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<body><div class="nonumber_header"><h2><a href="index.html">Supporters</a></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_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>
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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_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>
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<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>
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<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>
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<p class="sidebar">Thanks to all the <a
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<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。
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<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。
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<a href="https://github.com/mnielsen/neural-networks-and-deep-learning">Code repository</a></p>
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<a href="http://eepurl.com/BYr9L">Mailing list for book announcements</a>
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<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>
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<td>Anonymous</td>
<td>Ivan Adanja</td>
<td>Kartik Agaram</td>
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<td>Gui Ambros</td>
<td>Brent J. Anderson</td>
<td>Bennett Andrews</td>
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<td>Philip H. Austin</td>
<td>Kyrylo Azhytskyi</td>
<td>Darius Bacon</td>
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<td>Miëtek Bak</td>
<td>Thomas W. Ballinger</td>
<td>Pascal Belloncle</td>
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<td>Nelson Batalha</td>
<td>Richard Baxter</td>
<td>Maxim Baz</td>
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<td>Philippe Beaudoin</td>
<td>Marco Beri</td>
<td>Ariel Berwaldt</td>
</tr>
<tr>
<td>John Biesnecker</td>
<td>Mark Bloore</td>
<td>Paul Bloore</td>
</tr>
<tr>
<td>Aaron Paul Blossom</td>
<td>David Bonner</td>
<td>Leila Boujnane</td>
</tr>
<tr>
<td>Charles Brauer</td>
<td>Harrison Brown</td>
<td>Simon D. Burton</td>
</tr>
<tr>
<td>Nathan Campbell</td>
<td>Maria Del Carmen Anyo</td>
<td>Trey Causey</td>
</tr>
<tr>
<td>Alex Chamberlain</td>
<td>John Chaussard</td>
<td>Nikolay Chenkov</td>
</tr>
<tr>
<td>John Chia</td>
<td>Cheng kong Chit</td>
<td>Matias Varnum Christensen</td>
</tr>
<tr>
<td>Aaron Clauset</td>
<td>Dominic Cooney</td>
<td>Sidney Cox</td>
</tr>
<tr>
<td>Dominic Cummings</td>
<td>Paulo Darocha</td>
<td>Christopher Dawson</td>
</tr>
<tr>
<td>George Dean</td>
<td>Hendrik Demolder</td>
<td>Alexander v Dijk</td>
</tr>
<tr>
<td>Weiguang (Gavin) Ding</td>
<td>Amy Dodd</td>
<td>James K. Doherty</td>
</tr>
<tr>
<td>Michael J. Douglas</td>
<td>Daniel George Drumea</td>
<td>Igor Dzreyev</td>
</tr>
<tr>
<td>Jeff Elmore</td>
<td>Mark England</td>
<td>Brian Eoff</td>
</tr>
<tr>
<td>Geoff Ericksson</td>
<td>Daniel Fernandes</td>
<td>Chris Ferrie</td>
</tr>
<tr>
<td>Ivo Flipse</td>
<td>Jelle Foks</td>
<td>Mardini Fouad</td>
</tr>
<tr>
<td>Rod Frey</td>
<td>Curtis Frye</td>
<td>Manoel Galdino</td>
</tr>
<tr>
<td>Senthil Gandhi</td>
<td>Inmar Givoni</td>
<td>Jeffrey Gold</td>
</tr>
<tr>
<td>Vojimir Golem</td>
<td>Christopher Granade</td>
<td>Ilya Grigorik</td>
</tr>
<tr>
<td>Steven Grimm</td>
<td>Joel Grus</td>
<td>Miki Habryn</td>
</tr>
<tr>
<td>Ward M. Haggard</td>
<td>Russell Hanson</td>
<td>Kathryne Hawthorne</td>
</tr>
<tr>
<td>Frank Hecker</td>
<td>Pablo Loyola Heufemann</td>
<td>Jens Christian Hillerup</td>
</tr>
<tr>
<td>Isaac A. Hodes</td>
<td>J. Paul Hoest</td>
<td>Jordan Holcombe</td>
</tr>
<tr>
<td>Juan Rodriguez Hortala</td>
<td>Steve Houghton</td>
<td>Tommi Hovi</td>
</tr>
<tr>
<td>Jeremy Howard</td>
<td>Tatsuya Ishihara</td>
<td>Paweł Jacewicz</td>
</tr>
<tr>
<td>Amit Jain</td>
<td>Damian Jordan</td>
<td>Victor Joukov</td>
</tr>
<tr>
<td>Guilherme Juraszek</td>
<td>Erkin Kanlioglu</td>
<td>Bart Kastermans</td>
</tr>
<tr>
<td>Jason Kelly</td>
<td>Alasdair K. King</td>
<td>SGJ Kockelkoren</td>
</tr>
<tr>
<td>Douglas Kratky</td>
<td>Charles Krempeaux</td>
<td>Dragisa Krsmanovic</td>
</tr>
<tr>
<td>Jason Kyle</td>
<td>Samuel Lampa</td>
<td>Michael Lachanski</td>
</tr>
<tr>
<td>Alex Lang</td>
<td>Ethan Langevin</td>
<td>Elmar Langholz</td>
</tr>
<tr>
<td>Christian Langreiter</td>
<td>Eugene Lazutkin</td>
<td>Jimmy Lee</td>
</tr>
<tr>
<td>Matthew Leifer</td>
<td>Daniel Lemire</td>
<td>Fuzz Leonard</td>
</tr>
<tr>
<td>Anselm Levskaya</td>
<td>Joseph Lewis</td>
<td>Jian Liang</td>
</tr>
<tr>
<td>Greg Linden</td>
<td>Chris Lintott</td>
<td>Baiyang Liu</td>
</tr>
<tr>
<td>James Lloyd</td>
<td>Tobias Lohse</td>
<td>Damien Loïc</td>
</tr>
<tr>
<td>Sergey Lymar</td>
<td>Gholson J. Lyon</td>
<td>James McCoy</td>
</tr>
<tr>
<td>Brent McWatters</td>
<td>Jean Maillard</td>
<td>Benoit Maison</td>
</tr>
<tr>
<td>Vito Mandorino</td>
<td>Stephen Marney</td>
<td>Maurice Mauser</td>
</tr>
<tr>
<td>Spyridon Michalakis</td>
<td>Florian Minges</td>
<td>Melanie Mitchell</td>
</tr>
<tr>
<td>Takashi Miyazaki</td>
<td>Nathan Mosher</td>
<td>Mike Murray</td>
</tr>
<tr>
<td>Aditiyaa Nagarajan</td>
<td>Sandeep Nayak</td>
<td>Alexandru Nedel</td>
</tr>
<tr>
<td>Eric Amir Nichols</td>
<td>Ken Nickerson</td>
<td>Kate Nielsen</td>
</tr>
<tr>
<td>Wendy Nielsen</td>
<td>Michael Noll-Hussong</td>
<td>Antonio Macias Ojeda</td>
</tr>
<tr>
<td>Nicholas O'Neill</td>
<td>Tom Parslow</td>
<td>Joan Puigcerver i Perez</td>
</tr>
<tr>
<td>Juan Carlos Kuri Pinto</td>
<td>Uffe V. Poulsen</td>
<td>Brian Du Preez</td>
</tr>
<tr>
<td>Sujith Radhakrishna</td>
<td>Hannu Rajaniemi</td>
<td>Rahul Ravu</td>
</tr>
<tr>
<td>Julien Rebetez</td>
<td>Dave Revell</td>
<td>Brendan Rogers</td>
</tr>
<tr>
<td>Konstantin Root</td>
<td>Peter Rudenko</td>
<td>Cody Russell</td>
</tr>
<tr>
<td>Michael Russo</td>
<td>Ross Ryder</td>
<td>Arthur Safira</td>
</tr>
<tr>
<td>Josep Saldaña</td>
<td>Christopher Sammon</td>
<td>Andrés G. Saravia</td>
</tr>
<tr>
<td>Kathryn Schmitt</td>
<td>Maximilian Schoefmann</td>
<td>Tim Schröder</td>
</tr>
<tr>
<td>John D. Schulman</td>
<td>David Schwab</td>
<td>Jan Sedlák</td>
</tr>
<tr>
<td>Satish Shankar</td>
<td>Gareth Shepherd</td>
<td>Makimoto Shimpei</td>
</tr>
<tr>
<td>Ekaterina Shmeleva</td>
<td>Keith Siilats</td>
<td>Christopher Silvia</td>
</tr>
<tr>
<td>Leif-Gerrit Singer</td>
<td>Harkanwal Singh</td>
<td>Rajob K. Singh</td>
</tr>
<tr>
<td>John Skarha</td>
<td>Arfon Smith</td>
<td>Mark Smith</td>
</tr>
<tr>
<td>Ezekiel Smithburg</td>
<td>Xavier Snelgrove</td>
<td>Robert Solovay</td>
</tr>
<tr>
<td>Matthew Sottile</td>
<td>Chris Squibb</td>
<td>Helge Stahlmann</td>
</tr>
<tr>
<td>Jan Stette</td>
<td>John Stockton</td>
<td>Wim Stubbe</td>
</tr>
<tr>
<td>Timo Sulg</td>
<td>Dave Sullivan</td>
<td>Daniel Suo</td>
</tr>
<tr>
<td>James Tauber</td>
<td>Oskar Thorén</td>
<td>Ben Toner</td>
</tr>
<tr>
<td>Luke Toop</td>
<td>Christian Tschanz</td>
<td>Peter Tutelaers</td>
</tr>
<tr>
<td>Matthew Trentacoste</td>
<td>Alexander van Dijk</td>
<td>Gregg Vesonder</td>
</tr>
<tr>
<td>Ricardo Vidal</td>
<td>Wai Keen Vong</td>
<td>Will Walmsley</td>
</tr>
<tr>
<td>Georg Walther</td>
<td>Matt Wells</td>
<td>Karijn Wessing</td>
</tr>
<tr>
<td>Ryan Whitnah</td>
<td>Nick Williamson</td>
<td>Brett Witty</td>
</tr>
<tr>
<td>Charles Wooters</td>
<td>Yusuke Yambe</td>
<td>Artem Yankov</td>
</tr>
<tr>
<td>Doron Yotam</td>
<td>Benjamin Sichit Yu</td>
<td>Zolmeister</td>
</tr>
<tr>
<td></td>
<td></td>
<td></td>
</tr>
</table></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/>
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