-
Notifications
You must be signed in to change notification settings - Fork 7
/
Copy pathNg_DLMooc_c2wk3.html
1005 lines (930 loc) · 53.2 KB
/
Ng_DLMooc_c2wk3.html
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
<!DOCTYPE html>
<html lang="zh-Hant"
>
<head>
<title>[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks - mx's blog</title>
<!-- Using the latest rendering mode for IE -->
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="theme-color" content="#6b5594">
<meta name="msapplication-navbutton-color" content="#6b5594">
<meta name="apple-mobile-web-app-status-bar-style" content="#6b5594">
<link rel="manifest" href="/manifest.json">
<link rel="canonical" href="https://x-wei.github.io/Ng_DLMooc_c2wk3.html">
<meta name="author" content="mx" />
<meta name="keywords" content="deep learning" />
<meta name="description" content="Hyperparameter parameters Tips for hyperparam-tuning. Tuning process Many hyperparams to tune, mark importance by colors (red > yellow > purple): How to select set of values to explore ? Do NOT use grid search (grid of n * n) — this was OK in pre-DL era. try random values. reason: difficule to know which hyperparam ..." />
<meta property="og:site_name" content="mx's blog" />
<meta property="og:type" content="article"/>
<meta property="og:title" content="[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks"/>
<meta property="og:url" content="https://x-wei.github.io/Ng_DLMooc_c2wk3.html"/>
<meta property="og:description" content="Hyperparameter parameters Tips for hyperparam-tuning. Tuning process Many hyperparams to tune, mark importance by colors (red > yellow > purple): How to select set of values to explore ? Do NOT use grid search (grid of n * n) — this was OK in pre-DL era. try random values. reason: difficule to know which hyperparam ..."/>
<meta property="article:published_time" content="2017-10-23" />
<meta property="article:section" content="notes" />
<meta property="article:tag" content="deep learning" />
<meta property="article:author" content="mx" />
<meta property="og:image"
content="https://x-wei.github.io/Ng_DLMooc_c2wk3.png"/>
<!-- Bootstrap -->
<link href="https://x-wei.github.io/theme/css/bootstrap.min.css" rel="stylesheet">
<link href="https://x-wei.github.io/theme/css/font-awesome.min.css" rel="stylesheet">
<link href="https://x-wei.github.io/theme/css/pygments/manni.css" rel="stylesheet">
<link href="https://x-wei.github.io/theme/tipuesearch/tipuesearch.css" rel="stylesheet">
<link rel="stylesheet" href="https://x-wei.github.io/theme/css/style.css" type="text/css"/>
<link href="https://x-wei.github.io/feeds/atom.xml" type="application/atom+xml" rel="alternate"
title="mx's blog ATOM Feed"/>
<link href="https://x-wei.github.io/theme/css/material.min.css" rel="stylesheet">
<link href="https://x-wei.github.io/theme/css/ripples.css" rel="stylesheet">
</head>
<body>
<div style="display:none" id="title">[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks - mx's blog</div>
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-ex1-collapse">
<span class="sr-only">切换导航</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a href="https://x-wei.github.io/" class="navbar-brand">
mx's blog </a>
</div>
<div class="collapse navbar-collapse navbar-ex1-collapse">
<ul class="nav navbar-nav">
<li class="dropdown hidden-md hidden-lg hidden-xl">
<a class="dropdown-toggle" data-toggle="dropdown" href="javascript:void(0)">
<i class="fa fa-user"></i><span class="caret"></span>
</a>
<ul class="dropdown-menu">
</ul>
</li>
<ul class="nav navbar-nav hidden-xs hidden-sm">
</ul>
</ul>
<ul class="nav navbar-nav hidden-md hidden-lg hidden-xl">
<li class="dropdown hidden-md hidden-lg hidden-xl">
<a class="dropdown-toggle" data-toggle="dropdown" href="javascript:void(0)">
<i class="fa fa-folder-o"></i><span class="caret"></span>
</a>
<ul class="dropdown-menu">
<li >
<a href="https://x-wei.github.io/category/misc.html"><i class="fa fa-folder-o"></i> Misc</a>
</li>
<li >
<a href="https://x-wei.github.io/category/music.html"><i class="fa fa-folder-o"></i> Music</a>
</li>
<li class="active">
<a href="https://x-wei.github.io/category/notes.html"><i class="fa fa-folder-o"></i> Notes</a>
</li>
<li >
<a href="https://x-wei.github.io/category/soft.html"><i class="fa fa-folder-o"></i> Soft</a>
</li>
<li >
<a href="https://x-wei.github.io/category/tech.html"><i class="fa fa-folder-o"></i> Tech</a>
</li>
</ul>
</li>
</ul>
<ul class="nav navbar-nav hidden-xs hidden-sm">
<li >
<a href="https://x-wei.github.io/category/misc.html"><i class="fa fa-folder-o"></i> Misc</a>
</li>
<li >
<a href="https://x-wei.github.io/category/music.html"><i class="fa fa-folder-o"></i> Music</a>
</li>
<li class="active">
<a href="https://x-wei.github.io/category/notes.html"><i class="fa fa-folder-o"></i> Notes</a>
</li>
<li >
<a href="https://x-wei.github.io/category/soft.html"><i class="fa fa-folder-o"></i> Soft</a>
</li>
<li >
<a href="https://x-wei.github.io/category/tech.html"><i class="fa fa-folder-o"></i> Tech</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right hidden-sm hidden-md hidden-lg hidden-xl">
<li class="dropdown hidden-md hidden-lg hidden-xl">
<a class="dropdown-toggle" data-toggle="dropdown" href="javascript:void(0)">
<i class="fa fa-search"></i><span class="caret"></span>
</a>
<ul class="dropdown-menu">
<li><span>
<form class="navbar-search" action="/search.html">
<input type="text" class="search-query form-control col-lg-16" placeholder="Search" name="q" id="tipue_search_input" required>
</form></span>
</li>
</ul>
</li>
</ul>
<ul class="nav navbar-right navbar-form hidden-xs">
<li><span>
<form class="navbar-search" action="/search.html">
<input type="text" class="search-query form-control col-lg-16" placeholder="查找" name="q" id="tipue_search_input" required>
</form></span>
</li>
</ul>
<ul class="nav navbar-nav navbar-right hidden-xs">
<li><a href="https://x-wei.github.io/archives.html"><i class="fa fa-th-list"></i><span class="icon-label">Archive</span></a></li>
</ul>
</div>
<!-- /.navbar-collapse -->
</div>
</div> <!-- /.navbar -->
<!-- Banner -->
<!-- End Banner -->
<div class="container" style="min-height: 100%;height: auto !important;height: 100%;">
<div class="row" style="padding-bottom:80px;padding-top:80px;">
<div class="col-xl-21 col-lg-20 col-md-18">
<div id="loading-block">
<ol class="breadcrumb">
<li><a href="https://x-wei.github.io/" title="mx's blog"><i class="fa fa-home fa-lg"></i></a></li>
<li><a href="https://x-wei.github.io/category/notes.html" title="notes">notes</a></li>
<li class="active">[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks</li>
</ol>
<section id="content" class="article-content">
<article>
<header class="page-header jumbotron jumbotron-primary panel-primary" id="article-header">
<div class="panel-heading">
<h1>
[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks
<a href="https://x-wei.github.io/Ng_DLMooc_c2wk3.html"
rel="bookmark"
class="btn btn-primary btn-lg"
title="到 [Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks 的永久链接">
<i class="mdi-action-launch"></i>
</a>
</h1>
</div>
<div class="panel-body">
<div class="post-info">
<span class="published">
<time datetime="2017-10-23T00:00:00+02:00"><i class="fa fa-calendar"></i> Mon, 23 Oct 2017</time>
</span>
<span class="btn-group">
<a href="https://x-wei.github.io/tag/deep-learning.html" class="btn btn-primary btn-xs"><i class="fa fa-tag"></i> deep learning</a>
</span>
<span class="label label-default">Series</span>
Part 7 of «Andrew Ng Deep Learning MOOC»
</div><!-- /.post-info --> </div>
</header>
<div class="entry-content jumbotron" id="article-content">
<div class="panel panel-default">
<div class="panel-heading">
目录
</div>
<div class="panel-boy">
<div id="toc"><ul><li><a class="toc-href" href="#hyperparameter-parameters" title="Hyperparameter parameters">Hyperparameter parameters</a><ul><li><a class="toc-href" href="#tuning-process" title="Tuning process">Tuning process</a></li><li><a class="toc-href" href="#using-an-appropriate-scale-to-pick-hyperparameters" title="Using an appropriate scale to pick hyperparameters">Using an appropriate scale to pick hyperparameters</a></li><li><a class="toc-href" href="#hyperparameters-tuning-in-practice-pandas-vs-caviar" title="Hyperparameters tuning in practice: Pandas vs. Caviar">Hyperparameters tuning in practice: Pandas vs. Caviar</a></li></ul></li><li><a class="toc-href" href="#batch-normalization_1" title="Batch Normalization">Batch Normalization</a><ul><li><a class="toc-href" href="#normalizing-activations-in-a-network" title="Normalizing activations in a network">Normalizing activations in a network</a></li><li><a class="toc-href" href="#fitting-batch-norm-into-a-neural-network" title="Fitting Batch Norm into a neural network">Fitting Batch Norm into a neural network</a></li><li><a class="toc-href" href="#why-does-batch-norm-work" title="Why does Batch Norm work?">Why does Batch Norm work?</a></li><li><a class="toc-href" href="#batch-norm-at-test-time" title="Batch Norm at test time">Batch Norm at test time</a></li></ul></li><li><a class="toc-href" href="#multiclass-classification_1" title="Multiclass classification">Multiclass classification</a><ul><li><a class="toc-href" href="#softmax-regression" title="Softmax Regression">Softmax Regression</a></li><li><a class="toc-href" href="#training-a-softmax-classifier" title="Training a softmax classifier">Training a softmax classifier</a></li></ul></li><li><a class="toc-href" href="#introduction-to-programming-frameworks_1" title="Introduction to programming frameworks">Introduction to programming frameworks</a><ul><li><a class="toc-href" href="#deep-learning-frameworks" title="Deep learning frameworks">Deep learning frameworks</a></li><li><a class="toc-href" href="#tensorflow" title="TensorFlow">TensorFlow</a></li></ul></li></ul></div>
</div>
</div>
<h2 id="hyperparameter-parameters">Hyperparameter parameters</h2>
<p>Tips for hyperparam-tuning. </p>
<h3 id="tuning-process">Tuning process</h3>
<p>Many hyperparams to tune, mark importance by colors (red > yellow > purple):<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image.png"/> </p>
<p>How to select set of values to explore ? </p>
<ul>
<li>Do <strong>NOT</strong> use grid search (grid of n * n) </li>
</ul>
<p>— this was OK in pre-DL era. </p>
<ul>
<li><strong>try random values.</strong> </li>
</ul>
<p>reason: difficule to know which hyperparam is most important, by randomization, <em>can try out n</em>n distinct values for each hyperparam.*<br/>
In extreme case, one is <code>alpha</code>, the other is <code>epislon</code>. </p>
<ul>
<li>in grid search: only n distinct values of alpha are tried </li>
<li>in random choice: can have n*n distinct values of alpha </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image001.png"/> </p>
<ul>
<li><strong>Coarse to fine</strong> sample scheme: zoom in to smaller regions of hyperparam space and re-sample more densely. </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image002.png"/> </p>
<h3 id="using-an-appropriate-scale-to-pick-hyperparameters">Using an appropriate scale to pick hyperparameters</h3>
<p>"Sampling at random", but at <em>appropriate scale, not uniformly.</em><br/>
example: choice of alpha in [0.001, 1]<br/>
→ <em>sample uniformly at log scale</em> is more resonable: equal resources are used to search at each scale. </p>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image003.png"/> </p>
<p>implementation: </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">r = -4 * np.random.rand() # -4 <= r <= 0, uniformly at randome </span></span>
<span class="code-line"><span class="err">alpha = np.exp(10, r) # 10e-4 <= alpha <= 1.0</span></span>
</pre></div>
<p><em>sampling beta for exp-weighted-avg: </em>sample in the range of [0.9, 0.999]<br/>
→ convert to sampling 1-beta, which is in range [0.0001, 0.1] </p>
<h3 id="hyperparameters-tuning-in-practice-pandas-vs-caviar">Hyperparameters tuning in practice: Pandas vs. Caviar</h3>
<p>Tricks on how to <em>organize</em> hyper-param-tuning process. </p>
<p><em>re-test hyperparams occasionally:</em> intuitions get stale, re-evaluate hyperparams every several months. </p>
<p>Two major schools of training </p>
<ul>
<li><strong>Panda approach</strong>: <em>babysitting one model</em> </li>
</ul>
<p>Huge dataset, limited computing resources, can only train one model → babysit the model as it's training. Watch learning curve, try changing hyparams once a day.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image004.png"/> </p>
<ul>
<li><strong>Caviar approach</strong>: <em>train many models in parallel</em> </li>
</ul>
<p>Have enough computation power.<br/>
Different model/hyperparams being trained at the same time in parallel, pick the best one.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image005.png"/> </p>
<h2 id="batch-normalization_1">Batch Normalization</h2>
<p><strong>Batch normalization</strong>:<br/>
(in some cases) <em>makes NN much more robust, and DNN much easier to train.</em> </p>
<h3 id="normalizing-activations-in-a-network">Normalizing activations in a network</h3>
<p>In pre-DL: normalize inputs to speedup learning. "make contours round"<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image007.png"/><br/>
In NN: normalize the activation <code>a[l-1]</code> from previous layer could help (in practice, usually normalize <code>z[l-1]</code>.)<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image009.png"/> </p>
<p><strong>BatchNorm algo</strong>:<br/>
intermediate values at each layer: <code>z[l]</code><br/>
→ compute mean & variance<br/>
⇒ get normalized <code>z[l]_normed</code>. (mean=0, std=1)<br/>
→ <strong>trasform</strong> <code>z[l]_normed</code> to <code>z_tilde[l]</code> (mean=<code>beta</code>, std=<code>gamma</code>, <em>beta and gamma are learnable params</em>),<br/>
reason: for hidden units, want to move/stretch the support of hidden inputs, so as to profit from non-linearity of activation function. </p>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image011.png"/> </p>
<h3 id="fitting-batch-norm-into-a-neural-network">Fitting Batch Norm into a neural network</h3>
<p>Add batchnorm to NN: replace z[l] to z_tilde[l] at each layer before activation g[l].<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image012.png"/> </p>
<p>Extra params to learn: <code>gamma[l]</code> and <code>beta[l]</code> at each layer. </p>
<p>In practice: no need to implement all details of BN, use DL framework. </p>
<p><strong>No bias term (b) in BN</strong>:<br/>
z[l] = W[l] * a[l-1] + b[l]<br/>
but z[l] will be centered anyway → <code>b[l]</code> is not useful.<br/>
→ <code>b[l]</code> is replaced by <code>beta[l]</code><br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image014.png"/><br/>
Dimension of beta[l], gamma[l]: the same as b[l] ( = n[l] * 1). </p>
<h3 id="why-does-batch-norm-work">Why does Batch Norm work?</h3>
<p><strong>intuition 1</strong>: similar to normalizing input ("make contours round") </p>
<p><strong>intuition 2</strong>: weights in deeper layers are more robust to changes in ealier layer weights.<br/>
i.e. Robost to <em>data distribution changing</em>. ("<strong>covariant shift</strong>") </p>
<p>motivating example:<br/>
cat-classification, <em>trained all with black cats, but applied to colored cats</em>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image016.png"/> </p>
<p>For NN, consider the 3rd layer's units:<br/>
input features: a[2],<br/>
if cover the first 2 layers, this is a NN to map from a[2] to y_hat<br/>
⇒ but when weights w[2],b[2] are updated in GD, <em>a[2]'s distribution is always changing</em>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image017.png"/><br/>
<strong>intuition</strong>: With BN, a[2] are ensured to <em>always have the same mean/variance</em><br/>
→ "data distribution" is unchanged → later layers can learn more easily, independent of previous layer's weights' change. </p>
<p><strong>intuition 2</strong>: BN as <em>regularization</em><br/>
each minibatch is scaled by mean/var of just that minibatch<br/>
→ <em>add noise</em> to the transformation from z[l] to z_tilde[l].<br/>
⇒ similar to dropout, add noise to each layer's activations.<br/>
therefore BN have (<em>slight</em>) regularization effect (thie regularization effect gets smaller as minibatch size grows).<br/>
(This is an unintended side effect.) </p>
<h3 id="batch-norm-at-test-time">Batch Norm at test time</h3>
<p><em>At training time</em>, z[l] is standarlized <em>over each minibatch</em>.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image018.png"/><br/>
⇒ But at test time needs to treat examples one at a time.<br/>
→ estimate the value of meu/sigma2<br/>
⇒ using<em> exp-weighted-avg</em> estimator across minibatchs (with beta close to 1 → ~running average).<br/>
at test time, just use the latest value of this exp-weighted-avg estimation as meu/sigma2.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image019.png"/> </p>
<h2 id="multiclass-classification_1">Multiclass classification</h2>
<h3 id="softmax-regression">Softmax Regression</h3>
<p>So far: only binary classification<br/>
generalize logistic regression to >2 classes ⇒ <em>softmax regression</em>. </p>
<p><code>C</code> = #classes, = #units in output layer<br/>
each component in y_hat is probability of one class, y_hat is normalized.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image021.png"/> </p>
<p><strong>softmax layer</strong>: </p>
<ul>
<li>z[L] = W[L] * a[l-1] + b[L] — same as before </li>
<li>a[L] = y_hat = g(z[L]) </li>
</ul>
<p>activation function: <em>softmax</em><br/>
take exp(z[L]) --element-wise, and then normalize:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image023.png"/> </p>
<p>The softmax activation function is unusual because it takes a <em>vector</em> instead of scalar.<br/>
Softmax is generalization of logistic regression: decision boundary of a <em>single-layer (no hidden layer)</em> softmax is also <em>linear</em>:<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image025.png"/> </p>
<h3 id="training-a-softmax-classifier">Training a softmax classifier</h3>
<p><strong>understanding softmax</strong> </p>
<ul>
<li>"softmax" is in contrast to "<em>hardmax</em>": </li>
</ul>
<p>hardmax[i]= 1 if z_i=max else 0.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image026.png"/> </p>
<ul>
<li>When C = 2, softmax reduces to logistic regression. </li>
</ul>
<p>softmax(C=2) = [logistic-reg(), 1-logistic-reg] </p>
<p><strong>loss function</strong><br/>
recall: loss function in logistic regression<br/>
L(y, y_hat) = -1 * sum( y_i * log yhat_i + (1-y_i) * log(yhat_i) )<br/>
→ want y_hat big when y_i=1, small when y_i=0 </p>
<ul>
<li>training label y: one-hot encoding. </li>
<li>prediciton y_hat: probability vector </li>
</ul>
<p>loss function: </p>
<ul>
<li>if y_k=1, want to make yhat_k big </li>
</ul>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image027.png"/><br/>
→ max-likelihood estimation. </p>
<p><strong>GD with softmax</strong><br/>
fwdprop:<br/>
Z[L] --(softmax)--> a[L]=y_hat → L(y_hat, y)<br/>
backprop:<br/>
<em>dZ[L] = y_hat - y</em> </p>
<h2 id="introduction-to-programming-frameworks_1">Introduction to programming frameworks</h2>
<h3 id="deep-learning-frameworks">Deep learning frameworks</h3>
<p><img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image029.png"/> </p>
<h3 id="tensorflow">TensorFlow</h3>
<p>motivating problem: minimize cost function <code>J(w) = (w-5)^2</code> </p>
<ul>
<li><code>import tensorflow as tf</code> </li>
<li>
<p>define <em>parameter</em> to optimize:<br/>
<code>w = tf.Variable(0, dtype=tf.float32)</code> </p>
</li>
<li>
<p>define cost function:<br/>
<code>cost = tf.add(tf.add(w**2), tf.multiply(-10., w)), 25) # w^2 - 10w + 25
# also possible to use tf-reloaded operators:
cost = w**2 - 10 * w + 25</code></p>
</li>
<li>
<p>tells tf to minimize the cost with GD optimizer: </p>
</li>
</ul>
<p><code>train = tf.train.GradientDescentOptimizer(0.01).minimize(cost)</code><br/>
till now the <em>computation graph</em> is defined → backward derivatives are auto-computed.<br/>
<img alt="" class="img-responsive" src="../images/Ng_DLMooc_c2wk3/pasted_image030.png"/> </p>
<ul>
<li>start the training </li>
</ul>
<p>Quite idiomatic process:<br/>
initialize vars → create session → run operations in session </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">init = tf.global_variables_initializer() </span></span>
<span class="code-line"><span class="err">session = tf.Session() </span></span>
<span class="code-line"><span class="err">session.run(init) </span></span>
<span class="code-line"><span class="err">session.run(train) # run 1 iteration of training</span></span>
</pre></div>
<p>alternative format: </p>
<div class="highlight"><pre><span class="code-line"><span></span><span class="err">with tf.Session() as session: </span></span>
<span class="code-line"><span class="err"> session.run(init) </span></span>
<span class="code-line"><span class="err"> session.run(train)</span></span>
</pre></div>
<ul>
<li>To inspect the value of a parameter: <code>print(session.run(w))</code> </li>
<li>
<p>Run 1000 iters of GD: </p>
<p><code>for i in range(1000):
session.run(train)</code></p>
</li>
</ul>
<p><strong>Let loss function depends on training data:</strong> </p>
<ul>
<li>
<p>define training data as <em>placer holder</em>.<br/>
a placerholder is a variable whose value will be assigned later.<br/>
<code>x = tf.placeholder(tf.float32, [3,1])
cost = x[0][0] * w**2 + x[1][0] * w + x[2][0]</code></p>
</li>
<li>
<p>feed actual data value to placerholder: use <em>feed_dict</em> in session.run() </p>
<p><code>data = np.array([1., -10., 25.]).reshape((3,1)
session.run(train, feed_dict={x: data})</code></p>
</li>
</ul>
</div>
<div class="entry-content jumbotron" id="source-content" style="display: none">
<!-- <pre><code id="source-code">
</code></pre> -->
<div id="source-code"></div>
</div>
<!-- /.entry-content -->
<div class="row" id="prevnext">
<div class="col-xs-12">
<a href="https://x-wei.github.io/Ng_DLMooc_c2wk1.html" class="btn btn-default btn-lg" style="float:left;clear:both;background-color:#fff;">
<h4><i class="fa fa-arrow-left"></i>
[Improving Deep Neural Networks] week1. Practical aspects of Deep Learning
</h4>
</a>
</div>
<div class="col-xs-12">
<a href="https://x-wei.github.io/Ng_DLMooc_c2wk2.html" class="btn btn-default btn-lg" style="float:right;clear:both;background-color:#fff;">
<h4>
[Improving Deep Neural Networks] week2. Optimization algorithms<i class="fa fa-arrow-right"></i>
</h4>
</a>
</div>
</div>
<div class="panel panel-default" id="series">
<div class="panel-heading">
<h4>
Part 7 of series «Andrew Ng Deep Learning MOOC»：
</h4>
</div>
<ul class="list-group">
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c1wk1.html' style="text-align:left">[Neural Networks and Deep Learning] week1. Introduction to deep learning</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c1wk2.html' style="text-align:left">[Neural Networks and Deep Learning] week2. Neural Networks Basics</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c1wk3.html' style="text-align:left">[Neural Networks and Deep Learning] week3. Shallow Neural Network</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c1wk4.html' style="text-align:left">[Neural Networks and Deep Learning] week4. Deep Neural Network</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c2wk1.html' style="text-align:left">[Improving Deep Neural Networks] week1. Practical aspects of Deep Learning</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c2wk2.html' style="text-align:left">[Improving Deep Neural Networks] week2. Optimization algorithms</a></li>
<li class="list-group-item"><a class="btn btn-primary" href='https://x-wei.github.io/Ng_DLMooc_c2wk3.html' style="text-align:left">[Improving Deep Neural Networks] week3. Hyperparameter tuning, Batch Normalization and Programming Frameworks</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c3wk1.html' style="text-align:left">[Structuring Machine Learning Projects] week1. ML Strategy (1)</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c3wk2.html' style="text-align:left">[Structuring Machine Learning Projects] week2. ML Strategy (2)</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c4wk1.html' style="text-align:left">[Convolutional Neural Networks] week1. Foundations of Convolutional Neural Networks</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c4wk2.html' style="text-align:left">[Convolutional Neural Networks] week2. Deep convolutional models: case studies</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c4wk3.html' style="text-align:left">[Convolutional Neural Networks] week3. Object detection</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c4wk4.html' style="text-align:left">[Convolutional Neural Networks] week4. Special applications: Face recognition & Neural style transfer</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c5wk1.html' style="text-align:left">[Sequential Models] week1. Recurrent Neural Networks</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c5wk2.html' style="text-align:left">[Sequential Models] week2. Natural Language Processing & Word Embeddings</a></li>
<li class="list-group-item"><a class="btn btn-default" href='https://x-wei.github.io/Ng_DLMooc_c5wk3.html' style="text-align:left">[Sequential Models] week3. Sequence models & Attention mechanism</a></li>
</ul>
</div>
<section class="comments" id="comments">
<div class="panel-group" id="accordion" role="tablist" aria-multiselectable="true">
<div class="panel panel-primary">
<div class="panel-heading" role="tab" id="disqus-heading">
<h4 class="panel-title">
<a data-toggle="collapse" data-parent="#accordion" href="#disqus-comments" aria-expanded="true" aria-controls="disqus-comments">
<i class="fa fa-comments-o"></i> Disqus 留言
</a>
</h4>
</div>
<div id="disqus-comments" class="panel-collapse collapse.show" role="tabpanel" aria-labelledby="disqus-heading">
<div class="panel-body">
<div class="tab-pane fade active in" id="disqus-comments">
<div id="disqus_thread"></div>
<script type="text/javascript">
/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
var disqus_shortname = 'xweisblog'; // required: replace example with your forum shortname
var disqus_identifier = 'Ng_DLMooc_c2wk3';
var disqus_url = 'https://x-wei.github.io/Ng_DLMooc_c2wk3.html';
var disqus_config = function () {
this.language = "zh";
};
/* * * DON'T EDIT BELOW THIS LINE * * */
(function () {
var dsq = document.createElement('script');
dsq.type = 'text/javascript';
dsq.async = true;
dsq.src = '//' + disqus_shortname + '.disqus.com/embed.js';
(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
})();
</script>
<noscript>Please enable JavaScript to view the <a href="http://disqus.com/?ref_noscript">comments powered by
Disqus.</a></noscript>
<a href="http://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>
</div>
</div>
</div>
</div>
</div>
</section> </article>
</section>
</div>
<!-- Modal -->
<div class="modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
<div class="modal-dialog modal-lg">
<div class="modal-content">
<a data-dismiss="modal" href="javascript:void(0);">
<img id="mimg" src="" style="width:100%;height:auto">
</a>
</div>
</div><!-- /.modal-dialog -->
</div><!-- /.modal -->
</div>
<div class="col-xl-3 col-lg-4 col-md-6" id="sidebar">
<aside>
<section>
<div class="sidebar-container">
<div class="sidebar-item ">
<div class="panel panel-default">
<div class="panel-heading">
<h4>
<i class="fa fa-user fa-lg"></i>
<a href="https://x-wei.github.io/about.html">
关于 mx
</a>
</h4>
</div>
<div class="panel-body" id="aboutme">
<a href="https://x-wei.github.io/about.html"><img width="100%" src="https://x-wei.github.io/../images/mx.jpg"/></a>
<h3 style="text-align:center">
<a href="https://github.com/x-wei" target="_blank">
<i class="fa fa-github" style="text-align:center"></i></a>
<a href="https://weibo.com/u/1817154611" target="_blank">
<i class="fa fa-weibo" style="text-align:center"></i></a>
<a href="mailto:[email protected]" target="_blank">
<i class="mdi-communication-email" style="text-align:center"></i></a>
</h3>
<h4 class="widget-title">推荐文章</h4>
<div class="textwidget">
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/TeXmacs_intro.html">学术文章写作利器: TeXmacs介绍</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/hashcode2014-solved-by-LP.html">运筹的力量: 用线性规划解决Google 2014 HashCode问题</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/%E6%AD%A3%E5%88%99%E8%A1%A8%E8%BE%BE%E5%BC%8F%E5%85%A5%E9%97%A8%E7%AE%80%E4%BB%8B.html">正则表达式入门简介</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/%E6%88%91%E7%9A%84ubuntu10.04%E9%85%8D%E7%BD%AE%E6%80%BB%E7%BB%93.html">我的ubuntu10.04配置总结</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/PT-summery.html">2011巴黎高科(ParisTech)申请总结</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/GT-summery.html">用尽量少的时间考一个够用的分数--一点Tofel/GRE备考经验</a><br></li>
<li class="widget-container widget_text">
<a href="https://x-wei.github.io/pelican_github_blog.html">用pelican在github上创建自己的博客!</a><br></li>
</div>
<br><a href="https://www.polytechnique.edu/" target="_blank">
<img src="https://x-wei.github.io/images/x-logo.png" alt="X" width="180" border="0" />
</a><br/>
<br><a href="https://www.sjtu.edu.cn/">
<img src="https://x-wei.github.io/images/ssss.jpg" width="180" border="0" alt="上海西南某高校">
</a><br/>
<br>
<h4 class="widget-title">Visitors</h4>
<script type="text/javascript" src="//rf.revolvermaps.com/0/0/1.js?i=59olkba9w7e&s=220&m=3&v=true&r=false&b=000000&n=false&c=ff0000" async="async"></script>
<!-- hitwebcounter Code START -->
<a href="https://www.hitwebcounter.com/how-to/how-to-what-is-free-blog-counter.php" target="_blank">
<img src="https://hitwebcounter.com/counter/counter.php?page=5954927&style=0036&nbdigits=5&type=ip&initCount=0" title="web counter" Alt="web counter" border="0" ></a>
<br/>
</div>
</div>
</div>
<div class="sidebar-item ">
<div class="panel panel-default">
<div class="panel-heading">
<h4>
<a href="https://x-wei.github.io/tags.html"><i class="fa fa-tags fa-lg"></i><span class="icon-label">标签云</span></a>
</h4>
</div>
<div class="panel-body">
<ul class="list-group list-inline tagcloud" id="tags">
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/pelican.html">
pelican <sup> 6</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/google.html">
google <sup> 6</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/torch.html">
torch <sup> 6</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/tex.html">
tex <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/ba-li-gao-ke.html">
巴黎高科 <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/markdown.html">
markdown <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/linux.html">
linux <sup> 3</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/inf422.html">
inf422 <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/toefl.html">
Toefl <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/regex.html">
regex <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/git.html">
git <sup> 5</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/weka.html">
weka <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-1">
<a href="https://x-wei.github.io/tag/scala.html">
scala <sup> 12</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/opencv.html">
opencv <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/scrapy.html">
scrapy <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/gre.html">
GRE <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/lp.html">
LP <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/android.html">
android <sup> 9</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/pandas.html">
pandas <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/codejam.html">
codejam <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/fr.html">
fr <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/shell.html">
shell <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-1">
<a href="https://x-wei.github.io/tag/python.html">
python <sup> 13</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/simongarfunkel.html">
Simon&Garfunkel <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/french.html">
french <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/wai-guan.html">
外观 <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/zhong-wen-luan-ma.html">
中文乱码 <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/host.html">
host <sup> 3</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/ssh.html">
ssh <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/ubuntu.html">
ubuntu <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/java.html">
java <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/spark.html">
spark <sup> 6</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/tips.html">
tips <sup> 3</sup>
</a>
</li>
<li class="list-group-item tag-1">
<a href="https://x-wei.github.io/tag/deep-learning.html">
deep learning <sup> 28</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/c.html">
C++ <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-1">
<a href="https://x-wei.github.io/tag/algorithm.html">
algorithm <sup> 35</sup>
</a>
</li>
<li class="list-group-item tag-4">
<a href="https://x-wei.github.io/tag/texmacs.html">
TeXmacs <sup> 1</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/ml.html">
ml <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/eclipse.html">
eclipse <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/ocaml.html">
OCaml <sup> 8</sup>
</a>
</li>
<li class="list-group-item tag-2">
<a href="https://x-wei.github.io/tag/r.html">
R <sup> 4</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/chu-guo.html">
出国 <sup> 2</sup>
</a>
</li>
<li class="list-group-item tag-3">
<a href="https://x-wei.github.io/tag/kuai-jie-jian.html">
快捷键 <sup> 3</sup>
</a>
</li>
</ul>
</div>
</div>
</div>
<li class="list-group-item"><h4><i class="fa fa-tags fa-list-ul"></i><span class="icon-label">Series</span></h4>
<ul class="list-group">
<li class="list-group-item">
<h5></i> Previous article</h5>
<a href="https://x-wei.github.io/Ng_DLMooc_c2wk2.html">[Improving Deep Neural Networks] week2. Optimization algorithms</a>
</li>
<li class="list-group-item">
<h5>Next article</h5>
<a href="https://x-wei.github.io/Ng_DLMooc_c3wk1.html">[Structuring Machine Learning Projects] week1. ML Strategy (1)</a>
</li>
</ul>
</li>
<div class="sidebar-item hidden-xs">
<div class="panel panel-default">
<div class="panel-heading">
<h4>
<i class="fa fa-github fa-lg"></i><span class="icon-label">GitHub仓库</span>
</h4>
</div>
<div class="panel-body">
<div id="gh_repos">
<p class="list-group-item">Status updating...</p>
</div>
<a href="https://github.com/x-wei">@x-wei</a> on GitHub
</div>
</div>
</div>
</div>
</section>
<div class="panel panel-default hidden-xs hidden-sm" id="affix-toc">
<div class="panel-heading"><h4>
目录</h4>
</div>
<div class="panel-boy">
<div id="toc"><ul><li><a class="toc-href" href="#hyperparameter-parameters" title="Hyperparameter parameters">Hyperparameter parameters</a><ul><li><a class="toc-href" href="#tuning-process" title="Tuning process">Tuning process</a></li><li><a class="toc-href" href="#using-an-appropriate-scale-to-pick-hyperparameters" title="Using an appropriate scale to pick hyperparameters">Using an appropriate scale to pick hyperparameters</a></li><li><a class="toc-href" href="#hyperparameters-tuning-in-practice-pandas-vs-caviar" title="Hyperparameters tuning in practice: Pandas vs. Caviar">Hyperparameters tuning in practice: Pandas vs. Caviar</a></li></ul></li><li><a class="toc-href" href="#batch-normalization_1" title="Batch Normalization">Batch Normalization</a><ul><li><a class="toc-href" href="#normalizing-activations-in-a-network" title="Normalizing activations in a network">Normalizing activations in a network</a></li><li><a class="toc-href" href="#fitting-batch-norm-into-a-neural-network" title="Fitting Batch Norm into a neural network">Fitting Batch Norm into a neural network</a></li><li><a class="toc-href" href="#why-does-batch-norm-work" title="Why does Batch Norm work?">Why does Batch Norm work?</a></li><li><a class="toc-href" href="#batch-norm-at-test-time" title="Batch Norm at test time">Batch Norm at test time</a></li></ul></li><li><a class="toc-href" href="#multiclass-classification_1" title="Multiclass classification">Multiclass classification</a><ul><li><a class="toc-href" href="#softmax-regression" title="Softmax Regression">Softmax Regression</a></li><li><a class="toc-href" href="#training-a-softmax-classifier" title="Training a softmax classifier">Training a softmax classifier</a></li></ul></li><li><a class="toc-href" href="#introduction-to-programming-frameworks_1" title="Introduction to programming frameworks">Introduction to programming frameworks</a><ul><li><a class="toc-href" href="#deep-learning-frameworks" title="Deep learning frameworks">Deep learning frameworks</a></li><li><a class="toc-href" href="#tensorflow" title="TensorFlow">TensorFlow</a></li></ul></li></ul></div>
</div>
</div>
</aside>
</div>
</div>
</div>
<footer id="fcfooter">
<hr/>
<div class="container">
links :
<a href="https://farseerfc.github.com/">farseerfc</a>
<a href="https://hyhx2008.github.com/">H.Y.</a>
<a href="https://reginald1787.github.io/">reginald1787</a>
<a href="https://log.dofine.me/">dofine</a>
<div class="row">
<div class="col-md-14">
<p><small>
© 2020 mx
· 通过
<a href="https://docs.getpelican.com/" target="_blank">Pelican</a> 生成 <a rel="license" href="https://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="//i.creativecommons.org/l/by-nc-sa/4.0/80x15.png" /></a>
<!-- Content -->
<!-- licensed under a <a rel="license" href="https://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution 4.0 International License</a>, except where indicated otherwise. -->
</small></p>
</div>
</div>
</div>
<a href="#" class="btn btn-primary btn-fab btn-raised mdi-editor-vertical-align-top withripple" style="position:fixed;bottom:30px;right:30px;z-index:1000"></a>
</footer>
<script src="https://x-wei.github.io/theme/js/jquery.min.js"></script>
<!-- Include all compiled plugins (below), or include individual files as needed -->
<script src="https://x-wei.github.io/theme/js/bootstrap.min.js"></script>
<!-- Enable responsive features in IE8 with Respond.js (https://github.com/scottjehl/Respond) -->
<script src="https://x-wei.github.io/theme/js/respond.min.js"></script>
<!-- GitHub JS -->
<script type="text/javascript">
$(document).ready(function () {
if (!window.jXHR) {
var jxhr = document.createElement('script');
jxhr.type = 'text/javascript';
jxhr.src = 'https://x-wei.github.io/theme/js/jXHR.js';
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(jxhr, s);
}
github.showRepos({
user: 'x-wei',
count: 5,
skip_forks: false,
target: '#gh_repos'
});
});
</script>
<script src="https://x-wei.github.io/theme/js/github.js" type="text/javascript"></script>
<!-- End GitHub JS Code -->
<!-- Disqus -->
<script type="text/javascript">
/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
var disqus_shortname = 'xweisblog'; // required: replace example with your forum shortname
/* * * DON'T EDIT BELOW THIS LINE * * */
(function () {
var s = document.createElement('script');
s.async = true;
s.type = 'text/javascript';
s.src = '//' + disqus_shortname + '.disqus.com/count.js';
(document.getElementsByTagName('HEAD')[0] || document.getElementsByTagName('BODY')[0]).appendChild(s);
}());
</script>
<!-- End Disqus Code -->
<!-- Google Analytics -->
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-30756331-1']);
_gaq.push(['_trackPageview']);
(function () {
var ga = document.createElement('script');
ga.type = 'text/javascript';
ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(ga, s);
})();
</script>
<!-- End Google Analytics Code -->
<script src="https://x-wei.github.io/theme/js/ripples.min.js"></script>
<script src="https://x-wei.github.io/theme/js/material.min.js"></script>
<script src="https://x-wei.github.io/theme/js/jquery.bootstrap-autohidingnavbar.min.js"></script>
<script>
$(document).ready(function() {
$.material.init();
$("div.navbar").autoHidingNavbar();
$(".img-responsive").css("cursor","pointer").on('click',function(){
var sr=$(this).attr('src');
$('#mimg').attr('src',sr);
$('#myModal').modal('show');
});
$('#affix-toc').affix({
offset: {
top: function(){
if($('#affix-toc').hasClass("affix"))
return $('#sidebar').height();
return $('#sidebar').height() - $('#affix-toc').height();
},
bottom: function (){
return $("#fcfooter").offset().top -
$("#article-content").offset().top -
$("#article-content").height() + 20;
}
}
});
$('#affix-toc').width($('#sidebar').width());
});
$(window).resize(function () {
$('#affix-toc').width($('#sidebar').width());