forked from mnielsen/nnadl_site
-
Notifications
You must be signed in to change notification settings - Fork 34
/
Copy pathexercises_and_problems.html
250 lines (219 loc) · 19.5 KB
/
exercises_and_problems.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
<!DOCTYPE html>
<html lang="en">
<!-- Produced from a LaTeX source file. Note that the production is done -->
<!-- by a very rough-and-ready (and buggy) script, so the HTML and other -->
<!-- code is quite ugly! Later versions should be better. -->
<meta charset="utf-8">
<meta name="citation_title" content="ニューラルネットワークと深層学習">
<meta name="citation_author" content="Nielsen, Michael A.">
<meta name="citation_publication_date" content="2015">
<meta name="citation_fulltext_html_url" content="http://neuralnetworksanddeeplearning.com">
<meta name="citation_publisher" content="Determination Press">
<link rel="icon" href="nnadl_favicon.ICO" />
<title>ニューラルネットワークと深層学習</title>
<script src="assets/jquery.min.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {inlineMath: [['$','$']]},
"HTML-CSS":
{scale: 92},
TeX: { equationNumbers: { autoNumber: "AMS" }}});
</script>
<script type="text/javascript" src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
<link href="assets/style.css" rel="stylesheet">
<link href="assets/pygments.css" rel="stylesheet">
<link rel="stylesheet" href="http://code.jquery.com/ui/1.11.2/themes/smoothness/jquery-ui.css">
<style>
/* Adapted from */
/* https://groups.google.com/d/msg/mathjax-users/jqQxrmeG48o/oAaivLgLN90J, */
/* by David Cervone */
@font-face {
font-family: 'MJX_Math';
src: url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/eot/MathJax_Math-Italic.eot'); /* IE9 Compat Modes */
src: url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/eot/MathJax_Math-Italic.eot?iefix') format('eot'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/woff/MathJax_Math-Italic.woff') format('woff'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/otf/MathJax_Math-Italic.otf') format('opentype'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/svg/MathJax_Math-Italic.svg#MathJax_Math-Italic') format('svg');
}
@font-face {
font-family: 'MJX_Main';
src: url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/eot/MathJax_Main-Regular.eot'); /* IE9 Compat Modes */
src: url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/eot/MathJax_Main-Regular.eot?iefix') format('eot'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/woff/MathJax_Main-Regular.woff') format('woff'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/otf/MathJax_Main-Regular.otf') format('opentype'),
url('https://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/svg/MathJax_Main-Regular.svg#MathJax_Main-Regular') format('svg');
}
</style>
</head>
<body><div class="nonumber_header"><h2>On the exercises and problems</h2></div><div class="section"><div id="toc">
<p class="toc_title"><a href="index.html">ニューラルネットワークと深層学習</a></p><p class="toc_not_mainchapter"><a href="about.html">What this book is about</a></p><p class="toc_not_mainchapter"><a href="exercises_and_problems.html">On the exercises and problems</a></p><p class='toc_mainchapter'><a id="toc_using_neural_nets_to_recognize_handwritten_digits_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_using_neural_nets_to_recognize_handwritten_digits" src="images/arrow.png" width="15px"></a><a href="chap1.html">ニューラルネットワークを用いた手書き文字認識</a><div id="toc_using_neural_nets_to_recognize_handwritten_digits" style="display: none;"><p class="toc_section"><ul><a href="chap1.html#perceptrons"><li>Perceptrons</li></a><a href="chap1.html#sigmoid_neurons"><li>Sigmoid neurons</li></a><a href="chap1.html#the_architecture_of_neural_networks"><li>The architecture of neural networks</li></a><a href="chap1.html#a_simple_network_to_classify_handwritten_digits"><li>A simple network to classify handwritten digits</li></a><a href="chap1.html#learning_with_gradient_descent"><li>Learning with gradient descent</li></a><a href="chap1.html#implementing_our_network_to_classify_digits"><li>Implementing our network to classify digits</li></a><a href="chap1.html#toward_deep_learning"><li>Toward deep learning</li></a></ul></p></div>
<script>
$('#toc_using_neural_nets_to_recognize_handwritten_digits_reveal').click(function() {
var src = $('#toc_img_using_neural_nets_to_recognize_handwritten_digits').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_using_neural_nets_to_recognize_handwritten_digits").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_using_neural_nets_to_recognize_handwritten_digits").attr('src', 'images/arrow.png');
};
$('#toc_using_neural_nets_to_recognize_handwritten_digits').toggle('fast', function() {});
});</script><p class='toc_mainchapter'><a id="toc_how_the_backpropagation_algorithm_works_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_how_the_backpropagation_algorithm_works" src="images/arrow.png" width="15px"></a><a href="chap2.html">逆伝播の仕組み</a><div id="toc_how_the_backpropagation_algorithm_works" style="display: none;"><p class="toc_section"><ul><a href="chap2.html#warm_up_a_fast_matrix-based_approach_to_computing_the_output_from_a_neural_network"><li>Warm up: a fast matrix-based approach to computing the output from a neural network</li></a><a href="chap2.html#the_two_assumptions_we_need_about_the_cost_function"><li>The two assumptions we need about the cost function</li></a><a href="chap2.html#the_hadamard_product_$s_\odot_t$"><li>The Hadamard product, $s \odot t$</li></a><a href="chap2.html#the_four_fundamental_equations_behind_backpropagation"><li>The four fundamental equations behind backpropagation</li></a><a href="chap2.html#proof_of_the_four_fundamental_equations_(optional)"><li>Proof of the four fundamental equations (optional)</li></a><a href="chap2.html#the_backpropagation_algorithm"><li>The backpropagation algorithm</li></a><a href="chap2.html#the_code_for_backpropagation"><li>The code for backpropagation</li></a><a href="chap2.html#in_what_sense_is_backpropagation_a_fast_algorithm"><li>In what sense is backpropagation a fast algorithm?</li></a><a href="chap2.html#backpropagation_the_big_picture"><li>Backpropagation: the big picture</li></a></ul></p></div>
<script>
$('#toc_how_the_backpropagation_algorithm_works_reveal').click(function() {
var src = $('#toc_img_how_the_backpropagation_algorithm_works').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_how_the_backpropagation_algorithm_works").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_how_the_backpropagation_algorithm_works").attr('src', 'images/arrow.png');
};
$('#toc_how_the_backpropagation_algorithm_works').toggle('fast', function() {});
});</script><p class='toc_mainchapter'><a id="toc_improving_the_way_neural_networks_learn_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_improving_the_way_neural_networks_learn" src="images/arrow.png" width="15px"></a><a href="chap3.html">ニューラルネットワークの学習の改善</a><div id="toc_improving_the_way_neural_networks_learn" style="display: none;"><p class="toc_section"><ul><a href="chap3.html#the_cross-entropy_cost_function"><li>The cross-entropy cost function</li></a><a href="chap3.html#overfitting_and_regularization"><li>Overfitting and regularization</li></a><a href="chap3.html#weight_initialization"><li>Weight initialization</li></a><a href="chap3.html#handwriting_recognition_revisited_the_code"><li>Handwriting recognition revisited: the code</li></a><a href="chap3.html#how_to_choose_a_neural_network's_hyper-parameters"><li>How to choose a neural network's hyper-parameters?</li></a><a href="chap3.html#other_techniques"><li>Other techniques</li></a></ul></p></div>
<script>
$('#toc_improving_the_way_neural_networks_learn_reveal').click(function() {
var src = $('#toc_img_improving_the_way_neural_networks_learn').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_improving_the_way_neural_networks_learn").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_improving_the_way_neural_networks_learn").attr('src', 'images/arrow.png');
};
$('#toc_improving_the_way_neural_networks_learn').toggle('fast', function() {});
});</script><p class='toc_mainchapter'><a id="toc_a_visual_proof_that_neural_nets_can_compute_any_function_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_a_visual_proof_that_neural_nets_can_compute_any_function" src="images/arrow.png" width="15px"></a><a href="chap4.html">ニューラルネットワークが任意の関数を表現できることの視覚的証明</a><div id="toc_a_visual_proof_that_neural_nets_can_compute_any_function" style="display: none;"><p class="toc_section"><ul><a href="chap4.html#two_caveats"><li>Two caveats</li></a><a href="chap4.html#universality_with_one_input_and_one_output"><li>Universality with one input and one output</li></a><a href="chap4.html#many_input_variables"><li>Many input variables</li></a><a href="chap4.html#extension_beyond_sigmoid_neurons"><li>Extension beyond sigmoid neurons</li></a><a href="chap4.html#fixing_up_the_step_functions"><li>Fixing up the step functions</li></a><a href="chap4.html#conclusion"><li>Conclusion</li></a></ul></p></div>
<script>
$('#toc_a_visual_proof_that_neural_nets_can_compute_any_function_reveal').click(function() {
var src = $('#toc_img_a_visual_proof_that_neural_nets_can_compute_any_function').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_a_visual_proof_that_neural_nets_can_compute_any_function").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_a_visual_proof_that_neural_nets_can_compute_any_function").attr('src', 'images/arrow.png');
};
$('#toc_a_visual_proof_that_neural_nets_can_compute_any_function').toggle('fast', function() {});
});</script><p class='toc_mainchapter'><a id="toc_why_are_deep_neural_networks_hard_to_train_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_why_are_deep_neural_networks_hard_to_train" src="images/arrow.png" width="15px"></a><a href="chap5.html">ニューラルネットワークを訓練するのはなぜ難しいのか</a><div id="toc_why_are_deep_neural_networks_hard_to_train" style="display: none;"><p class="toc_section"><ul><a href="chap5.html#the_vanishing_gradient_problem"><li>The vanishing gradient problem</li></a><a href="chap5.html#what's_causing_the_vanishing_gradient_problem_unstable_gradients_in_deep_neural_nets"><li>What's causing the vanishing gradient problem? Unstable gradients in deep neural nets</li></a><a href="chap5.html#unstable_gradients_in_more_complex_networks"><li>Unstable gradients in more complex networks</li></a><a href="chap5.html#other_obstacles_to_deep_learning"><li>Other obstacles to deep learning</li></a></ul></p></div>
<script>
$('#toc_why_are_deep_neural_networks_hard_to_train_reveal').click(function() {
var src = $('#toc_img_why_are_deep_neural_networks_hard_to_train').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_why_are_deep_neural_networks_hard_to_train").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_why_are_deep_neural_networks_hard_to_train").attr('src', 'images/arrow.png');
};
$('#toc_why_are_deep_neural_networks_hard_to_train').toggle('fast', function() {});
});</script>
<p class='toc_mainchapter'><a id="toc_deep_learning_reveal" class="toc_reveal" onMouseOver="this.style.borderBottom='1px solid #2A6EA6';" onMouseOut="this.style.borderBottom='0px';"><img id="toc_img_deep_learning" src="images/arrow.png" width="15px"></a><a href="chap6.html">深層学習</a><div id="toc_deep_learning" style="display: none;"><p class="toc_section"><ul><a href="chap6.html#introducing_convolutional_networks"><li>Introducing convolutional networks</li></a><a href="chap6.html#convolutional_neural_networks_in_practice"><li>Convolutional neural networks in practice</li></a><a href="chap6.html#the_code_for_our_convolutional_networks"><li>The code for our convolutional networks</li></a><a href="chap6.html#recent_progress_in_image_recognition"><li>Recent progress in image recognition</li></a><a href="chap6.html#other_approaches_to_deep_neural_nets"><li>Other approaches to deep neural nets</li></a><a href="chap6.html#on_the_future_of_neural_networks"><li>On the future of neural networks</li></a></ul></p></div>
<script>
$('#toc_deep_learning_reveal').click(function() {
var src = $('#toc_img_deep_learning').attr('src');
if(src == 'images/arrow.png') {
$("#toc_img_deep_learning").attr('src', 'images/arrow_down.png');
} else {
$("#toc_img_deep_learning").attr('src', 'images/arrow.png');
};
$('#toc_deep_learning').toggle('fast', function() {});
});</script>
<p class="toc_not_mainchapter"><a href="sai.html">
Appendix: 知性のある <i>シンプルな</i> アルゴリズムはあるか?</a></p>
<p class="toc_not_mainchapter"><a href="acknowledgements.html">Acknowledgements</a></p><p class="toc_not_mainchapter"><a href="faq.html">Frequently Asked Questions</a></p>
<hr>
<span class="sidebar_title">Sponsors</span>
<br/>
<a href='http://www.ersatz1.com/'><img src='assets/ersatz.png' width='140px' style="padding: 0px 0px 10px 8px; border-style: none;"></a>
<a href='http://gsquaredcapital.com/'><img src='assets/gsquared.png' width='150px' style="padding: 0px 0px 10px 10px; border-style: none;"></a>
<a href='http://www.tineye.com'><img src='assets/tineye.png' width='150px'
style="padding: 0px 0px 10px 8px; border-style: none;"></a>
<a href='http://www.visionsmarts.com'><img
src='assets/visionsmarts.png' width='160px' style="padding: 0px 0px
0px 0px; border-style: none;"></a> <br/>
<!--
<p class="sidebar">Thanks to all the <a
href="supporters.html">supporters</a> who made the book possible.
Thanks also to all the contributors to the <a
href="bugfinder.html">Bugfinder Hall of Fame</a>. </p>
<p class="sidebar">The book is currently a beta release, and is still
under active development. Please send error reports to
[email protected]. For other enquiries, please see the <a
href="faq.html">FAQ</a> first.</p>
-->
<p class="sidebar">著者と共にこの本を作り出してくださった<a
href="supporters.html">サポーター</a>の皆様に感謝いたします。
また、<a
href="bugfinder.html">バグ発見者の殿堂</a>に名を連ねる皆様にも感謝いたします。
また、日本語版の出版にあたっては、<a
href="translators.html">翻訳者</a>の皆様に深く感謝いたします。
</p>
<p class="sidebar">この本は目下のところベータ版で、開発続行中です。
エラーレポートは [email protected] まで、日本語版に関する質問は [email protected] までお送りください。
その他の質問については、まずは<a
href="faq.html">FAQ</a>をごらんください。</p>
<hr>
<span class="sidebar_title">Resources</span>
<p class="sidebar">
<a href="https://github.com/mnielsen/neural-networks-and-deep-learning">Code repository</a></p>
<p class="sidebar">
<a href="http://eepurl.com/BYr9L">Mailing list for book announcements</a>
</p>
<p class="sidebar">
<a href="http://eepurl.com/0Xxjb">Michael Nielsen's project announcement mailing list</a>
</p>
<hr>
<a href="http://michaelnielsen.org"><img src="assets/Michael_Nielsen_Web_Small.jpg" width="160px" style="border-style: none;"/></a>
<p class="sidebar">
著：<a href="http://michaelnielsen.org">Michael Nielsen</a> / 2014年9月-12月 <br > 訳：<a href="https://github.com/nnadl-ja/nnadl_site_ja">「ニューラルネットワークと深層学習」翻訳プロジェクト</a>
</p>
</div>
</p><p>It's not uncommon for technical books to include an admonition fromthe author that readers must do the exercises and problems. I alwaysfeel a little peculiar when I read such warnings. Will something badhappen to me if I don't do the exercises and problems? Of course not.I'll gain some time, but at the expense of depth of understanding.Sometimes that's worth it. Sometimes it's not.</p><p>So what's worth doing in this book? My advice is that you reallyshould attempt most of the exercises, and you should aim <em>not</em> todo most of the problems.</p><p>You should do most of the exercises because they're basic checks thatyou've understood the material. If you can't solve an exerciserelatively easily, you've probably missed something fundamental. Ofcourse, if you do get stuck on an occasional exercise, just move on- chances are it's just a small misunderstanding on your part, ormaybe I've worded something poorly. But if most exercises are astruggle, then you probably need to reread some earlier material.</p><p>The problems are another matter. They're more difficult than theexercises, and you'll likely struggle to solve some problems. That'sannoying, but, of course, patience in the face of such frustration isthe only way to truly understand and internalize a subject.</p><p>With that said, I don't recommend working through all the problems.What's even better is to find your own project. Maybe you want to useneural nets to classify your music collection. Or to predict stockprices. Or whatever. But <em>find a project you care about</em>. Thenyou can ignore the problems in the book, or use them simply asinspiration for work on your own project. Struggling with a projectyou care about will teach you far more than working through any numberof set problems. Emotional commitment is a key to achieving mastery.</p><p>Of course, you may not have such a project in mind, at least up front.That's fine. Work through those problems you feel motivated to workon. And use the material in the book to help you search for ideas forcreative personal projects.</p><p><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/></p><p></p><p></p><p></p><p></div><div class="footer"> <span class="left_footer"> In academic work,
please cite this book as: Michael A. Nielsen, "Neural Networks and
Deep Learning", Determination Press, 2015
<br/>
<br/>
This work is licensed under a <a rel="license"
href="http://creativecommons.org/licenses/by-nc/3.0/deed.en_GB"
style="color: #eee;">Creative Commons Attribution-NonCommercial 3.0
Unported License</a>. This means you're free to copy, share, and
build on this book, but not to sell it. If you're interested in
commercial use, please <a
href="mailto:[email protected]">contact me</a>.
</span>
<span class="right_footer">
Last update: Sun Dec 21 14:49:05 2014
<br/>
<br/>
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc/3.0/deed.en_GB"><img alt="Creative Commons Licence" style="border-width:0" src="http://i.creativecommons.org/l/by-nc/3.0/88x31.png" /></a>
</span>
</div>
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-44208967-1', 'neuralnetworksanddeeplearning.com');
ga('send', 'pageview');
</script>
</body>
</html>