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<!DOCTYPE html>
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<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">
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<title>ニューラルネットワークと深層学習</title>
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<body><div class="nonumber_header"><h2>What this book is about</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>
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});</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>
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});</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>
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});</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>Deep learning<div id="toc_deep_learning" style="display: none;"><p class="toc_section"><ul><li>Convolutional neural networks</li><li>Pretraining</li><li>Recurrent neural networks, Boltzmann machines, and other models</li><li>Is there a universal thinking algorithm?</li><li>On the future of neural networks</li></ul></p></div>
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});</script><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/>
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<!--
<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>
<!-- Neural networks are one of the most beautiful programming paradigms
ever invented. -->
ニューラルネットワークはこれまで発明されたなかでも最も美しいプログラミングパラダイムの一つです。
<!-- In the conventional approach to programming, we tell
the computer what to do, breaking big problems up into many small,
precisely defined tasks that the computer can easily perform. -->
プログラミングする従来の方法では、私達は、解きたい大きな問題を、コンピュータにも実行できるよう明確に定義された無数の小さなタスクに分割し、コンピュータが何をすべきかを逐一指示します。
<!--
By
contrast, in a neural network we don't tell the computer how to solve
our problem. Instead, it learns from observational data, figuring out
its own solution to the problem at hand.</p><p> -->
これに対し、ニューラルネットワークを使う場合、私達はコンピュータに直接問題の解き方を指示しません。
そのかわり、コンピュータは観測データから学習し、問題の解き方を自ら編み出すのです。
<!--Automatically learning from data sounds promising. However, until
2006 we didn't know how to train neural networks to surpass more
traditional approaches, except for a few specialized problems. What
changed in 2006 was the discovery of techniques for learning in
so-called deep neural networks. These techniques are now known as
deep learning. They've been developed further, and today deep neural
networks and deep learning achieve outstanding performance on many
important problems in computer vision, speech recognition, and natural
language processing. They're being deployed on a large scale by
companies such as Google, Microsoft, and Chinese search giant Baidu.-->
データから自動的に学習するということは、見込みがあるように思えます。しかし、ニューラルネットワークを訓練して伝統的な手法より良い結果を出させる方法は、2006年までは分かっていませんでした。例外はいくつかの特殊な問題だけでした。
2006年に起きた変化というのは、いわゆるディープニューラルネットワークの学習のための手法が新たに発見されたことでした。これらの手法は現在では深層学習(ディープラーニング)として知られています。
そして手法がさらに進歩した結果、コンピュータビジョン、音声認識、自然言語処理における多くの重要な問題で、ディープニューラルネットワークと深層学習は優れた実績を達成しています
Google、Microsoft、そして中国の検索の巨人であるBaiduといった企業では、深層学習が大規模に活用されています。
</p><p>
<!--The purpose of this book is to help you master the core concepts of
neural networks, including modern techniques for deep learning. After
working through the book you will have written code that uses neural
networks and deep learning to solve complex pattern recognition
problems. And you will have a foundation to use neural networks and
deep learning to attack problems of your own devising.-->
この本の目的は、深層学習の新しい手法を含むニューラルネットワークの中心的な概念をあなたが習得するのを助けることです。
この本に取り組んだ後には、あなたはコードを書き終わっているでしょう。そのコードは、複雑なパターン認識の問題を解くために、ニューラルネットワークと深層学習とを用いるものです。
そして、ニューラルネットワークと深層学習を用いて自分自身が考え出した問題に取り組むための、基礎的な知識が身についているでしょう。
</p><p><h3><a name="a_principle-oriented_approach"></a><a href="#a_principle-oriented_approach">A principle-oriented approach</a></h3></p><p>One conviction underlying the book is that it's better to obtain a
solid understanding of the core principles of neural networks and deep
learning, rather than a hazy understanding of a long laundry list of
ideas. If you've understood the core ideas well, you can rapidly
understand other new material. In programming language terms, think
of it as mastering the core syntax, libraries and data structures of a
new language. You may still only "know" a tiny fraction of the
total language - many languages have enormous standard libraries -
but new libraries and data structures can be understood quickly and
easily.</p><p>This means the book is emphatically not a tutorial in how to use some
particular neural network library. If you mostly want to learn your
way around a library, don't read this book! Find the library you wish
to learn, and work through the tutorials and documentation. But be
warned. While this has an immediate problem-solving payoff, if you
want to understand what's really going on in neural networks, if you
want insights that will still be relevant years from now, then it's
not enough just to learn some hot library. You need to understand the
durable, lasting insights underlying how neural networks work.
Technologies come and technologies go, but insight is forever.</p><p><h3><a name="a_hands-on_approach"></a><a href="#a_hands-on_approach">A hands-on approach</a></h3></p><p>We'll learn the core principles behind neural networks and deep
learning by attacking a concrete problem: the problem of teaching a
computer to recognize handwritten digits. This problem is extremely
difficult to solve using the conventional approach to programming.
And yet, as we'll see, it can be solved pretty well using a simple
neural network, with just a few tens of lines of code, and no special
libraries. What's more, we'll improve the program through many
iterations, gradually incorporating more and more of the core ideas
about ニューラルネットワークと深層学習.</p><p>This hands-on approach means that you'll need some programming
experience to read the book. But you don't need to be a professional
programmer. I've written the code in Python (version 2.7), which,
even if you don't program in Python, should be easy to understand with
just a little effort. Through the course of the book we will develop
a little neural network library, which you can use to experiment and
to build understanding. All the code is available for download
<a href="https://github.com/mnielsen/neural-networks-and-deep-learning">here</a>.
Once you've finished the book, or as you read it, you can easily pick
up one of the more feature-complete neural network libraries intended
for use in production.</p><p>On a related note, the mathematical requirements to read the book are
modest. There is some mathematics in most chapters, but it's usually
just elementary algebra and plots of functions, which I expect most
readers will be okay with. I occasionally use more advanced
mathematics, but have structured the material so you can follow even
if some mathematical details elude you. The one chapter which uses
heavier mathematics extensively is <a href="chap2.html">Chapter 2</a>, which
requires a little multivariable calculus and linear algebra. If those
aren't familiar, I begin <a href="chap2.html">Chapter 2</a> with a
discussion of how to navigate the mathematics. If you're finding it
really heavy going, you can simply skip to the
<a href="chap2.html#the_backpropagation_algorithm">summary</a> of the
chapter's main results. In any case, there's no need to worry about
this at the outset.</p><p>It's rare for a book to aim to be both principle-oriented and
hands-on. But I believe you'll learn best if we build out the
fundamental ideas of neural networks. We'll develop living code, not
just abstract theory, code which you can explore and extend. This way
you'll understand the fundamentals, both in theory and practice, and
be well set to add further to your knowledge.</p><p></p><p></p><p></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
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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>.
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