AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習;...

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AI/機械学習/深層学習入門 201982大阪大学データビリティフロンティア機構 中島悠太

Transcript of AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習;...

Page 1: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

AI/機械学習/深層学習入門

2019年8月2日大阪大学データビリティフロンティア機構

中島悠太

Page 2: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

自己紹介• 中島悠太大阪大学データビリティフロンティア機構准教授

• 略歴••• 2012• 2015• 2017

• 研究分野• コンピュータビジョン; CV• パターン認識; PR• (自然言語処理; NLP)

-2012: Ph.D Course, Osaka University2012: Visiting Scholar, UNC Charlotte-2016: Assistant Prof., Nara Institute for Science and Technology-2016: Visiting Scholar, CMU-2017: Current Position

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今日の内容• AI? 機械学習? 深層学習?

• なぜ今深層学習か?

• ニューラルネットワークの訓練

• ニューラルネットワークの問題

• 最近の取り組み

• 深層学習利用の例

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AI?機械学習?深層学習?

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AI関連の分野の関係

人工知能; Artificial Intelligence, AI

機械学習; Machine Learning, ML

表現学習; Representation Learning, RL

深層学習; Deep Learning, DL

•ルールベース•エキスパートシステム

•サポートベクトルマシン•ロジスティック回帰•リッジ回帰• (浅い) ニューラルネットワーク

• (浅い) オートエンコーダ•辞書学習

•ディープニューラルネットワーク•制限ボルツマンマシン

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機械学習のカテゴリ機械学習

教師あり学習

• 識別

• 回帰

• 検出

• セグメンテーション

教師なし学習

• 次元削減

• クラスタリング

強化学習…

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なぜ今深層学習か?

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いままでの機械学習と深層学習の違い• 今までの機械学習

• 深層学習

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特徴抽出器 識別器

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Class label

“cat”

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マッピング

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Class label

“cat”

Page 9: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

ニューラルネットワークの構成要素• 全結合層:

• 画像の場合は畳み込み層

• 活性化関数(非線形性):• Hyperbolic tangent• ReLU• etc.

• ロス関数:

• Others:• バッチ正規化• プーリング• etc.

全結合層

活性化関数

全結合層

活性化関数

ロス関数

h = Wx+ b<latexit sha1_base64="kkWpxS4h7ewksvkQbSyWsYp6kWM=">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</latexit><latexit sha1_base64="kkWpxS4h7ewksvkQbSyWsYp6kWM=">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</latexit><latexit sha1_base64="kkWpxS4h7ewksvkQbSyWsYp6kWM=">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</latexit><latexit sha1_base64="kkWpxS4h7ewksvkQbSyWsYp6kWM=">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</latexit>

y = �(h)<latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit>

�(h) = max(0, h)<latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">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</latexit><latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">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</latexit><latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">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</latexit>

�(h) = tanh(h)<latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit>

Output y<latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit>

Input x<latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit>

t<latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit>

教師信号

f(x)

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全結合層

活性化関数

L(x, t)<latexit sha1_base64="ZWQHyVxiGrfol6tYU9WAWn9TgfA=">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</latexit>

Page 10: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

ニューラルネットワークのいいところ

全結合層

活性化関数

全結合層

活性化関数

Output

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全結合層

活性化関数

x<latexit sha1_base64="Qj4U1j/Mx929t2ieD/QbKvBgPOI=">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</latexit><latexit sha1_base64="Qj4U1j/Mx929t2ieD/QbKvBgPOI=">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</latexit><latexit sha1_base64="Qj4U1j/Mx929t2ieD/QbKvBgPOI=">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</latexit>

全結合層

活性化関数

Page 11: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

事前学習とファインチューニング

• 事前学習; Pretraining• やりたいタスクと関係するけど、違うタスクで学習• 例) 画像認識タスクで事前学習、画像のキャプショニングで利用

• 大量のデータを使える可能性がある!?

• ファインチューニング; Fine-tuning• 事前学習したニューラルネットワークを、やりたいタスクで再学習• 付け替えた先だけ学習してもOK• 付け替えた先と同時に、事前学習した部分を再学習してもOK

• やりたいタスクで使えるデータが少ない場合でもうまくいく!?

全結合層

活性化関数

全結合層

活性化関数

全結合層

活性化関数

全結合層

活性化関数

全結合層

活性化関数

Page 12: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

ニューラルネットワークの訓練

Page 13: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

ニューラルネットワークの構成要素(再掲)• 全結合層:

• 画像の場合は畳み込み層

• 活性化関数(非線形性):• Hyperbolic tangent• ReLU• etc.

• ロス関数:

• Others:• バッチ正規化• プーリング• etc.

全結合層

活性化関数

全結合層

活性化関数

ロス関数

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y = �(h)<latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit><latexit sha1_base64="LZuXmJY/Hvr0FzepabxkSatbrQI=">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</latexit>

�(h) = max(0, h)<latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">AAACeXichVHLSgMxFD0d3/VVHwvBTbUoVURutaAIguDGpa+qYKXMjGkbnBcz02It/oA/4MKNCiLqZ7jxB1z4CeJSwYUuvJ0OiIp6Q5KTk3tuThLNMaTnEz1ElIbGpuaW1rZoe0dnV3esp3fDs0uuLjK6bdjulqZ6wpCWyPjSN8SW4wrV1Ayxqe0t1vY3y8L1pG2t+xVH7JhqwZJ5qas+U7lYf9aTBVNNFsfms6a6n6SJeHEsF0vQJAUR/wlSIUggjGU7doksdmFDRwkmBCz4jA2o8LhtIwWCw9wOqsy5jGSwL3CIKGtLnCU4Q2V2j8cCr7ZD1uJ1raYXqHU+xeDusjKOEbqnK3qmO7qhR3r/tVY1qFHzUuFZq2uFk+s+Glh7/Vdl8uyj+Kn607OPPGYDr5K9OwFTu4Ve15cPjp/X5lZHqqN0Tk/s/4we6JZvYJVf9IsVsXqCKH9A6vtz/wQbU5MpxivpxEI6/IpWDGIYSX7vGSxgCcvI8LkHOMUVriNvypCSVMbrqUok1PThSyjTHweykJs=</latexit><latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">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</latexit><latexit sha1_base64="OGOx8LVL+sJcFmit/3vNVSDAGyY=">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</latexit>

�(h) = tanh(h)<latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">AAACeXichVHLSgMxFD0d3/U1PhaCm2qpVBeSqqAIguDGpVZrC1bKzJi2wXkxkxZs8Qf8ARduVBBRP8ONP+DCTxCXCi504e10QLSoNyQ5Obnn5iTRXVP4krHHiNLW3tHZ1d0T7e3rHxhUh4Z3fKfiGTxjOKbj5XTN56aweUYKafKc63HN0k2e1Q/WGvvZKvd84djb8tDle5ZWskVRGJokqqCO5n1RsrRkeTq2EstLzS4TLKhxNsuCiLWCVAjiCGPDUa+Qxz4cGKjAAocNSdiEBp/aLlJgcInbQ504j5AI9jmOECVthbI4ZWjEHtBYotVuyNq0btT0A7VBp5jUPVLGkGAP7Jq9sHt2y57Yx6+16kGNhpdDmvWmlruFweOxrbd/VRbNEuUv1Z+eJYpYCrwK8u4GTOMWRlNfrZ28bC2nE/UpdsGeyf85e2R3dAO7+mpcbvL0KaL0Aamfz90KduZmU4Q3F+KrC+FXdGMck0jSey9iFevYQIbOreEM17iJvCsTSlKZaaYqkVAzgm+hzH8CV6+QxA==</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">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</latexit><latexit sha1_base64="+aYzdaK2XVCSpQ7+k4ZgAIOnSik=">AAACeXichVHLSgMxFD0d3/U1PhaCm2qpVBeSqqAIguDGpVZrC1bKzJi2wXkxkxZs8Qf8ARduVBBRP8ONP+DCTxCXCi504e10QLSoNyQ5Obnn5iTRXVP4krHHiNLW3tHZ1d0T7e3rHxhUh4Z3fKfiGTxjOKbj5XTN56aweUYKafKc63HN0k2e1Q/WGvvZKvd84djb8tDle5ZWskVRGJokqqCO5n1RsrRkeTq2EstLzS4TLKhxNsuCiLWCVAjiCGPDUa+Qxz4cGKjAAocNSdiEBp/aLlJgcInbQ504j5AI9jmOECVthbI4ZWjEHtBYotVuyNq0btT0A7VBp5jUPVLGkGAP7Jq9sHt2y57Yx6+16kGNhpdDmvWmlruFweOxrbd/VRbNEuUv1Z+eJYpYCrwK8u4GTOMWRlNfrZ28bC2nE/UpdsGeyf85e2R3dAO7+mpcbvL0KaL0Aamfz90KduZmU4Q3F+KrC+FXdGMck0jSey9iFevYQIbOreEM17iJvCsTSlKZaaYqkVAzgm+hzH8CV6+QxA==</latexit>

Output y<latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">AAACZHichVHLSsNAFD2Nr1qrrRZBEKRYKq7KRAqKq4Ibl33YB9RSkjitoWkSkrRQiz+gW8WFKwUR8TPc+AMu+gOCuKzgxoW3aUC0qHeYmTNn7rlzZkY2NdV2GOv5hLHxickp/3RgJjg7FwrPLxRso2UpPK8YmmGVZMnmmqrzvKM6Gi+ZFpeassaLcmNnsF9sc8tWDX3P6Zi80pTqulpTFckhKtOphmMswdyIjgLRAzF4kTbCt9jHAQwoaKEJDh0OYQ0SbGpliGAwiaugS5xFSHX3OY4RIG2LsjhlSMQ2aKzTquyxOq0HNW1XrdApGnWLlFHE2RO7Y332yO7ZC/v4tVbXrTHw0qFZHmq5WQ2dLOXe/1U1aXZw+KX607ODGrZcryp5N11mcAtlqG8fXfRz29l4d41ds1fyf8V67IFuoLfflJsMz14iQB8g/nzuUVDYSIiEM8lYKul9hR/LWMU6vfcmUthFGnk6l+MUZzj3PQtBISIsDlMFn6eJ4FsIK5/0GInr</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">AAACZHichVHLSsNAFD2Nr1qrrRZBEKRYKq7KRAqKq4Ibl33YB9RSkjitoWkSkrRQiz+gW8WFKwUR8TPc+AMu+gOCuKzgxoW3aUC0qHeYmTNn7rlzZkY2NdV2GOv5hLHxickp/3RgJjg7FwrPLxRso2UpPK8YmmGVZMnmmqrzvKM6Gi+ZFpeassaLcmNnsF9sc8tWDX3P6Zi80pTqulpTFckhKtOphmMswdyIjgLRAzF4kTbCt9jHAQwoaKEJDh0OYQ0SbGpliGAwiaugS5xFSHX3OY4RIG2LsjhlSMQ2aKzTquyxOq0HNW1XrdApGnWLlFHE2RO7Y332yO7ZC/v4tVbXrTHw0qFZHmq5WQ2dLOXe/1U1aXZw+KX607ODGrZcryp5N11mcAtlqG8fXfRz29l4d41ds1fyf8V67IFuoLfflJsMz14iQB8g/nzuUVDYSIiEM8lYKul9hR/LWMU6vfcmUthFGnk6l+MUZzj3PQtBISIsDlMFn6eJ4FsIK5/0GInr</latexit><latexit sha1_base64="JdYEc2e/Wb2b5VTnyuHjrlS9J1M=">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</latexit>

Input x<latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit>

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教師信号

f(x)

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sha1_base64="pNbcj3NpK98tXpPOs/xTlVli50w=">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</latexit>

全結合層

活性化関数

L(x, t)<latexit sha1_base64="ZWQHyVxiGrfol6tYU9WAWn9TgfA=">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</latexit>

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ニューラルネット、どうやって学習するの?

• 確率的勾配降下法; Stochastic gradient descent• 勾配降下法(aka 最急降下法)の一種

• 誤差逆伝播法; Back-propagation• 連鎖律(chain rule; 合成関数の微分)

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勾配降下法• (NNの)パラメータ をどんどん更新して関数を最小化

は や のすべての値は学習率

• 確率的勾配降下法は、勾配降下法の一種:• データセットをランダムに並び替え• データセットを小さい塊

(mini-batch)に分割into B mini-batches

• 勾配降下法をmini-batchに適用

✓<latexit sha1_base64="CPMMUXlBzWIqoiwan4WNoM0nWpk=">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</latexit>

✓ ✓ � ↵@L

@✓<latexit sha1_base64="PkpAicVbXB21YaObyPOZ9EIoz7w=">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</latexit>

W<latexit sha1_base64="JDpNcH5uLVTLupPgdE5OEOCtsOM=">AAACZHichVHLSsNAFD2N7/poVQRBkGJRXJUbFRQ3Fty4bNXaQhVJ4lRD0yQkaUGLP6BbRdSVgoj4Ba7d+AMu/AFBXFZw48KbtCBa1DvMzJkz99w5M6Pahu56RE8hqaW1rb2jsyvc3dPbF4n2D6y5VtnRREazDMvJqYorDN0UGU/3DJGzHaGUVENk1eKiv5+tCMfVLXPV27XFRknZNvWCrikeU+nsZjROCQoi1gzkBogv3J36cZayotdYxxYsaCijBAETHmMDClxuecgg2MxtoMqcw0gP9gX2EWZtmbMEZyjMFnnc5lW+wZq89mu6gVrjUwzuDitjGKdHuqEaPdAtvdDHr7WqQQ3fyy7Pal0r7M3IwfDK+7+qEs8edr5Uf3r2UMBc4FVn73bA+LfQ6vrK3kltZX55vDpBl/TK/i/oie75BmblTbtKi+VzhPkD5J/P3QzWphLydGIqTfHkDOrRiRGMYZLfexZJLCGFDJ8rcIgjHIeepR5pUBqqp0qhhmYQ30Ia/QQHcI5Y</latexit>

b<latexit sha1_base64="UMj9xksbZGAk668cvE2cJ6/kBuU=">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</latexit>

✓<latexit sha1_base64="CPMMUXlBzWIqoiwan4WNoM0nWpk=">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</latexit>

↵<latexit sha1_base64="anJh4W6pvlf+ZSk8kB5iSTLO6Cs=">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</latexit>

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(確率的)勾配降下法のいろいろな亜種• (Vanilla) stochastic gradient descent algorithm

• Stochastic gradient descent with momentum

• AdaGrad

• RMSProp

• Adam

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シンプルなニューラルネットワークの例

h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">AAADEHichVFLa9RQFD6JrxofnepGcHNxaJvBdriJhYpQGHHjwkVf0yk0JdzEO5PQvMi9M2Sc9g+4dOPClYKI9A+4E3Ej7l30J4jLCm5ceG4SkFrUE5L7nXO+78u593pZFApJ6ZGmnzl77vyFqYvGpctXrk43Zq5tiXSY+7zrp1Gab3tM8ChMeFeGMuLbWc5Z7EW85+09UP3eiOciTJNNOc74bswGSdgPfSax5DYOg3kyt0IGrmUW+6TnWgvEc60WWVGYFOS2SonjGIGiOSIcxMwM5hXBkSwJEBst1R9XNrYZKBtb2diVjU2C0sZWtEdmsUDkvrMZcMlapafkhZyItC9jViz6eSrEIk9knmbjgxNkw200aZuWQU4DqwZNqGM1bbwBBx5DCj4MIQYOCUjEETAQ+OyABRQyrO3CBGs5orDsczgAA7VDZHFkMKzu4XeA2U5dTTBXnqJU+/iXCN8clQRm6Rf6lh7TT/SQfqU//+o1KT3ULGNcvUrLM3f66Y2NH/9VxbhKCH6r/jmzhD7cLWcNcfasrKhd+JV+9OT58ca99dnJHH1Fv+H8L+kR/Yg7SEbf/ddrfP0FqAuw/jzu02DLblt32vbaUrOzVF/FFNyEW2DieS9DBx7CKnTB12a0Za2j3def6e/09/qHiqprteY6nAj98y+Ygbz6</latexit>

Linearity

Activation

Linearity

Loss

inputx<latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">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</latexit><latexit sha1_base64="MQ2Wn/quWMCC8abSWNLYORWSBvk=">AAACZHichVFNSwJBGH7cvswsLQmCICQxOsUYQtFJ6NLRj/wAE9ndRlvcL3ZXyaQ/UNeiQ6eCiOhndOkPdPAPBNHRoEuHXteFKKneYWaeeeZ93nlmRjJVxXYY6/qEkdGx8Qn/ZGAqOD0TCs/OFWyjack8LxuqYZUk0eaqovO8ozgqL5kWFzVJ5UWpsd3fL7a4ZSuGvuu0TV7RxLqu1BRZdIjKHFbDMbbG3IgOg4QHYvAibYRvsYd9GJDRhAYOHQ5hFSJsamUkwGASV0GHOIuQ4u5zHCNA2iZlccoQiW3QWKdV2WN1Wvdr2q5aplNU6hYpo4izJ3bHeuyR3bMX9vFrrY5bo++lTbM00HKzGjpZyL3/q9JodnDwpfrTs4MaNl2vCnk3XaZ/C3mgbx1d9HJb2XhnhV2zV/J/xbrsgW6gt97kmwzPXiJAH5D4+dzDoLC+liCcScZSSe8r/FjEMlbpvTeQwg7SyNO5HKc4w7nvWQgKEWF+kCr4PE0E30JY+gTyGInq</latexit>

h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">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</latexit>

h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">AAADEHichVFLa9RQFD6JrxofnepGcHNxaJvBdriJhYpQGHHjwkVf0yk0JdzEO5PQvMi9M2Sc9g+4dOPClYKI9A+4E3Ej7l30J4jLCm5ceG4SkFrUE5L7nXO+78u593pZFApJ6ZGmnzl77vyFqYvGpctXrk43Zq5tiXSY+7zrp1Gab3tM8ChMeFeGMuLbWc5Z7EW85+09UP3eiOciTJNNOc74bswGSdgPfSax5DYOg3kyt0IGrmUW+6TnWgvEc60WWVGYFOS2SonjGIGiOSIcxMwM5hXBkSwJEBst1R9XNrYZKBtb2diVjU2C0sZWtEdmsUDkvrMZcMlapafkhZyItC9jViz6eSrEIk9knmbjgxNkw200aZuWQU4DqwZNqGM1bbwBBx5DCj4MIQYOCUjEETAQ+OyABRQyrO3CBGs5orDsczgAA7VDZHFkMKzu4XeA2U5dTTBXnqJU+/iXCN8clQRm6Rf6lh7TT/SQfqU//+o1KT3ULGNcvUrLM3f66Y2NH/9VxbhKCH6r/jmzhD7cLWcNcfasrKhd+JV+9OT58ca99dnJHH1Fv+H8L+kR/Yg7SEbf/ddrfP0FqAuw/jzu02DLblt32vbaUrOzVF/FFNyEW2DieS9DBx7CKnTB12a0Za2j3def6e/09/qHiqprteY6nAj98y+Ygbz6</latexit>

t<latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit><latexit sha1_base64="MMgHjpXlkeOHsPydpO4ACxuWX/s=">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</latexit>Supervision

⇥ = {W1, b1,W2, b2}<latexit sha1_base64="oWzyno4B/d0+pz0l7GSSUby2dBM=">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</latexit>

勾配降下法に必要な勾配は・・・@L

@W2<latexit sha1_base64="Pxru4wmRkRwzMY2u4xPkOqjca5k=">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</latexit>

@L

@b2<latexit sha1_base64="miJAPZ9zPsileaOkzs2fN7AE1wk=">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</latexit>

@L

@W1<latexit sha1_base64="1bbEPHLcLRxNdO8/1HOsSoKlXtE=">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</latexit>

@L

@b1<latexit sha1_base64="JvUIuhDr2Jz/iltKAxQdZIu54Eo=">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</latexit>

L(x, t|⇥) = XE(y, t|⇥)<latexit sha1_base64="2MvwaCjB2IRiiRGaTJcopLiTMsg=">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</latexit>

Page 18: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

誤差逆伝播法; Back-propagation, back-prop• 連鎖律: @f(g(x))

@x=

@f

@g

@g

@x<latexit sha1_base64="40ADY/eZvfOjj7dTNVvzEuIuWOY=">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</latexit>

@L

@W2=

@L

@y

@y

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h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">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</latexit>

L(x, t|⇥) = XE(y, t|⇥)<latexit sha1_base64="2MvwaCjB2IRiiRGaTJcopLiTMsg=">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</latexit>

@L

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@L

@h=

@L

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h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">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</latexit>

@L

@h0 =@L

@h

@h

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@L

@W1=

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h0 = g1(x|W1, b1) = W1x+ b1

h = �(h0) = tanh(h0)

y = g2(h|W2, b2) = W2h+ b2

L(x, t|⇥) = softmax-cross-entropy(x, t|⇥)<latexit sha1_base64="ftxYxNo3LE/yKA4i0yfD5P1kQWE=">AAADEHichVFLa9RQFD6JrxofnepGcHNxaJvBdriJhYpQGHHjwkVf0yk0JdzEO5PQvMi9M2Sc9g+4dOPClYKI9A+4E3Ej7l30J4jLCm5ceG4SkFrUE5L7nXO+78u593pZFApJ6ZGmnzl77vyFqYvGpctXrk43Zq5tiXSY+7zrp1Gab3tM8ChMeFeGMuLbWc5Z7EW85+09UP3eiOciTJNNOc74bswGSdgPfSax5DYOg3kyt0IGrmUW+6TnWgvEc60WWVGYFOS2SonjGIGiOSIcxMwM5hXBkSwJEBst1R9XNrYZKBtb2diVjU2C0sZWtEdmsUDkvrMZcMlapafkhZyItC9jViz6eSrEIk9knmbjgxNkw200aZuWQU4DqwZNqGM1bbwBBx5DCj4MIQYOCUjEETAQ+OyABRQyrO3CBGs5orDsczgAA7VDZHFkMKzu4XeA2U5dTTBXnqJU+/iXCN8clQRm6Rf6lh7TT/SQfqU//+o1KT3ULGNcvUrLM3f66Y2NH/9VxbhKCH6r/jmzhD7cLWcNcfasrKhd+JV+9OT58ca99dnJHH1Fv+H8L+kR/Yg7SEbf/ddrfP0FqAuw/jzu02DLblt32vbaUrOzVF/FFNyEW2DieS9DBx7CKnTB12a0Za2j3def6e/09/qHiqprteY6nAj98y+Ygbz6</latexit>

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@L

@b1=

@L

@h0@h0

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✓@L

@x=

@L

@h0@h0

@x

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Page 19: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

ニューラルネットワークの問題

Page 20: AI/機械学習/深層学習入門 -  · 機械学習; Machine Learning, ML 表現学習; Representation Learning, RL 深層学習; Deep Learning, DL •ルールベース •エキスパートシステム

Universal approximation theoremによると・・・• ニューラルネットワークは(任意の/ある種の)関数を近似できる(らしい)

• パラメータの数が多いとよりよい近似になる(らしい)

• 層の数が多い方がいい(らしい)

• 一方で、全結合層は大量のパラメータの塊• 入力1,000、出力1,000の全結合層1つのパラメータの数は

1,001,000個!

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パラメータの数の比較

• AlexNet

• VGG-19

• GoogLeNet

• ResNet

Performance

0.16

0.088?

0.07

0.036

# layers

8

19

22

152

# Parameters

61M

138M

11M

25M

How does this happen?

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過学習

• 識別器が学習に使ったデータに過剰に適応して(学習データでの性能が高い)、学習に使ってないデータでの性能が低下

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どうしたらいい?• 畳み込み層の利用• 正則化• Dropout• Weight decay

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その他の問題• 勾配消失• ReLU関数とその変種• バッチ正規化• Skip-connection• Squeeze and excitation

• ハイパーパラメータチューニング(層の数、学習率、etc.)• ベイズ最適化• 勘と経験

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最近の取り組み「形式知」の組み込み

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「形式知」の有効活用• 形式知

• テキスト• で与えられるTripletの集合• 知識グラフ• 数式 ex) ,

• 形式知を使う方法が確立されると・・・• 形式知化が難しいところは暗黙知を抽出する学習で、形式知で記述できるものは形式知で

• 形式知を追加することで賢くなるエージェント• 形式知の自動獲得

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絵画の自動分類

In Guernica, Pablo Picasso, by means of his own style built upon many artistic influences, such as Cubism or African art, expressed his emotions against war inspired by its historical and political context.

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絵画の自動分類のための知識(抜粋)

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モデル

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結果

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深層学習利用の例

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核物理データの識別に向けた共同研究の紹介

• フレーバー識別日本物理学会全国大会岸田,岩崎他機械学習を用いたフレーバー識別用ツールの開発

• 可変長データの3クラス識別問題• cc / bb / udsイベントに分類

• 従来は、低次元の「表現」を手で設計して、浅いNNで識別

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深層学習の実力発揮!• 少しだけ、データを確認

とりあえず、作ってみよう!

・・・

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コード(200+行)• 必要なモジュールのロード• データの読み込み

• ニューラルネットのモデルの定義

• 評価• 各種設定&学習

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学習結果

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Takeaway message• 深層学習は機械学習の一種• 非常に簡単、便利

• 特徴量抽出の設計が不要(その分野の知識はいらない!?)• 深層学習の中身は簡単な掛け算足し算がほとんど

• 忘れてはいけない色々な問題点• 過学習• 勾配消失• ハイパーパラメータチューニング

プログラム担当行事委員より技術研修会をより意義あるものとするため、技術研修会アンケートへの回答をお願いいたします。

QRコードから⇒URL:https://forms.gle/UKTQsYiJiqCcGEme7

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