\n",
" OUTPUT:\n",
" - model: gurobi model with new hidden constrains\n",
" \"\"\"\n",
" # Sanity check!\n",
" assert len(z) == weights.shape[1]\n",
" assert len(z_hat) == weights.shape[0]\n",
" \n",
" # add constraint to model\n",
" for i_out in range(len(z_hat)):\n",
" constr = LinExpr() + np.asscalar(biases[i_out])\n",
" for s in range(len(z)):\n",
" constr += z[s] * np.asscalar(weights[i_out, s])\n",
"\n",
" model.addConstr(z_hat[i_out] == constr, \\\n",
" name=\"hidden_constr_\" + str(layerno) + \"_\" + str(i_out))\n",
" \n",
" model.update()\n",
" return model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def add_relu_activation_constraint(model, layerno, z_hat, z, LB, UB):\n",
" \"\"\"\n",
" This function computes “which side” of the ReLU the pre-ReLU activations lies on.\n",
" INPUT:\n",
" - model: gurobi model\n",
" - layerno: layer number from which z_hat belong\n",
" - z_hat: gurobi variables for pre-relu input\n",
" - z: gurobi variables for relu output\n",
" - LB: lower bound of inputs to a relu layer\n",
" - UB: upper bound of inputs to a relu layer\n",
" OUTPUT:\n",
" - model: gurobi model with new ReLU constrains\n",
" \"\"\"\n",
" # Sanity check!\n",
" assert len(z) == len(UB)\n",
" \n",
" # iterate over each pre-relu neuron activation\n",
" for j in range(len(UB)):\n",
" u = np.asscalar(UB[j])\n",
" l = np.asscalar(LB[j])\n",
"\n",
" if u <= 0:\n",
" model.addConstr(z[j] == 0, \\\n",
" name=\"relu_constr_deac_\" + str(layerno) + \"_\" + str(j))\n",
" elif l > 0:\n",
" model.addConstr(z[j] == z_hat[j], \\\n",
" name=\"relu_constr_deac_\" + str(layerno) + \"_\" + str(j))\n",
" else:\n",
" alpha = u/(u - l)\n",
" model.addConstr(z[j] >= 0 , \\\n",
" name=\"relu_const_ambi_pos_\" + str(layerno) + \"_\" + str(j))\n",
" model.addConstr(z[j] >= z_hat[j], \\\n",
" name=\"relu_const_ambi_hid_\" + str(layerno) + \"_\" + str(j))\n",
" model.addConstr(z[j] <= alpha * (z_hat[j] - l), \\\n",
" name=\"relu_const_ambi_lin_\" + str(layerno) + \"_\" + str(j))\n",
" model.update()\n",
" return model"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def call_linear_solver(model, z_hat):\n",
" \"\"\"\n",
" This function computes lower and upper bound for given objective function and model\n",
" INPUT:\n",
" - model: gurobi model\n",
" - z_hat: gurobi variable to optimize for\n",
" OUTPUT:\n",
" - LB: lower bound of variable\n",
" - UB: upper bound of variable\n",
" \"\"\"\n",
" # Find Lower Bound\n",
" model.setObjective(z_hat, GRB.MINIMIZE)\n",
" model.update()\n",
" model.optimize()\n",
"\n",
" if model.status == GRB.Status.OPTIMAL:\n",
" LB = model.objVal\n",
" else:\n",
" raise(RuntimeError('[Min] Error. Not Able to retrieve bound. Gurobi Model. Not Optimal.'))\n",
" \n",
" # reset model \n",
" model.reset()\n",
"\n",
" # Find Upper Bound\n",
" model.setObjective(z_hat, GRB.MAXIMIZE)\n",
" model.update()\n",
" model.optimize()\n",
"\n",
" if model.status == GRB.Status.OPTIMAL:\n",
" UB = model.objVal\n",
" else:\n",
" raise(RuntimeError('[Max] Error. Not Able to retrieve bound. Gurobi Model. Not Optimal.'))\n",
" \n",
" # reset model \n",
" model.reset()\n",
" \n",
" return LB, UB"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define operations on abstract domain using Box approximations"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def get_relu_bounds_using_box(man, input_LB, input_UB, num_in_pixels):\n",
" '''\n",
" This function calculates the bounds of a ReLU operation. \n",
" INPUT:\n",
" - man: pointer to elina manager\n",
" - input_LB: lower bound of the inputs to the ReLU\n",
" - input_UB: upper bound of the inputs to the ReLU\n",
" - num_in_pixels: number of inputs to ReLU\n",
" \n",
" OUTPUT:\n",
" - output_LB: lower bound of the outputs from ReLU layer\n",
" - output_UB: upper bound of the outputs from ReLU layer\n",
" - num_out_pixels: number of outputs of ReLI layer\n",
" '''\n",
" itv = elina_interval_array_alloc(num_in_pixels)\n",
"\n",
" ## Populate the interval\n",
" for i in range(num_in_pixels):\n",
" elina_interval_set_double(itv[i], input_LB[i], input_UB[i])\n",
"\n",
" ## construct input abstraction\n",
" element = elina_abstract0_of_box(man, 0, num_in_pixels, itv)\n",
" elina_interval_array_free(itv, num_in_pixels)\n",
" \n",
" # ------------------------------------------------------------------\n",
" # Handle ReLU Layer\n",
" # ------------------------------------------------------------------\n",
" num_out_pixels = num_in_pixels\n",
" \n",
" element = relu_box_layerwise(man, True, element,0, num_in_pixels)\n",
" \n",
" # get bounds for each output neuron\n",
" bounds = elina_abstract0_to_box(man,element)\n",
" \n",
" # get bounds for each output neuron\n",
" bounds = elina_abstract0_to_box(man,element)\n",
" \n",
" output_LB = np.zeros((num_out_pixels, 1), float)\n",
" output_UB = np.zeros((num_out_pixels, 1), float)\n",
" for j in range(num_out_pixels):\n",
" output_LB[j] = bounds[j].contents.inf.contents.val.dbl\n",
" output_UB[j] = bounds[j].contents.sup.contents.val.dbl\n",
" \n",
" # free out the memory allocations\n",
" elina_interval_array_free(bounds, num_out_pixels)\n",
" elina_abstract0_free(man, element)\n",
" \n",
" return output_LB, output_UB, num_out_pixels"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def get_hidden_bounds_using_box(man, weights, biases, input_LB, input_UB, num_in_pixels, verbose=False):\n",
" '''\n",
" This function calculates the bounds of a ReLU operation followed by a hidden layer. \n",
" INPUT:\n",
" - man: pointer to elina manager\n",
" - weights: weights of the hidden layer\n",
" - biases: biases of the hidden layer\n",
" - input_LB: lower bound of the inputs to the hidden layer\n",
" - input_UB: upper bound of the inputs to the hidden layer\n",
" - num_in_pixels: number of inputs to the input layer\n",
" \n",
" OUTPUT:\n",
" - output_LB: lower bound of the outputs from hidden layer\n",
" - output_UB: upper bound of the outputs from hidden layer\n",
" - num_out_pixels: number of outputs of hidden layer\n",
" '''\n",
" itv = elina_interval_array_alloc(num_in_pixels)\n",
"\n",
" ## Populate the interval\n",
" for i in range(num_in_pixels):\n",
" elina_interval_set_double(itv[i], input_LB[i], input_UB[i])\n",
"\n",
" ## construct input abstraction\n",
" element = elina_abstract0_of_box(man, 0, num_in_pixels, itv)\n",
" elina_interval_array_free(itv, num_in_pixels)\n",
" \n",
" # ------------------------------------------------------------------\n",
" # Handle Affine Layer\n",
" # ------------------------------------------------------------------\n",
"\n",
" # calculate number of outputs\n",
" num_out_pixels = len(weights)\n",
" \n",
" if verbose:\n",
" print(\"[Network] Input pixels: \" + str(num_in_pixels))\n",
" print(\"[Network] Shape of weights: \" + str(np.shape(weights)))\n",
" print(\"[Network] Shape of biases: \" + str(np.shape(biases)))\n",
" print(\"[Network] Out pixels: \" + str(num_out_pixels))\n",
"\n",
" # Create number of neurons in the layer and populate it\n",
" # with the number of inputs to each neuron in the layer\n",
" dimadd = elina_dimchange_alloc(0, num_out_pixels) \n",
" for i in range(num_out_pixels):\n",
" dimadd.contents.dim[i] = num_in_pixels\n",
"\n",
" # Add dimensions to an ElinaAbstract0 pointer i.e. element\n",
" elina_abstract0_add_dimensions(man, True, element, dimadd, False)\n",
" elina_dimchange_free(dimadd)\n",
"\n",
" # Create the linear expression associated each neuron\n",
" var = num_in_pixels\n",
" for i in range(num_out_pixels):\n",
" tdim = ElinaDim(var)\n",
" linexpr0 = generate_linexpr0(weights[i], biases[i], num_in_pixels)\n",
" # Parallel assignment of several dimensions of an ElinaAbstract0 by using an ElinaLinexpr0Array\n",
" element = elina_abstract0_assign_linexpr_array(man, True, element, tdim, linexpr0, 1, None)\n",
" var += 1\n",
"\n",
" # Pointer to which semantics we want to follow.\n",
" dimrem = elina_dimchange_alloc(0, num_in_pixels)\n",
" for i in range(num_in_pixels):\n",
" dimrem.contents.dim[i] = i\n",
" \n",
" # Remove dimensions from an ElinaAbstract0\n",
" elina_abstract0_remove_dimensions(man, True, element, dimrem)\n",
" elina_dimchange_free(dimrem)\n",
" \n",
" # get bounds for each output neuron\n",
" bounds = elina_abstract0_to_box(man,element)\n",
" \n",
" output_LB = np.zeros((num_out_pixels, 1), float)\n",
" output_UB = np.zeros((num_out_pixels, 1), float)\n",
" for j in range(num_out_pixels):\n",
" output_LB[j] = bounds[j].contents.inf.contents.val.dbl\n",
" output_UB[j] = bounds[j].contents.sup.contents.val.dbl \n",
" \n",
" # free out the memory allocations\n",
" elina_interval_array_free(bounds, num_out_pixels)\n",
" elina_abstract0_free(man, element)\n",
" \n",
" return output_LB, output_UB, num_out_pixels"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Define function to verify the neural network"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def verify_network(LB_N0, UB_N0, LB_NN, UB_NN, label, num_input_pixels = 784, num_out_pixels = 10):\n",
" '''\n",
" This function verifies the network given the bounds of the input layer and the final layer of the network.\n",
" INPUT:\n",
" - LB_N0: lower bounds of the preturbed input image\n",
" - UB_N0: unpper bounds of the preturbed input image\n",
" - LB_NN: lower bounds of the final layer of neural network\n",
" - UB_NN: upper bounds of the final layer of neural network\n",
" - label: true label of the input image\n",
" - num_input_pixels: number of pixels in the input image (for MNIST, default: 784)\n",
" - num_out_pixels: number of neurons in the last layer of the network (for MNIST, default: 10)\n",
" \n",
" OUTPUT:\n",
" - predicted_label: label predicted by the neural network\n",
" - verified_flag: boolean variable, true if the network is robust to perturbation\n",
" '''\n",
" \n",
" # if epsilon is zero, try to classify else verify robustness \n",
" verified_flag = True\n",
" predicted_label = 0\n",
" if(LB_N0[0]==UB_N0[0]):\n",
" for i in range(num_out_pixels):\n",
" inf = LB_NN[i]\n",
" flag = True\n",
" for j in range(num_out_pixels):\n",
" if(j!=i):\n",
" sup = UB_NN[j]\n",
" if(inf<=sup):\n",
" flag = False\n",
" break\n",
" if(flag):\n",
" predicted_label = i\n",
" break \n",
" else:\n",
" inf = LB_NN[label]\n",
" for j in range(num_out_pixels):\n",
" if(j!=label):\n",
" sup = UB_NN[j]\n",
" if(inf<=sup):\n",
" predicted_label = label\n",
" verified_flag = False\n",
" break\n",
"\n",
" if(verified_flag):\n",
" print(\"verified\")\n",
" else:\n",
" print(\"can not be verified\") \n",
" \n",
" return predicted_label, verified_flag"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Functions to perform different analysis"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# function to perform box analysis for all layers in the neural network nn\n",
"def perform_box_analysis(nn, LB_N0, UB_N0, start=0, end=None, verbose = False):\n",
" # create a list to store the bounds found through box approximation\n",
" \n",
" LB_hidden_box_list = []\n",
" UB_hidden_box_list = []\n",
"\n",
" # create manager for Elina\n",
" man = elina_box_manager_alloc()\n",
"\n",
" # initialize variables for the network iteration\n",
" numlayer = nn.numlayer \n",
" nn.ffn_counter = 0\n",
"\n",
" # for input image\n",
" input_LB = LB_N0.copy()\n",
" input_UB = UB_N0.copy()\n",
" num_in_pixels = len(LB_N0)\n",
" \n",
" if verbose:\n",
" print(\"Input Layer, size: \" + str(len(LB_N0)))\n",
" print('---------------')\n",
"\n",
" for layerno in range(numlayer):\n",
" if verbose:\n",
" print(\"Layer Number: \" + str(layerno + 1))\n",
"\n",
" if(nn.layertypes[layerno] in ['ReLU', 'Affine']):\n",
" if verbose:\n",
" print(\"Layer Type: %s\" % nn.layertypes[layerno])\n",
"\n",
" # read the layer weights and biases\n",
" weights = nn.weights[nn.ffn_counter]\n",
" biases = nn.biases[nn.ffn_counter]\n",
" np.ascontiguousarray(weights, dtype=np.double)\n",
" np.ascontiguousarray(biases, dtype=np.double)\n",
"\n",
" # ------------------------------------------------------------------\n",
" # Handle Affine Layer\n",
" # ------------------------------------------------------------------\n",
" output_LB, output_UB, num_out_pixels = get_hidden_bounds_using_box(man, weights, biases, input_LB, input_UB, num_in_pixels, verbose)\n",
"\n",
" # Add bounds to the list\n",
" LB_hidden_box_list.append(output_LB.copy())\n",
" UB_hidden_box_list.append(output_UB.copy())\n",
" # Prepare variables for next layer\n",
" input_LB = output_LB.copy()\n",
" input_UB = output_UB.copy()\n",
" num_in_pixels = num_out_pixels\n",
" nn.ffn_counter += 1 \n",
"\n",
" # ------------------------------------------------------------------\n",
" # Handle ReLU Layer\n",
" # ------------------------------------------------------------------\n",
" if(nn.layertypes[layerno] == \"ReLU\"):\n",
" output_LB, output_UB, num_out_pixels = get_relu_bounds_using_box(man, input_LB, input_UB, num_in_pixels)\n",
"\n",
" # Prepare variables for next layer\n",
" input_LB = output_LB.copy()\n",
" input_UB = output_UB.copy()\n",
"\n",
" if verbose:\n",
" print(\"[OUTPUT] Bounds: \")\n",
" output_LB, output_UB = output_LB.squeeze(), output_UB.squeeze()\n",
" pprint(np.stack((output_LB, output_UB), axis=1))\n",
" \n",
" if verbose:\n",
" print('---------------')\n",
"\n",
" else:\n",
" print(' net type not supported')\n",
" if verbose:\n",
" print(\"Output Layer, size: \" + str(len(output_LB)))\n",
"\n",
" elina_manager_free(man)\n",
" \n",
" # for last layer of the netowork is ReLU\n",
" LB_NN = LB_hidden_box_list[-1].copy()\n",
" UB_NN = UB_hidden_box_list[-1].copy()\n",
"\n",
" if nn.layertypes[-1] == \"ReLU\" :\n",
" num_out = len(LB_hidden_box_list[-1])\n",
" for i in range(num_out):\n",
" if LB_hidden_box_list[-1][i] < 0 :\n",
" LB_NN[i] = 0 \n",
" if UB_hidden_box_list[-1][i] < 0 :\n",
" UB_NN[i] = 0 \n",
" \n",
" return LB_hidden_box_list, UB_hidden_box_list, LB_NN.squeeze(), UB_NN.squeeze()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def perform_linear_over_box_approximation(nn, LB_N0, UB_N0, LB_hidden_box_list, UB_hidden_box_list, verbose = False):\n",
" # initialize variables for the network iteration\n",
" numlayer = nn.numlayer \n",
" nn.ffn_counter = 0\n",
" num_in_pixels = len(LB_N0)\n",
" \n",
" m = get_model()\n",
" \n",
" # We follow the following notations:\n",
" # z_hat_{i} = W_i * z_i + b_i, where i = {1, . . . , k}, and z_hat_{k} = y (ouput of NN)\n",
" # z_i = max(z_hat_{i-1} , 0), where i = {2, . . . , k}, and z_1 = x (input to NN)\n",
"\n",
" # Create variables for all layers and append to the list \n",
" m, z, z_hat = add_all_vars(m, numlayer, LB_N0, UB_N0, UB_hidden_box_list)\n",
" m.update()\n",
" \n",
" if verbose: \n",
" # Sanity check!\n",
" # Size of z should be number of relu activation layers + 1 (for input)\n",
" print(\"Number of relu layers: {0}\".format(len(z)))\n",
" # Size of z_hat should be number of hidden layers\n",
" print(\"Number of hidden layers: {0}\".format(len(z_hat)))\n",
" print(\"Size of last hidden layer: {0}\".format(len(z_hat[-1])))\n",
" print(\"------------------------------\")\n",
"\n",
" nn.ffn_counter = 0\n",
"\n",
" # Adding weights constraints for k layers\n",
" for layerno in range(numlayer):\n",
" if(nn.layertypes[layerno] in ['ReLU', 'Affine']):\n",
" # read the layer weights and biases\n",
" weights = nn.weights[nn.ffn_counter]\n",
" biases = nn.biases[nn.ffn_counter]\n",
" np.ascontiguousarray(weights, dtype=np.float)\n",
" np.ascontiguousarray(biases, dtype=np.float)\n",
"\n",
" # add affine constraint\n",
" add_hidden_constraint(m, layerno, z[layerno], z_hat[layerno], weights, biases)\n",
" \n",
" # update counter for next iteration\n",
" nn.ffn_counter += 1\n",
" else:\n",
" raise(\"Not a valid layer!\")\n",
" \n",
" m.update()\n",
"\n",
" # Adding relu constraints for (k-1) layers. The loop starts from z_2 since z_1 is input\n",
" for i in range(1, numlayer): \n",
" # add relu constraint\n",
" if (nn.layertypes[layerno] in [\"ReLU\"]):\n",
" add_relu_activation_constraint(m, layerno, z_hat[i-1], z[i], LB_hidden_box_list[i-1], UB_hidden_box_list[i-1])\n",
"\n",
" m.update()\n",
"\n",
" # storing upper and lower bounds for last layer\n",
" UB = np.zeros_like(nn.biases[-1])\n",
" LB = np.zeros_like(nn.biases[-1])\n",
" numlayer = nn.numlayer \n",
"\n",
" # Solving for each neuron in the output layer to collect bounds\n",
" # i.e. z_hat_{-1} where -1 denotes the last array in list\n",
" for i_out in range(len(UB)): \n",
" LB[i_out], UB[i_out] = call_linear_solver(m, z_hat[-1][i_out])\n",
" \n",
" # for last layer of the netowork is ReLU\n",
" LB_NN = LB\n",
" UB_NN = UB\n",
" \n",
" if nn.layertypes[-1] == \"ReLU\" :\n",
" num_out = len(UB_NN)\n",
"\n",
" for i in range(num_out):\n",
" if LB[i] < 0 :\n",
" LB_NN[i] = 0 \n",
" if UB[i] < 0 :\n",
" UB_NN[i] = 0 \n",
" \n",
" return LB_NN.squeeze(), UB_NN.squeeze()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def get_model(single_thread=False):\n",
" \"\"\"\n",
" Get Gurobi model\n",
" \"\"\"\n",
" m = Model(\"LP\")\n",
" m.setParam(\"outputflag\", False)\n",
"\n",
" # disable parallel Gurobi solver\n",
" m.setParam(\"Method\", 1) # dual simplex\n",
" if single_thread:\n",
" m.setParam(\"Threads\", 1) # only 1 thread\n",
" return m"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def add_all_vars(m, numlayer, LB_N0, UB_N0, UB_hidden_box_list, verbose=True):\n",
" \"\"\"\n",
" Add and create all variables of neural network to gurobi model.\n",
" INPUT:\n",
" - m: Gurobi model\n",
" - numlayer: Number of Layers\n",
" - LB_N0: Lower Bound of perturbed image input\n",
" - UB_N0: Upper Bound of perturbed image input\n",
" - UB_hidden_box_list: List of upper Bounds from box approximation (needed to set upper bound of ReLU outputs)\n",
" OUTPUT:\n",
" - m: Gurobi model with newly added variables\n",
" - z: List of Gurobi variables corresponding to pre-ReLU Layer (hidden)\n",
" - z_hat: List of Gurobi variables corresponding to post-ReLU Layer\n",
"\n",
" \"\"\"\n",
" \n",
" # for output of each ReLU\n",
" z = []\n",
" # for output of each hidden layer\n",
" z_hat = []\n",
" \n",
" # Create variables of input image\n",
" num_in_pixels = len(LB_N0)\n",
" img_vars = m.addVars(num_in_pixels, lb=LB_N0, ub=UB_N0, \\\n",
" vtype=GRB.CONTINUOUS, name=\"input_layer\")\n",
" z.append(img_vars)\n",
" \n",
" # Create variables for all layers and append to the list \n",
" for i in range(numlayer):\n",
" # for layers before the final layer, z_hat and z exists\n",
" if i < (numlayer - 1):\n",
"\n",
" UB_relu = UB_hidden_box_list[i].squeeze().copy()\n",
" for j in range(len(UB_hidden_box_list[i])):\n",
" bound = UB_hidden_box_list[i][j]\n",
" UB_relu[j] = max(0, bound)\n",
" UB_relu.squeeze() \n",
"\n",
" # middle layer, has both z and z hat\n",
" z_hat_hidden = m.addVars(len(UB_hidden_box_list[i]), lb=-np.inf, ub=np.inf, \\\n",
" vtype=GRB.CONTINUOUS, name=\"hidden_layer_\" + str(i))\n",
" z_relu = m.addVars(len(UB_hidden_box_list[i]), lb=0.0, ub = UB_relu,\\\n",
" vtype=GRB.CONTINUOUS, name=\"relu_layer_\" + str(i))\n",
" # append to the list\n",
" z_hat.append(z_hat_hidden)\n",
" z.append(z_relu)\n",
" # for last layer, only z_hat exists\n",
" else: \n",
" z_hat_hidden = m.addVars(len(UB_hidden_box_list[i]), lb=-np.inf, ub=np.inf, \\\n",
" vtype=GRB.CONTINUOUS, name=\"output_layer\") \n",
" # append to the list\n",
" z_hat.append(z_hat_hidden)\n",
"\n",
" m.update()\n",
" \n",
" if verbose:\n",
" # Sanity check!\n",
" # Size of z should be number of relu activation layers + 1 (for input)\n",
" print(\"Number of relu layers: {0}\".format(len(z)))\n",
" # Size of z_hat should be number of hidden layers\n",
" print(\"Number of hidden layers: {0}\".format(len(z_hat)))\n",
" print(\"Size of last hidden layer: {0}\".format(len(z_hat[-1])))\n",
" \n",
" return m, z, z_hat"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def perform_linear_layerwise(nn, numlayer, LB_N0, UB_N0, lp_list, \n",
" LB_hidden_box_list, UB_hidden_box_list, verbose=True):\n",
" \"\"\"\n",
" Get final bounds using linear programming layerwise. If lp_freq > 1 linear bounds are only calculated every \n",
" lp_freq'th layer.\n",
" INPUT:\n",
" - nn: Neural Network as defined in initial code (contains layertypes, weights, etc.)\n",
" - numlayer: Number of Layers\n",
" - LB_N0: Lower Bound of perturbed image input\n",
" - UB_N0: Upper Bound of perturbed image input\n",
" - lp_list: Layerno to start solvingbounds by LP \n",
" - prob: probability to select a neuron\n",
" - LB_hidden_box_list: List of upper Bounds from box approximation\n",
" - UB_hidden_box_list: List of upper Bounds from box approximation\n",
" OUTPUT:\n",
" - LB_NN: Lower bounds of neural network output\n",
" - UB_NN: Upper bounds of neural network output\n",
" \"\"\"\n",
" \n",
" # Sanity check\n",
" assert len(lp_list) != 0\n",
" assert LB_hidden_box_list is not None \n",
" assert UB_hidden_box_list is not None\n",
"\n",
"\n",
" # create manager for Elina\n",
" man = elina_box_manager_alloc()\n",
" \n",
" # create gurobi model\n",
" m = get_model()\n",
" # create all gurobi variables for the network\n",
" m, z, z_hat = add_all_vars(m, numlayer, LB_N0, UB_N0, UB_hidden_box_list)\n",
" \n",
" # initialize counter\n",
" nn.ffn_counter = 0\n",
" \n",
" # Adding weights constraints for k layers\n",
" for layerno in range(numlayer):\n",
" if(nn.layertypes[layerno] in ['ReLU', 'Affine']):\n",
" # read the layer weights and biases\n",
" weights = nn.weights[nn.ffn_counter]\n",
" biases = nn.biases[nn.ffn_counter]\n",
" np.ascontiguousarray(weights, dtype=np.float)\n",
" np.ascontiguousarray(biases, dtype=np.float)\n",
"\n",
" # output shape of the layer\n",
" n_in = weights.shape[1]\n",
" n_out = weights.shape[0]\n",
"\n",
" # create variables to store bounds of hidden layer\n",
" LB_hat = np.zeros(n_out, float)\n",
" UB_hat = np.zeros(n_out, float)\n",
"\n",
" # add affine constraint\n",
" add_hidden_constraint(m, layerno, z[layerno], z_hat[layerno], weights, biases)\n",
" \n",
" # for initial layers use original box bounds\n",
" if layerno < lp_list[0] or layerno == 0:\n",
" LB_hat, UB_hat = LB_hidden_box_list[layerno].copy() , UB_hidden_box_list[layerno].copy()\n",
" # for the last layer\n",
" elif layerno == numlayer - 1:\n",
" for i_out in range(n_out):\n",
" LB_hat[i_out], UB_hat[i_out] = call_linear_solver(m, z_hat[layerno][i_out])\n",
" break;\n",
" else: \n",
" if (layerno in lp_list) or layerno != numlayer-1:\n",
" # find new bounds for the hidden layer using linear solver\n",
" for i_out in range(n_out):\n",
" LB_hat[i_out], UB_hat[i_out] = call_linear_solver(m, z_hat[layerno][i_out]) \n",
" else:\n",
" # find new bounds for the hidden layer using box solver\n",
" LB, UB, n_out = get_relu_bounds_using_box(man, LB_hat_prev, UB_hat_prev, n_in)\n",
" LB_hat, UB_hat, n_out = get_hidden_bounds_using_box(man, weights, biases, \n",
" LB, UB, n_out, verbose)\n",
" # add relu constraint\n",
" if layerno < (numlayer - 1) and nn.layertypes[layerno] in [\"ReLU\"]:\n",
" add_relu_activation_constraint(m, layerno, z_hat[layerno], z[layerno + 1], LB_hat, UB_hat)\n",
" \n",
" # preparation for next iteration \n",
" LB_hat_prev, UB_hat_prev = LB_hat.copy(), UB_hat.copy()\n",
" \n",
" m.update()\n",
"\n",
" # update counter for next iteration\n",
" nn.ffn_counter += 1\n",
" else:\n",
" raise(\"Not a valid layer!\")\n",
" \n",
" # Set bounds of last performed layer to output\n",
" LB_NN = LB_hat\n",
" UB_NN = UB_hat\n",
" # If last Layer is RELU change last lower and upper bounds accordingly.\n",
" if nn.layertypes[-1] == \"ReLU\" :\n",
" num_out = len(UB_hat)\n",