$30 off During Our Annual Pro Sale. View Details »

論文紹介:Neural Architecture Search with Bayesian Optimisation and Optimal Transport [Kandasamy et al., NIPS 2018]

S.Shota
November 27, 2018

論文紹介:Neural Architecture Search with Bayesian Optimisation and Optimal Transport [Kandasamy et al., NIPS 2018]

2018年11月27日の論文紹介ゼミにて,使用したスライドです.

文献情報:
- K. Kandasamy, W. Neiswanger, J. Schneider, B. Poczos, and E. Xing, “Neural Architecture Search with Bayesian Optimisation and Optimal Transport,” in Proceedings of Thirty-second Conference on Neural Information Processing Systems (NIPS 2018), 2018.
- https://arxiv.org/abs/1802.07191

S.Shota

November 27, 2018
Tweet

More Decks by S.Shota

Other Decks in Technology

Transcript

  1. Neural Architecture Search with Bayesian
    Optimisation and Optimal Transport
    K. Kandasamy, W. Neiswanger, J. Schneider, B. Poczos, and E. Xing
    NIPS 2018
    2018.11.27|文献紹介
    斉藤翔汰
    横浜国立大学大学院 環境情報学府 情報メディア環境学専攻
    情報メディア学コース 白川真一研究室 博士課程前期2年

    View Slide

  2. 文献情報と選んだ理由
    文献情報
    K. Kandasamy, W. Neiswanger, J. Schneider, B. Poczos, and E. Xing,
    “Neural Architecture Search with Bayesian Optimisation and Optimal
    Transport,” in Proceedings of Thirty-second Conference on Neural
    Information Processing Systems (NIPS 2018), 2018.
    選んだ理由
    n 構造探索に関する最新の論文であるため
    n 「構造間の距離」を定義したとのことで,他の構造探索の
    論文とは異なる視点であったため興味を持った
    2

    View Slide

  3. 概要
    構造間の距離 OTMANN + Bayesian Optimization
    n NNの構造間の距離 OTMANN を提案
    n OTMANNを使ってカーネルを設計し,Bayesian Optimization
    で最適化する手法NASBOTを提案
    n 6つの回帰問題+CIFAR-10において,NASBOTは他の手法と
    同等以上の精度を持つ構造を獲得
    n NASBOTで得た構造は,どのデータセットにおいても
    複数の出力層と長いスキップ結合を持っていた
    3

    View Slide

  4. Introduction
    Bayesian Optimization (BO)
    n ベイズモデルに基づくBlack-Box最適化手法のひとつ
    n 機械学習ではSVMの正則化係数などの最適化に使用
    n 従来研究では探索空間が連続であるものが多い
    Gaussian Process (GP) based BO
    n BOでは事前分布にガウス過程を置くことが多い
    n GP based BOでは2点の類似度をカーネルの形で表現
    n 探索空間が連続であるとき,カーネルとしてGaussian,
    Laplacian,Matérnがよく用いられる
    4

    View Slide

  5. Introduction
    BOを構造探索に適用する際の問題点
    n ニューラルネットワーク(NN)の構造探索では,
    探索空間が離散であるため先ほどのカーネルを使用できない
    n BOを適用するためには構造の類似度を定量化する必要がある
    Contribution
    1. ニューラルネットワークの構造間の(擬)距離OTMANNを開発
    - OTMANNは最適輸送問題を解くことで効率的に求められる
    2. 構造探索のためのBOフレームワークNASBOTを提案
    - NASBOTにおける獲得関数の最適化は進化計算で実行
    5

    View Slide

  6. Set up|A brief review of GP based BO
    Notation
    n 目的関数(validation accuracy):
    n 探索空間:
    n 構造:
    n 構造に対する評価値:
    n 観測点:
    n 平均関数:
    n カーネル(共分散)関数:
    n 評価値のベクトル表現:
    n カーネルに関する変数:
    6
    f
    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
    AAAEk3icnVNNb9NAEJ0UAyV89AMhIXGxSIsQQtE6h6bApYIe4FDRpE1bqY4q290EU8e2bCe0WPkDcAVx4AQSB8R/4MKFP8ChPwFxLBIXDrwdO0F8JEisZXvm7cybt7O7dui5cSLEYWHimHb8xMnJU8XTZ86em5qemd2Ig27kyIYTeEG0ZVux9FxfNhI38eRWGEmrY3ty0967o+Y3ezKK3cBfTw5C2exYbd9tuY6VAKq1dqZLolypLhrC0NkQNyoDo6obZcGjRPlYDWYK78mkXQrIoS51SJJPCWyPLIrxbJNBgkJgTUrpIRCLIngux0jqUxH5XeASURbQPXzb8LZz1IeveGNmcFDJwxshU6d58Um8FUfio3gnPovvI7lS5lB6DvC3s1wZ7kw9ubj27Z9ZHfwTevAza6zmhFq0yFpdaA8ZUatwsvze4xdHazfr8+kV8Vp8gf5X4lB8wAr83lfnTU3WXzL7MnKyLkawVnIF98EngShP9eAaqpgc04ZKVa/PqpVv0vUh9r+MFu3/wZhho3uWYL4FLnUO4rGRNtiyeR/+I97bDlfwcaKUjjpXN4c7YONJGeVe4lVrsbAqHTVd2B4yxzGu/8YYwUoZHTAm3A0fikNkK93j+Fy2+nzOm3/Reg9zJv4lzJtcpcj3RUKvST3ek6zzKiLLt+Hvs23zad8dcuo0x3FzOVMR93VwKfXRxkalbMCuGaWlhfzmTtIlukxXwVWlJbpLq9SAEklP6Rk91y5ot7Tb2nIWOlHIc87TL0Nb+QHvpPUd
    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
    AAAEk3icnVNNb9NAEJ0UAyV89AMhIXGxSIsQQtE6h6bApYIe4FDRpE1bqY4q290EU8e2bCe0WPkDcAVx4AQSB8R/4MKFP8ChPwFxLBIXDrwdO0F8JEisZXvm7cybt7O7dui5cSLEYWHimHb8xMnJU8XTZ86em5qemd2Ig27kyIYTeEG0ZVux9FxfNhI38eRWGEmrY3ty0967o+Y3ezKK3cBfTw5C2exYbd9tuY6VAKq1dqZLolypLhrC0NkQNyoDo6obZcGjRPlYDWYK78mkXQrIoS51SJJPCWyPLIrxbJNBgkJgTUrpIRCLIngux0jqUxH5XeASURbQPXzb8LZz1IeveGNmcFDJwxshU6d58Um8FUfio3gnPovvI7lS5lB6DvC3s1wZ7kw9ubj27Z9ZHfwTevAza6zmhFq0yFpdaA8ZUatwsvze4xdHazfr8+kV8Vp8gf5X4lB8wAr83lfnTU3WXzL7MnKyLkawVnIF98EngShP9eAaqpgc04ZKVa/PqpVv0vUh9r+MFu3/wZhho3uWYL4FLnUO4rGRNtiyeR/+I97bDlfwcaKUjjpXN4c7YONJGeVe4lVrsbAqHTVd2B4yxzGu/8YYwUoZHTAm3A0fikNkK93j+Fy2+nzOm3/Reg9zJv4lzJtcpcj3RUKvST3ek6zzKiLLt+Hvs23zad8dcuo0x3FzOVMR93VwKfXRxkalbMCuGaWlhfzmTtIlukxXwVWlJbpLq9SAEklP6Rk91y5ot7Tb2nIWOlHIc87TL0Nb+QHvpPUd
    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
    X
    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
    x 2 X
    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
    Dn = {(xi, yi
    )}n
    i=1
    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
    AAAEv3icnVNNb9NAEJ2UACV8NIULEheLtKhAFa1zoAWpUhE9wAHR71aqi2W7m3Sp41i2Exos/wFunDhwAokD4gdwQyAu/AEO/QmIY5G4cODtOA3io0FiLdszb2fevJ3ddUNfxYkQe4WhI8Wjx44PnyidPHX6zEh59Oxq3GpHnlzxWn4rWnedWPoqkCuJSny5HkbSabq+XHN3bun5tY6MYtUKlpNuKDebTiNQdeU5CSC7fNVqOsm25/jpXGanQWbMGFY6sWurSaNrq8uGld0HaqdqxszsckVUa1PTpjANNsT12oExZZhVwaNCvTHfGi28JYu2qEUetalJkgJKYPvkUIxng0wSFALbpJQeAHEogqc4RlJGJeS3gUtEOUB38G3A2+ihAXzNGzODh0o+3giZBo2LT+KV2BcfxWvxWXw/lCtlDq2ni7+b58rQHnl8funbP7Oa+Ce0/TNroOaE6jTNWhW0h4zoVXh5fufR0/2lG4vj6SXxQnyB/udiT3zACoLOV+/lglx8xuxzyMm7GMG621NwD3wSiPZ0D66gisUxDajU9TJWrX2LJvvY/zI6tPsHY44d3rME83Vw6XMQD4x0wZbPB/Af8t42uUKAE6V1LHJ1q78DLp6UUe4lXr0WB6syUFPB9pE5iHH5N8YIVsroAWPC3QigOES21j2IT7GV8Tnf/IvWO5iz8K9g3uIqJb4vEnot6vCe5J3XEXm+C3+XbZdP+1af06AxjhvrMZVwXw8upXG4sVqrmrAXzMrstd7NHaYLdJEmwDVFs3Sb5mkFSp7QG3pH74s3i41iUAzz0KFCL+cc/TKK3R8TzQYv
    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
    y = f(x) + ✏ 2 R, ✏ ⇠ N(0, ⌘2)
    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
    AAAEhHicnVM9b9RAEJ0LhgQTSCIaJJoTlyCEULRHQ6CKgAIKRHLJJZHiU2T79o4l/pK9dyRY9wfSUlBQgUSB+A80NPwBivwERBkkGgrejs0hcuSQWMv2zNuZN29nd70kUJkW4rAycco6fWZy6qx9bto+f2Fmdnoji3upL5t+HMTpludmMlCRbGqlA7mVpNINvUBuerv3zPxmX6aZiqN1vZ/IVuh2I9VRvqsBrezM1sSi4FEdNeqlUaNyxHOVD+RQm2LyqUchSYpIww7IpQzPNtVJUAKsRTk9BeJSCk9xjKQB2cjvAZeIcoHu4tuFt12iEXzDmzGDj0oB3hSZVVoQn8U7cSQ+iffii/hxIlfOHEbPPv5ekSuTnZmDS2vf/5kV4q/pye+ssZo1dWiJtSpoTxgxq/CL/P7zl0drdxoL+VXxRnyF/tfiUHzECqL+N//tqmy8Yvb7yCm6mMJ6VCp4DD4JxHimB9dRxeGYLlSaegNWbXyHbgyx/2V0aW+EscBO7pnGfAdc5hxkYyM9sBXzEfxnvLchV4hwooyOBld3hjvg4ckZ5V7iNWtxsaoqairYATLHMa4fY0xh5Yz+YtTcjQiKE2Qb3eP4FFsDPuetv2h9iDkH/xrmHa5i832R0OtQn/ek6LyJKPI9+Htse3za20POKs1z3HzJZOO61o9fzlFj4+ZiHfaqoCm6TFfoGihu0TI9oBVqQkCbDuiFddG6bS0X13qiUt7vOfpjWHd/Ar4v8nw=
    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
    AAAE3nicnVM9axRBGH4TT43nRxJtBJvFS+SiIcxd4UVBCGihgppcPiF7nrubucuY/WJ3cyYu11oIYqlgpWAhNv4CGxv/gEIqbcUygo2Fz7x7OT9zgrPMzvv5vM+8M2OHrooTIbb6+vfk9u7bP3Agf/DQ4SODQ8NHF+JgPXLkvBO4QbRkW7F0lS/nE5W4cimMpOXZrly01y5q/2JLRrEK/LlkM5Q1z2r6qqEcK4GpPnR107hgNIobY8YZw5RhrNzAN0yF6VnJqm2n1fb4T45YeZnHsdz0ersotDOxbqbl9lh9qCAmypXJkigZLIhz5R2hYpQmBI8CdcZ0MNz3mkxaoYAcWiePJPmUQHbJohjfMpVIUAhbjVK6DYtFETTFMZLalEf+OuwSURasa/g3oS13rD50jRszgoNKLmaETINGxTvxQmyLt+Kl+CS+7YqVMobms4nVznJlWB+8f3z26z+zPKwJrf7I6sk5oQZNMlcF7iFb9C6cLL9199H27PnqaHpKPBOfwf+p2BJvsAO/9cV5PiOrTxj9EnKyLkaQrnUY3ACehEVrugenUcXkmCZY6nptZq11k8a7tv9FtGjjD8TMtnvPEvgbwNL3IO4ZaQMt8/vQ7/DZelzBx43SPKpc3eyegI0vZSv3ElPvxcKuDNRUkF1k9kKc+w0xgpSydQcx4W74YBwiW/PuhadYavM9r/2F6xX4TKwF+E2ukuf3IsHXpBafSdZ5HZHl29A3WLb5tq90MQ0a4biRDlIe73XnURq7CwvliRLkmVJh6mzn5Q7QCTpJRWBVaIou0zTNg8krek8f6GPuVu5e7kHuYRba39fJOUa/jNzj7xMPESw=
    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
    µ : X ! R
    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
    AAAEu3icnVM9bxNBEB0HA8F8xIEGieaEE0AIWXsucIiEFAkKKBCJEyeWcpZ1d1nbl9yX7s5Owsl/AImaggokCkRJCzQ0/AGK/AREGSQaCt7O2UZ8xEjs6e5m3s68eTu7a4WuEydCHOSmjuWPnzg5fapw+szZczPF2fPrcdCLbFm3AzeIGpYZS9fxZT1xElc2wkianuXKDWvnjprf6MsodgJ/LdkPZdMzO77TdmwzAdQqXjW83qJmeGbStU03bQw0I3I63cSMomA3wy0rrQ1axZIoV6oLutA1NsStysioanpZ8CjRcCwHs7n3ZNAWBWRTjzyS5FMC2yWTYjybpJOgEFiTUtoGYlIEz+EYSQMqIL8HXCLKBLqDbwfe5hD14SvemBlsVHLxRsjUaF58Eq/EofgoXovP4vuRXClzKD37+FtZrgxbM48vrn77Z5aHf0Ldn1kTNSfUpgXW6kB7yIhahZ3l9x89PVxdrM2nV8QL8QX6n4sD8QEr8Ptf7ZcrsvaM2e8iJ+tiBOvBUMFD8EkgylM9uI4qBsd0oFLVG7Bq5Rt0Y4z9L6NJe38wZtjRPUsw3waXOgfxxEgLbNm8D3+X99bjCj5OlNJR4+rGeAcsPCmj3Eu8ai0mVqWhpgPbReYkxrXfGCNYKaMjxoS74UNxiGylexKfw9aAz3nzL1rvY87Av4R5g6sU+L5I6DWoz3uSdV5FZPkW/D22LT7tW2NOjeY4bm7IVMB9HV1K7WhjvVLWYa/opaWbw5s7TZfoMl0DV5WW6B4tUx1KntAbekvv8rfzdn4772ahU7lhzgX6ZeR7PwA0HgWK
    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
     : X2 ! R
    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
    AAAEwnicnVO7bhNBFL0JBoJ5xIEGiWaFE4QQssYuSEgViRRQIBLnZSlrrNnN2N5kX+xunITFP0CNREEFEgXiDyhoQsEPUOQTEGWQaCg4c3djxCNGYla7e++Ze889c2fGCl0nToQ4GBk9UTh56vTYmeLZc+cvjJcmLq7GwXZkqxU7cIOoYclYuY6vVhIncVUjjJT0LFetWVt39PxaT0WxE/jLyV6omp7s+E7bsWUCqFWqmFsyDOWsYXoy6drSTRv9h2mtb5iR0+kmMoqCnWzOstJ6v1Uqi0pteqYqqgYb4nbtyJg2qhXBo0z5WAgmRt6TSRsUkE3b5JEinxLYLkmK8axTlQSFwJqU0iYQSRE8h2MU9amI/G3gClES6Ba+HXjrOerD17wxM9io5OKNkGnQlPgk3ohD8VG8FZ/F92O5UubQevbwt7JcFbbGn15e+vbPLA//hLo/s4ZqTqhNM6zVgfaQEb0KO8vvPX5+uDRbn0qviVfiC/S/FAdiHyvwe1/t14uq/oLZ55GTdTGCdT9X8AB8Coj2dA9uoIrJMR2o1PX6rFr7Jt0cYP/LKGn3D8YMO75nCebb4NLnIB4aaYEtm/fh7/DeelzBx4nSOupc3RzsgIUnZZR7iVevRWJVBmo6sF1kDmNc/o0xgpUyesSYcDd8KA6RrXUP43PY6vM5b/5F6z3MmfiXMW9ylSLfFwW9JvV4T7LO64gs34K/y7bFp31jwGnQJMdN5kxF3NejS2kcb6zWKlXYi9Xy3K385o7RFbpK18E1TXN0lxZoBUqe0Tvapw+F+cJm4VEhzkJHR/KcS/TLKDz5AQkuCIM=
    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
    Y = yi 2 Rn
    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
    AAAEsHicnVNNb9NAEJ2UACV8NIULEhws0iKEULTOgRQkpEpwgAOiTb+C6hDZ7iZ169iW7YQGKxeO/AEOnEBCAnGCH8CFC3+AQ38C4lgkLhx4O3aC+EiQWMv2zNuZN29nd63AdaJYiP3c1KH84SNHp48Vjp84eWqmOHt6PfK7oS3XbN/1w7plRtJ1PLkWO7Er60EozY7lyg1r96aa3+jJMHJ8bzXuB7LRMdue03JsMwbULJ6/r93Q+s3EGWiG42lGx4y3LSupDR4k3qBZLIlypbqgC11jQ1yrDI2qppcFjxJlY8mfzb0ng7bIJ5u61CFJHsWwXTIpwrNJOgkKgDUooR0gJoXwHI6RNKAC8rvAJaJMoLv4tuFtZqgHX/FGzGCjkos3RKZG8+KTeC0OxEfxRnwW38dyJcyh9PTxt9JcGTRnnpxd+fbPrA7+MW3/zJqoOaYWLbBWB9oDRtQq7DS/9+jpwcr12nxyUbwQX6D/udgXH7ACr/fVfrksa8+Y/RZy0i6GsO5mCu6BTwJRnurBZVQxOKYNlaregFUr36ArI+x/GU3a+4Mxxcb3LMZ8C1zqHEQTIy2wpfMe/Ie8tx2u4OFEKR01rm6MdsDCkzDKvcSr1mJiVRpqOrBdZE5iXP2NMYSVMDpkjLkbHhQHyFa6J/E5bA34nDf+ovUO5gz8S5g3uEqB74uEXoN6vCdp51VEmm/B32Pb4tO+NeLUaI7j5jKmAu7r8FJq4431SlmHvayXFq9mN3eaztEFugSuKi3SbVqiNSh5TK/oLb3LV/L1fDNvpqFTuSznDP0y8js/ABEwAF8=
    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
    AAAEsHicnVNNb9NAEJ2UACV8NIULEhws0iKEULTOgRQkpEpwgAOiTb+C6hDZ7iZ169iW7YQGKxeO/AEOnEBCAnGCH8CFC3+AQ38C4lgkLhx4O3aC+EiQWMv2zNuZN29nd63AdaJYiP3c1KH84SNHp48Vjp84eWqmOHt6PfK7oS3XbN/1w7plRtJ1PLkWO7Er60EozY7lyg1r96aa3+jJMHJ8bzXuB7LRMdue03JsMwbULJ6/r93Q+s3EGWiG42lGx4y3LSupDR4k3qBZLIlypbqgC11jQ1yrDI2qppcFjxJlY8mfzb0ng7bIJ5u61CFJHsWwXTIpwrNJOgkKgDUooR0gJoXwHI6RNKAC8rvAJaJMoLv4tuFtZqgHX/FGzGCjkos3RKZG8+KTeC0OxEfxRnwW38dyJcyh9PTxt9JcGTRnnpxd+fbPrA7+MW3/zJqoOaYWLbBWB9oDRtQq7DS/9+jpwcr12nxyUbwQX6D/udgXH7ACr/fVfrksa8+Y/RZy0i6GsO5mCu6BTwJRnurBZVQxOKYNlaregFUr36ArI+x/GU3a+4Mxxcb3LMZ8C1zqHEQTIy2wpfMe/Ie8tx2u4OFEKR01rm6MdsDCkzDKvcSr1mJiVRpqOrBdZE5iXP2NMYSVMDpkjLkbHhQHyFa6J/E5bA34nDf+ovUO5gz8S5g3uEqB74uEXoN6vCdp51VEmm/B32Pb4tO+NeLUaI7j5jKmAu7r8FJq4431SlmHvayXFq9mN3eaztEFugSuKi3SbVqiNSh5TK/oLb3LV/L1fDNvpqFTuSznDP0y8js/ABEwAF8=
    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
    AAAEsHicnVNNb9NAEJ2UACV8NIULEhws0iKEULTOgRQkpEpwgAOiTb+C6hDZ7iZ169iW7YQGKxeO/AEOnEBCAnGCH8CFC3+AQ38C4lgkLhx4O3aC+EiQWMv2zNuZN29nd63AdaJYiP3c1KH84SNHp48Vjp84eWqmOHt6PfK7oS3XbN/1w7plRtJ1PLkWO7Er60EozY7lyg1r96aa3+jJMHJ8bzXuB7LRMdue03JsMwbULJ6/r93Q+s3EGWiG42lGx4y3LSupDR4k3qBZLIlypbqgC11jQ1yrDI2qppcFjxJlY8mfzb0ng7bIJ5u61CFJHsWwXTIpwrNJOgkKgDUooR0gJoXwHI6RNKAC8rvAJaJMoLv4tuFtZqgHX/FGzGCjkos3RKZG8+KTeC0OxEfxRnwW38dyJcyh9PTxt9JcGTRnnpxd+fbPrA7+MW3/zJqoOaYWLbBWB9oDRtQq7DS/9+jpwcr12nxyUbwQX6D/udgXH7ACr/fVfrksa8+Y/RZy0i6GsO5mCu6BTwJRnurBZVQxOKYNlaregFUr36ArI+x/GU3a+4Mxxcb3LMZ8C1zqHEQTIy2wpfMe/Ie8tx2u4OFEKR01rm6MdsDCkzDKvcSr1mJiVRpqOrBdZE5iXP2NMYSVMDpkjLkbHhQHyFa6J/E5bA34nDf+ovUO5gz8S5g3uEqB74uEXoN6vCdp51VEmm/B32Pb4tO+NeLUaI7j5jKmAu7r8FJq4431SlmHvayXFq9mN3eaztEFugSuKi3SbVqiNSh5TK/oLb3LV/L1fDNvpqFTuSznDP0y8js/ABEwAF8=
    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
    ki = (x, xi
    ), k0
    i
    = (x0, xi
    )
    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
    K 2 Rn⇥n, Kij = (xi, xj
    )
    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
    AAAE0HicnVNNb9NAEJ2UACV8tIULEheLtKigKtrkQAsCqRIcQBWiTT+luo1sd5NuajuW7YYUy0Jc+wc4cKISB8R/4MKlV5A49CcgjkXiwoG347SIjwQJW/bOvJ1583Z21w5cFcVCHOQGTuRPnjo9eKZw9tz5C0PDIxeXotZ26MhFp+W2whXbiqSrfLkYq9iVK0EoLc925bK9dU/PL7dlGKmWvxDvBHLNsxq+qivHigHVhu/MGKbyDdOz4k3bTqrpegIvVp6MDD+dMGZqiWqmxl3D3LKCwBrvwAeMoZlerw0XRakyOVUWZYMNcatyZEwa5ZLgp0jdZ7Y1kntHJm1QixzaJo8k+RTDdsmiCO8qlUlQAGyNEmoCsSiEpzhGUkoF5G8Dl4iygG7h34C32kV9+Jo3YgYHlVx8ITINGhOfxBtxKPbFW/FZfO/JlTCH1rOD0c5yZVAb2r08/+2fWR7GmDZ/ZvXVHFOdplirgvaAEb0KJ8tvP31xOH+7OpZcE3viC/S/EgfiPVbgt786r+dk9SWz30dO1sUQ1qOugsfgk0C0p3twA1VMjmlApa6XsmrtmzRxjP0vo0WdPxgzrHfPYszXwaXPQdQ30gZbNu/Df8J763EFHydK66hydfN4B2y8CaPcS3x6LRZWZaCmgu0isx/jwm+MIayE0SPGmLvhQ3GAbK27H59iK+VzvvYXrQ8xZ2IsYt7kKgW+LxJ6TWrznmSd1xFZvg2/w7bNp33jmNOgUY4b7TIVcF+PLqXR21iqlMqw58rF6ZvdmztIV+gqjYNrkqbpAc3SIpTs0T59oI/5ar6Tf5Z/noUO5Lo5l+iXJ7/7A4qcDLw=
    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

    View Slide

  7. Set up|A brief review of GP based BO
    事後分布の計算
    n ある観測点 が与えられたときの事後分布 を考える
    n 事後分布の平均関数:
    n 事後分布のカーネル:
    探索点の決定と獲得関数
    n 事後分布のもとで獲得関数 を最大化する点を次に探索
    n 獲得関数として,Expected improvementを採用
    - ガウス過程のもとであれば,期待値部分は明に計算可能
    7
    Dn
    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
    f | Dn
    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
    µn
    (x) = k>

    K + ⌘2I
    ⌘ 1
    Y
    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
    n
    x, x0 =  x, x0 k>

    K + ⌘2I
    ⌘ 1
    k0
    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
    AAAFAHicnVO/b9NAFH4pAUr40RQWJJYTaWmBtroUxC8JqRIMVAjR361UJ5HtXlITx7bsS0ixsjDyDzAwgYQEYkCsDCwszEgM/RMQY5FgYOC7c5IK2gSJs2y/99173/vu3Z0VuE4kOd9ODRxIHzx0ePBI5uix4yeGssMnVyK/Htpi2fZdP1yzzEi4jieWpSNdsRaEwqxZrli1qrfU/GpDhJHje0tyKxCFmlnxnLJjmxJQKesaVTMIzFLstZjhirIcZ80J1hxjRuhUNuV5dpMlEfvPTrJqMTakH3Sz77KLzBDSLE6z2U5YMZ7Mt1h1rJTN8alLl6/zac72GvkprkeO2mPOH059IIM2yCeb6lQjQR5J2C6ZFOFZpzxxCoAVKKYHQEwK4Tk6RlCLMsivAxeIMoFW8a3AW2+jHnzFG2kGG5VcvCEyGY3yL/w13+Gf+Bv+lf/qyRVrDqVnC38ryRVBaejJ6cUf/8yq4S9pczerr2ZJZbqmtTrQHmhErcJO8huPnu4s3lgYjc/xF/wb9D/n2/wjVuA1vtsv58XCM81+GzlJF0NY99oK7oNPAFGe6sEFVDF0TAUqVb2WVq18gya62P8ymtTcw5hgvXsmMV8GlzoHUd9IC2zJvAf/od7bmq7g4UQpHQu6utHdAQtPrFHdS7xqLSZWxVDTge0isx/j0l+MIaxYox1GqbvhQXGAbKW7H5+jrZY+54V9tM5izsA/h3lDV8no+yKg16CG3pOk8yoiybfgN7Vt6dO+0eVkNKLjRtpMGdzXzqVkvY2V6ak87Hmem7nSvrmDdIbO0ji4rtIM3aE5WoaSz/QzlUoNpB+nX6Xfpt8loQOpds4p+mOk3/8G51oaBA==
    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
    '
    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
    't
    (x) = E
    h
    max
    n
    0, f(x) arg maxi t 1
    f(xi
    )
    o
    | Dn
    i
    AAAFIHicnVPLbtNAFL0pAUp4NIVNJTZD06IWtdWkIF4SUiWKBAtE361UV9HYnSRDbcfYbkix/AOIPQtWVGKB+Ac2bLpDLFiUP0DsKBIbFpwZp0FQGiRs2XPvufeee+ZlB66KYs53cz1H8kePHe89UTh56vSZvmL/2aWosRk6ctFpuI1wxRaRdJUvF2MVu3IlCKXwbFcu2xu3dXy5KcNINfyFeCuQa56o+aqqHBEDqhSfWU0RBnVVSeJ0pDXKbjHLE3HdtpM7KbNcWY3xt0PhbOhAax9K+Bir6vxxZomwhkglUYxZNfmIxWy8nOpoRY0yK1S1OgpA5qn1jNwRbjKdVhI/7YRD06JSLPGJy1du8EnODhrlCW6eErWfmUZ/7i1ZtE4NcmiTPJLkUwzbJUER3lUqE6cA2Bol9BCIoBCeMjmSUiqgfhO4RJYAuoF/Dd5qG/Xha97IMDjo5OILUclomH/kr/ke3+Fv+Gf+41CuxHBoPVsY7axWBpW+pwPz3/9Z5WGMqf6rqqvmmKp03WhV0B4YRM/CyeqbT57vzd+cG04u8m3+Bfpf8l3+DjPwm9+cV7Ny7oVhn0ZNtoohrPttBQ/AJ4FoT6/BJXSxTE4NKnW/1KjWvkVjHex/GQW1DjBm2OFrFiNeBZc+B1HXTBtsWdyH/9jsrWc6+DhRWsec6W51dsDGmxjUrCU+PReBWTH0VLBdVHZjXPiDMYSVGHSfMTar4UNxgGqtuxufMlZqzvnaX7TeQ8zCWELcMl0K5r5I6LWoafYkW3mdkdXb8FvGts1pX+9wMhoyeUNtpgLu6/6lZIcbS5MTZdiz5dLU1fbN7aXzNEgj4LpGU3SXZmgRSr7mBnIXcoP57fxO/n3+Q5bak2vXnKPfnvynn2lPKB8=
    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
    AAAFIHicnVPLbtNAFL0pAUp4NIVNJTZD06IWtdWkIF4SUiWKBAtE361UV5HtTpKhtmPsaUix/AOIPQtWVGKB+Ac2bLpDLFiUP0DsKBIbFpwZp0FQGiRs2XPvufeee+blhJ6MFee7uZ4j+aPHjveeKJw8dfpMX7H/7FLc2Ixcseg2vEa04tix8GQgFpVUnlgJI2H7jieWnY3bOr7cFFEsG8GC2grFmm/XAlmVrq0AVYrPrKYdhXVZSVQ60hplt5jl26ruOMmdlFmeqCr8nch2N3SgtQ8lfIxVdf44s+yohkglkYxZNfGIKTZeTnW0IkeZFclaHQUg8+V6Ru7aXjKdVpIg7YQj06JSLPGJy1du8EnODhrlCW6eErWfmUZ/7i1ZtE4NcmmTfBIUkILtkU0x3lUqE6cQ2Bol9BCITRE8aXIEpVRA/SZwgSwb6Ab+NXirbTSAr3ljw+Cik4cvQiWjYf6Rv+Z7fIe/4Z/5j0O5EsOh9WxhdLJaEVb6ng7Mf/9nlY9RUf1XVVfNiqp03WiV0B4aRM/CzeqbT57vzd+cG04u8m3+Bfpf8l3+DjMImt/cV7Ni7oVhn0ZNtooRrPttBQ/AJ4BoT6/BJXSxTE4NKnW/1KjWvkVjHex/GW1qHWDMsMPXTCFeBZc+B3HXTAdsWTyA/9jsrW86BDhRWsec6W51dsDBmxjUrCU+PRcbs2LoKWF7qOzGuPAHYwQrMeg+ozKrEUBxiGqtuxufNFZqzvnaX7TeQ8zCWELcMl0K5r4I6LWoafYkW3mdkdU78FvGdsxpX+9wMhoyeUNtpgLu6/6lZIcbS5MTZdizvDR1tX1ze+k8DdIIuK7RFN2lGVqEkq+5gdyF3GB+O7+Tf5//kKX25No15+i3J//pJ2j/KB4=
    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
    AAAFIHicnVPLbtNAFL0pAUp4NIVNJTZD06IWtdWkIF4SUiWKBAtE361UV9HYnSRDbcfYbkix/AOIPQtWVGKB+Ac2bLpDLFiUP0DsKBIbFpwZp0FQGiRs2XPvufeee+ZlB66KYs53cz1H8kePHe89UTh56vSZvmL/2aWosRk6ctFpuI1wxRaRdJUvF2MVu3IlCKXwbFcu2xu3dXy5KcNINfyFeCuQa56o+aqqHBEDqhSfWU0RBnVVSeJ0pDXKbjHLE3HdtpM7KbNcWY3xt0PhbOhAax9K+Bir6vxxZomwhkglUYxZNfmIxWy8nOpoRY0yK1S1OgpA5qn1jNwRbjKdVhI/7YRD06JSLPGJy1du8EnODhrlCW6eErWfmUZ/7i1ZtE4NcmiTPJLkUwzbJUER3lUqE6cA2Bol9BCIoBCeMjmSUiqgfhO4RJYAuoF/Dd5qG/Xha97IMDjo5OILUclomH/kr/ke3+Fv+Gf+41CuxHBoPVsY7axWBpW+pwPz3/9Z5WGMqf6rqqvmmKp03WhV0B4YRM/CyeqbT57vzd+cG04u8m3+Bfpf8l3+DjPwm9+cV7Ny7oVhn0ZNtoohrPttBQ/AJ4FoT6/BJXSxTE4NKnW/1KjWvkVjHex/GQW1DjBm2OFrFiNeBZc+B1HXTBtsWdyH/9jsrWc6+DhRWsec6W51dsDGmxjUrCU+PReBWTH0VLBdVHZjXPiDMYSVGHSfMTar4UNxgGqtuxufMlZqzvnaX7TeQ8zCWELcMl0K5r5I6LWoafYkW3mdkdXb8FvGts1pX+9wMhoyeUNtpgLu6/6lZIcbS5MTZdiz5dLU1fbN7aXzNEgj4LpGU3SXZmgRSr7mBnIXcoP57fxO/n3+Q5bak2vXnKPfnvynn2lPKB8=
    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

    View Slide

  8. Set up|A mathematical formalism for NN
    構造の表現方法
    n NNは層の集合 と有向接続の集合
    で構成:
    n 有向接続は層番号のペアで表現
    n ある層 は種類 とユニット数
    で表現
    n 入力が複数ある場合は,
    入力を全てチャンネル方向に結合
    8
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: conv5, 32
    (1024)
    5: max-pool, 1
    (32)
    6: fc, 16
    (512)
    7: softmax
    (235)
    8: op
    (235)
    (a)
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 16
    (256)
    4: conv3, 16
    (256)
    5: conv5, 32
    (1024)
    6: max-pool, 1
    (32)
    7: fc, 16
    (512)
    8: softmax
    (235)
    9: op
    (235)
    (b)
    0: ip
    (240)
    1: conv7, 16
    (16)
    2: conv5, 32
    (512)
    3: conv3 /2, 16
    (256)
    4: conv3, 16
    (256)
    5: avg-pool, 1
    (32)
    6: max-pool, 1
    (16)
    7: max-pool, 1
    (16)
    8: fc, 16
    (512)
    12: fc, 16
    (512)
    9: conv3, 16
    (256)
    10: softmax
    (120)
    13: softmax
    (120)
    11: max-pool, 1
    (16)
    14: op
    (240)
    (c)
    Figure 1: An illustration of
    architectures. In each layer
    the layer, followed by the
    conv3), and then the numb
    (e.g. number of filters). Th
    output layers are pink while
    (softmax) layers are green.
    From Section 3: The layer
    noted in parentheses. The fo
    the normalised and unnorm
    tances d,
    ¯
    d . All self dista
    i.e. d(G, G) = ¯
    d(G, G) =
    malised: d(a, b) = 175.1,
    1479.3, d(b, c) = 1621.4. N
    ¯
    d(a, b) = 0.0286, ¯
    d(a, c)
    ¯
    d(b, c) = 0.2625.
    2
    Figure 1
    L
    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
    AAAEnXicnVNNaxNRFL2po9b40VY3gguDaUVEwksVv1YFFRSqtmnTFDKhzExf0rHzxcxLbB3yB9yLC0FRcCH+Bzdu/AMu+hPEZQU3LjzvzjSiNRF8w8zce969555333t25LmJEmKnMHbAOHjo8PiR4tFjx09MTE6dXEnCbuzIuhN6YbxqW4n03EDWlas8uRrF0vJtTzbszVt6vtGTceKGwbLajmTLtzqB23YdSwFqmr6lNhzLS+f7a5NlUbl85YaYFaX9RrUieJQpHwvhVOEDmbROITnUJZ8kBaRge2RRgqdJVRIUAWtRSo+AWBTDczlGUp+KyO8Cl4iygG7i24HXzNEAvuZNmMFBJQ9vjMwSzYjP4p3YFZ/Ee/FF/BjKlTKH1rONv53lymht4unppe//zPLxV7TxK2ukZkVtus5aXWiPGNGrcLL83pPnu0s3azPpefFGfIX+12JHfMQKgt435+2irL1g9tvIyboYw7qfK3gIPglEe7oHF1HF5JgOVOp6fVatfZMuDbD/ZbRoax9jhg3vmcJ8G1z6HCQjI22wZfMB/Me8tz5XCHCitI4aVzcHO2DjSRnlXuLVa7GwqhJqurA9ZI5iXP6DMYaVMrrHqLgbARRHyNa6R/G5bPX5nLf+ovUe5kz8y5g3uUqR74uEXpN6vCdZ53VElm/D32Lb5tO+PuAs0TTHTedMRdzXvUtZGm6szFaqsBdFee5qfnPH6QydowvgukZzdJcWqM6re0Yv6ZVx1rhjzBsPstCxQp5zin4bRuMnN735eg==
    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
    E
    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
    AAAEnXicnVNLaxNRFD6po9b4aKsbwYXBtCIi4aaKr1VBCwo+2rRpCplQ7kxv0rHzYmYSW4f8AffiQlAUXIj/wY0b/4CL/gRxWcGNC797ZhrRmgjeYWbO+e453/nuufdaoevEiRA7hbEDxsFDh8ePFI8eO35iYnLq5EocdCNb1e3ADaJVS8bKdXxVT5zEVathpKRnuaphbd7S842eimIn8JeT7VC1PNnxnbZjywRQ0/RksmFLN53vr02WReXylRtiVpT2G9WK4FGmfCwEU4UPZNI6BWRTlzxS5FMC2yVJMZ4mVUlQCKxFKT0CIimC53CMoj4Vkd8FrhAlgW7i24HXzFEfvuaNmcFGJRdvhMwSzYjP4p3YFZ/Ee/FF/BjKlTKH1rONv5XlqnBt4unppe//zPLwT2jjV9ZIzQm16TprdaA9ZESvws7ye0+e7y7drM2k58Ub8RX6X4sd8REr8Hvf7LeLqvaC2W8jJ+tiBOt+ruAh+BQQ7ekeXEQVk2M6UKnr9Vm19k26NMD+l1HS1j7GDBveswTzbXDpcxCPjLTAls378B/z3npcwceJ0jpqXN0c7ICFJ2WUe4lXr0ViVSXUdGC7yBzFuPwHYwQrZXSPMeFu+FAcIlvrHsXnsNXnc976i9a7mDPxL2Pe5CpFvi8Kek3q8Z5kndcRWb4Ff4tti0/7+oCzRNMcN50zFXFf9y5labixMlupwl4U5bmr+c0dpzN0ji6A6xrN0R1aoDqv7hm9pFfGWWPeuGc8yELHCnnOKfptGI2fGm35cw==
    ll(u)
    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
    lu(u)
    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
    AAAEl3icnVNNb9NAEJ0UAyV8tIULiEtEWlQQijYF8XWhEgiVA6JJm7ZSHVW2u0m39ZdsJ7RY+QNcOALiBBIHxH/gwoU/wKE/AXEsEhcOvB27QVASJNayPfN25s3b2V07dFWcCLFbGDlkHD5ydPRY8fiJk6fGxidOL8VBJ3JkwwncIFqxrVi6ypeNRCWuXAkjaXm2K5ftrbt6frkro1gF/mKyE8qmZ7V91VKOlQBquJ3pzqW18bKoXL12S8yI0kGjWhE8ypSP+WCi8IFMWqeAHOqQR5J8SmC7ZFGMZ5WqJCgE1qSUNoFYFMFTHCOpR0Xkd4BLRFlAt/Btw1vNUR++5o2ZwUElF2+EzBJNic/indgTn8R78UX8GMiVMofWs4O/neXKcG3s6dmF7//M8vBPaONX1lDNCbXoJmtV0B4yolfhZPndJ8/3Fm7Xp9KL4o34Cv2vxa74iBX43W/O25qsv2L2e8jJuhjBepgreAQ+CUR7ugeXUcXkmDZU6no9Vq19k670sf9ltGj7AGOGDe5ZgvkWuPQ5iIdG2mDL5n34j3lvPa7g40RpHXWubvZ3wMaTMsq9xKvXYmFVJdRUsF1kDmNc/IMxgpUyus+YcDd8KA6RrXUP41Ns9ficN/+i9QHmTPzLmDe5SpHvi4Rek7q8J1nndUSWb8PfZtvm077e5yzRJMdN5kxF3Nf9S1kabCzNVKqwa6I8ez2/uaN0ni7QNLhu0CzN0Tw1oETRM3pBL41zxh3jvjGXhY4U8pwz9Nswaj8BZl/2aw==
    G = (L, E)
    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

    View Slide

  9. Set up|A mathematical formalism for NN
    出力層は複数存在してもよい
    n NNは少なくとも1つ以上の出力を
    持つものとする
    n 複数の出力層が存在する場合は,
    各出力層からの出力を平均した結果
    を最終出力と定義
    n 文献中では出力層をdecision layer,
    最終出力をoutput layerと表記
    9
    6
    0: ip
    (240)
    1: conv7, 16
    (16)
    2: conv5, 32
    (512)
    3: conv3 /2, 16
    (256)
    4: conv3, 16
    (256)
    5: avg-pool, 1
    (32)
    6: max-pool, 1
    (16)
    7: max-pool, 1
    (16)
    8: fc, 16
    (512)
    12: fc, 16
    (512)
    9: conv3, 16
    (256)
    10: softmax
    (120)
    13: softmax
    (120)
    11: max-pool, 1
    (16)
    14: op
    (240)
    (c)
    Figure 1: An illustration of some CNN
    architectures. In each layer, i: indexes
    the layer, followed by the label (e.g
    conv3), and then the number of units
    (e.g. number of filters). The input and
    output layers are pink while the decision
    (softmax) layers are green.
    From Section 3: The layer mass is de-
    noted in parentheses. The following are
    the normalised and unnormalised dis-
    tances d,
    ¯
    d . All self distances are 0,
    i.e. d(G, G) = ¯
    d(G, G) = 0. Unnor-
    malised: d(a, b) = 175.1, d(a, c) =
    1479.3, d(b, c) = 1621.4. Normalised:
    ¯
    d(a, b) = 0.0286, ¯
    d(a, c) = 0.2395,
    ¯
    d(b, c) = 0.2625.
    Figure 1

    View Slide

  10. The OTMANN Distance
    距離の設計指針
    n 要件:層の計算量・種類・接続方法の違いを表現可能
    n 2つの構造を一致させるために必要な変更コストに着目
    n OTMANN:2つの構造を一致させるための最小コスト
    - OTMANN:Optimal Transport Metrics for Architectures of Neural Networks
    OTMANNの構成要素
    1. 接続や種類などの構造の変更コスト
    2. 2つの構造を一致させるための最小コストの求め方
    10

    View Slide

  11. The OTMANN Distance|Layer masses
    計算量を考慮した層の重み
    n 各層に応じた重み を考える
    n 層の計算量を考慮したいため,チャンネル数に着目
    11
    層の種類 重みの計算方法
    入力層・出力層・最終出力 0.1 × すべての層の重みの和
    畳み込み層・全結合層 前層の出力チャンネル数 × 出力チャンネル数
    プーリング層 入力チャンネル数
    lm(u)
    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
    AAAEl3icnVNNb9NAEJ0UAyV8tIULiEtEWlQQijYF8XWhEgiVA6JJm7ZSHVW2u0m39ZdsJ7RY+QNcOALiBBIHxH/gwoU/wKE/AXEsEhcOvB27QVASJNayPfN25s3b2V07dFWcCLFbGDlkHD5ydPRY8fiJk6fGxidOL8VBJ3JkwwncIFqxrVi6ypeNRCWuXAkjaXm2K5ftrbt6frkro1gF/mKyE8qmZ7V91VKOlQBquN5059LaeFlUrl67JWZE6aBRrQgeZcrHfDBR+EAmrVNADnXII0k+JbBdsijGs0pVEhQCa1JKm0AsiuApjpHUoyLyO8AloiygW/i24a3mqA9f88bM4KCSizdCZommxGfxTuyJT+K9+CJ+DORKmUPr2cHfznJluDb29OzC939mefgntPEra6jmhFp0k7UqaA8Z0atwsvzuk+d7C7frU+lF8UZ8hf7XYld8xAr87jfnbU3WXzH7PeRkXYxgPcwVPAKfBKI93YPLqGJyTBsqdb0eq9a+SVf62P8yWrR9gDHDBvcswXwLXPocxEMjbbBl8z78x7y3HlfwcaK0jjpXN/s7YONJGeVe4tVrsbCqEmoq2C4yhzEu/sEYwUoZ3WdMuBs+FIfI1rqH8Sm2enzOm3/R+gBzJv5lzJtcpcj3RUKvSV3ek6zzOiLLt+Fvs23zaV/vc5ZokuMmc6Yi7uv+pSwNNpZmKlXYNVGevZ7f3FE6TxdoGlw3aJbmaJ4aUKLoGb2gl8Y5445x35jLQkcKec4Z+m0YtZ9Ez/Zj
    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
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: conv5, 32
    (1024)
    5: max-pool, 1
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 16
    (256)
    4: conv3, 16
    (256)
    5: conv5, 32
    (1024)
    6: max-pool, 1
    0: ip
    (240)
    1: conv7, 16
    (16)
    2: conv5, 32
    (512)
    3: conv3 /2, 16
    (256)
    4: conv3, 16
    (256)
    5: avg-pool, 1
    (32)
    6: max-pool, 1
    7: max-pool, 1
    (16)
    9: conv3, 16
    (256)
    11: max-pool, 1
    Fig
    arc
    the
    co
    (e.
    ou
    (so
    Fro
    no
    0: ip
    (235)
    conv3, 16
    (16)
    conv3, 16
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    0: ip
    (240)
    1: conv7, 16
    (16)
    2: conv5, 32 4: conv3, 16
    Figure 1: An il
    architectures. I
    the layer, follo
    conv3), and th
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: conv5, 32
    (1024)
    5: max-pool, 1
    (32)
    6: fc, 16
    (512)
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 16
    (256)
    4: conv3, 16
    (256)
    5: conv5, 32
    (1024)
    6: max-pool, 1
    (32)
    7: fc, 16
    (512)
    0: ip
    (240)
    1: conv7, 16
    (16)
    2: conv5, 32
    (512)
    3: conv3 /2, 16
    (256)
    4:
    5: avg-pool, 1
    (32)
    6: max-pool, 1
    (16)
    8: fc, 16
    (512)
    12: fc, 16
    (512)
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: conv5, 32
    (1024)
    5: max-pool, 1
    (32)
    6: fc, 16
    (512)
    7: softmax
    (235)
    8: op
    (235)
    0: ip
    (235)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 16
    (256)
    4: conv3, 16
    (256)
    5: conv5, 32
    (1024)
    6: max-pool, 1
    (32)
    7: fc, 16
    (512)
    8: softmax
    (235)
    9: op
    (235)
    2:
    5: a
    10:
    (
    Figure 1. (b)
    層の重みの計算例: () 内が層の重み

    View Slide

  12. The OTMANN Distance|Path lengths
    接続関係の定量化
    n 接続関係を定量化するために,2つの層の間の経路長を導入
    n 入力層からある層 までの経路長と
    ある層 から最終出力までの経路長を3種類計算
    - 最短経路長 ,最大経路長 ,ランダムウォーク時の経路長の期待値
    n 経路長はそれぞれ線形オーダー で計算可能
    12
    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
    sp
    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
    AAAEnXicnVO9bhNBEB4HA8EE4iAKJBoLJwhFKFrTgKiQoIAC4ThxHJQz1t557Ry5P92tTZKTX4AXoKABJIrAO9DQ8AIUeQREGSQaCr6dO4xIiJHY093NfDvzzbezu3bkuYkWYr8wdaJ48tTp6TOlszPnzs+W52bWknAQO6rphF4Yr9syUZ4bqKZ2tafWo1hJ3/ZUy966a+ZbQxUnbhis6p1ItX3ZD9ye60gNqFO+aHWVp+WT1PKl3oz9NIlGo065KpYEj8pRo5YbVcpHPZwrfCCLuhSSQwPySVFAGrZHkhI8G1QjQRGwNqX0FIikGJ7LMYpGVEL+ALhClAS6hW8f3kaOBvANb8IMDip5eGNkVmhBfBZ74kB8Eu/FF/HjWK6UOYyeHfztLFdFndnnl1a+/zPLx1/T5u+siZo19egWa3WhPWLErMLJ8oe7Lw5WbjcW0qvijfgK/a/FvviIFQTDb87bZdV4yez3kJN1MYb1MFfwCHwKiPFMDxZRxeKYPlSaeiNWbXyLro+x/2WUtH2EMcOO75nGfA9c5hwkEyNtsGXzAfxnvLc+VwhwooyOBle3xjtg40kZ5V7iNWuRWFUFNV3YHjInMa4eYoxhpYz+YtTcjQCKI2Qb3ZP4XLZGfM7bf9H6AHMW/lXMW1ylxPdFQa9FQ96TrPMmIsu34W+zbfNp7445KzTPcfM5Uwn3tXb4dh411m4s1WAvC5qmy3SFroHiJt2h+1SnJgTs0ivao3fFxWK92Mpu9lQhv+IX6I9RfPwTivH8yw==
    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
    AAAEqHicnVPNbtNAEJ6UACX8NAUOSFwi0iJUoWhTkPg5VYIDHBBp2jRFdYhsZ5Oa+k/2JrS18gK8AAcugMSh8A5cuPACHPoIiGORuHDg27EbBKWpxFq2Z76d+ebb2V0rdJ1YCbGbmziWP37i5OSpwukzZ89NFafPr8RBP7Jlww7cIFq1zFi6ji8bylGuXA0jaXqWK5vWxj093xzIKHYCf1lthbLlmT3f6Tq2qQC1ixeNjnSV+TQxPFOtR14Sh8Nhu1gWlRs374h5UTpoVCuCR5myUQumcx/JoA4FZFOfPJLkk4LtkkkxnjWqkqAQWIsSegbEpAiewzGShlRAfh+4RJQJdAPfHry1DPXha96YGWxUcvFGyCzRrPgidsSe+Cw+iK/i56FcCXNoPVv4W2muDNtTLy4t/Tgyy8Nf0frvrLGaFXXpNmt1oD1kRK/CTvMH2y/3lu7WZ5Or4q34Bv1vxK74hBX4g+/2u0VZf8Xs95GTdjGC9ShT8Bh8Eoj2dA/mUMXgmB5U6npDVq19g66PsP9lNGnzAGOKHd4zhfkuuPQ5iMdGWmBL5334z3lvPa7g40RpHXWubox2wMKTMMq9xKvXYmJVJdR0YLvIHMe4/BdjBCthdJ9RcTd8KA6RrXWP43PYGvI5b/1D60PMGfiXMW9wlQLfFwm9Bg14T9LO64g034K/ybbFp70z4izRDMfNZEwF3Nf9S1k63FiZr1RhL4ryQjW7uZN0ma7QNXDdogV6QDVqQMk2vaYdep+fy9fyzfyTNHQil+VcoD9G3voFYzD+Ag==
    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
    lp
    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
    rw
    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
    AAAEqHicnVPLbtNAFL0pAUp4NAUWSGwi0iJUoWhSkHisKsECFog0bZqiukS2M0lN/ZI9SR9WfoAfYMEGkFgU/oENG36ART8BsSwSGxacuXaDoCRIjGX73jP3nnvmzowVuk6shNjPTRzLHz9xcvJU4fSZs+emitPnV+KgF9myYQduEK1aZixdx5cN5ShXroaRND3LlU1r856eb/ZlFDuBv6x2QrnumV3f6Ti2qQC1iheNtnSV+TQxPFNtRF4SbQ0GrWJZVG7cvCPmRemoUa0IHmXKRi2Yzn0gg9oUkE098kiSTwq2SybFeNaoSoJCYOuU0DMgJkXwHI6RNKAC8nvAJaJMoJv4duGtZagPX/PGzGCjkos3QmaJZsVnsScOxCfxXnwRP0ZyJcyh9ezgb6W5MmxNPb+09P2fWR7+ijZ+ZY3VrKhDt1mrA+0hI3oVdprf331xsHS3PptcFW/EV+h/LfbFR6zA73+z3y7K+ktmv4+ctIsRrEeZgsfgk0C0p3swhyoGx3ShUtcbsGrtG3R9iP0vo0nbRxhTbHTPFOY74NLnIB4baYEtnffhb/HeelzBx4nSOupc3RjugIUnYZR7iVevxcSqSqjpwHaROY5x+Q/GCFbC6CGj4m74UBwiW+sex+ewNeBzvv4XrQ8xZ+BfxrzBVQp8XyT0GtTnPUk7ryPSfAv+NtsWn/b2kLNEMxw3kzEVcF8PL2VptLEyX6nCXhTlhWp2cyfpMl2ha+C6RQv0gGrUgJJdekV79C4/l6/lm/knaehELsu5QL+NvPUTfFX+CA==
    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
    O(|E|)
    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

    View Slide

  13. The OTMANN Distance
    OTMANN
    n 2つのNN と の距離を測りたい
    n 2つの層の重みを一致させる変換行列 を考える
    n 各ペナルティを最小にする変換行列 を求め,
    そのときのペナルティの合計値を距離とする
    13
    G1 = (L1, E1)
    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
    G2 = (L2, E2)
    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
    Z 2 Rn1
    ⇥n2
    +
    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
    Z
    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
    AAACZHichVFNSwJBGH7cvsysLAmCICQxOsmrRV8noUvHrLTIRHa3sRbX3WV3FUz6A3UtOnQqiIh+Rpf+QIf+QBAdDbp06HU1IsJ6h5l55pn3eeeZGcXSNcclevJJXd09vX3+/sBAcHBoODQymnXMiq2KjGrqpr2tyI7QNUNkXM3VxbZlC7ms6GJLKa0097eqwnY009h0a5bIl+V9Qytqquwyld4phKIUTy4t0uxS5DdIxMmLKNqxZoZusIs9mFBRQRkCBlzGOmQ43HJIgGAxl0edOZuR5u0LHCHA2gpnCc6QmS3xuM+rXJs1eN2s6XhqlU/RudusjCBGj3RLDXqgO3qhj4616l6Nppcaz0pLK6zC8PH4xvu/qjLPLg6+VX96dlHEoudVY++WxzRvobb01cPzxsbyeqw+TVf0yv4v6Ynu+QZG9U29Tov1CwT4A75eOdIZZJPxBOP0XDQ13/4KPyYwhRl+7wWksIo1ZPhcgROc4sz3LAWlsDTWSpV8bU0YP0Ka/ARqWIor
    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
    層の種類の違い
    に関するペナルティ
    層数の差
    に関するペナルティ
    conv3 conv5 max-pool avg-pool fc
    v3 0 0.2 1 1 1
    v5 0.2 0 1 1 1
    -pool 1 1 0 0.25 1
    -pool 1 1 0.25 0 1
    1 1 1 1 0
    Table 1: An example label mis
    cost matrix M. There is zero c
    matching identical layers, < 1 c
    similar layers, and infinite cost f
    parate layers.
    lks from the input uip
    to u. As the layers of a neural network can be topologically ordere
    path lengths are well defined and finite. Further, for any s 2 {sp,lp,rw} and t 2 {ip,op}
    e computed for all u 2 L, in O(|E|) time (see Appendix A.3 for details).
    e now ready to describe OTMANN. Given two networks G1 = (L1, E1), G2 = (L2, E2
    layers respectively, we will attempt to match the layer masses in both networks.
    Rn1
    ⇥n2
    +
    be such that Z(i, j) denotes the amount of mass matched between layer i 2
    2
    . The OTMANN distance is computed by solving the following optimisation problem
    minimise
    Z
    lmm(Z) + nas(Z) + ⌫str str(Z)
    subject to
    X
    j2L2
    Zij  `m(i),
    X
    i2L1
    Zij  `m(j), 8i, j
    abel mismatch term lmm
    , penalises matching masses that have different labels, wh
    経路長
    に関するペナルティ

    View Slide

  14. The OTMANN Distance
    :Label mismatch penalty
    n ,
    n 層の種類の差異を定量化したペナルティ
    n 「3x3 convと5x5 convは近く,3x3 convとmax poolingは
    遠い」などの層の種類の差異を表現
    14
    conv3 conv5 max-pool avg-pool fc
    conv3 0 0.2 1 1 1
    conv5 0.2 0 1 1 1
    max-pool 1 1 0 0.25 1
    avg-pool 1 1 0.25 0 1
    fc 1 1 1 1 0
    Table 1: An example label mismatch
    cost matrix M. There is zero cost for
    matching identical layers, < 1 cost for
    similar layers, and infinite cost for dis-
    parate layers.
    for walks from the input uip
    to u. As the layers of a neural network can be topologically ordered1, the
    above path lengths are well defined and finite. Further, for any s 2 {sp,lp,rw} and t 2 {ip,op}, s
    t
    (u)
    can be computed for all u 2 L, in O(|E|) time (see Appendix A.3 for details).
    lmm
    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
    Cij = M(ll(i), ll( j))
    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
    AAAErHicnVPNbtNAEJ6UACX8NIVLJS4WaVGCqmidAylISJXKAQ4VbZq0leIost1NcOo4lu2Elig8AC/AgRMIDgjBI3Dhwgtw6CMgjkXiwoFvx0kQP0klbNk78+3MN9/O7lq+64SREEeJmVPJ02fOzp5Lnb9w8dJcev7ydtjpBras2B23E+xaZihdx5OVyIlcuesH0mxbrtyx9tfU/E5PBqHT8crRoS9rbbPpOQ3HNiNA9fTCWr3vtAbaHW0967pZJ7esYWjlcvV0RuQLxRVd6Bob4lZhZBQ1PS/4ydDw2ejMJz6QQXvUIZu61CZJHkWwXTIpxFslnQT5wGrUpxYQkwJ4DsdIGlAK+V3gElEm0H38m/CqQ9SDr3hDZrBRycUXIFOjJfFZvBHH4pN4K76IHxO5+syh9BxitOJc6dfnni5sfT8xq40xooe/sqZqjqhBK6zVgXafEbUKO87vPX52vHW7tNS/Ll6Kr9D/QhyJj1iB1/tmv96UpefMfhc5cRcDWOtDBQ/AJ4EoT/XgBqoYHNOESlVvwKqVb9DyGPtfRpMO/mKMsck9izDfAJc6B+HUSAts8bwH/xHvbZsreDhRSkeJqxvjHbDw9hnlXuJTazGxKg01HdguMqcxlv9gDGD1GR0xRtwND4p9ZCvd0/gctgZ8zmv/0HofcwbGDOYNrpLi+yKh16Ae70nceRUR51vwD9i2+LTvjTk1WuS4xSFTCvd1dCm1ycZ2Ia/D3tQzqzeHN3eWrtI1yoKrSKt0jzaoAiVP6BW9o/fJfLKcrCZrcehMYphzhX57ko2fJIb8xw==
    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
    AAAErHicnVPNbtNAEJ6UACX8NIVLJS4WaVGCqmidAylISJXKAQ4VbZq0leIost1NcOo4lu2Elig8AC/AgRMIDgjBI3Dhwgtw6CMgjkXiwoFvx0kQP0klbNk78+3MN9/O7lq+64SREEeJmVPJ02fOzp5Lnb9w8dJcev7ydtjpBras2B23E+xaZihdx5OVyIlcuesH0mxbrtyx9tfU/E5PBqHT8crRoS9rbbPpOQ3HNiNA9fTCWr3vtAbaHW0967pZJ7esYWjlcvV0RuQLxRVd6Bob4lZhZBQ1PS/4ydDw2ejMJz6QQXvUIZu61CZJHkWwXTIpxFslnQT5wGrUpxYQkwJ4DsdIGlAK+V3gElEm0H38m/CqQ9SDr3hDZrBRycUXIFOjJfFZvBHH4pN4K76IHxO5+syh9BxitOJc6dfnni5sfT8xq40xooe/sqZqjqhBK6zVgXafEbUKO87vPX52vHW7tNS/Ll6Kr9D/QhyJj1iB1/tmv96UpefMfhc5cRcDWOtDBQ/AJ4EoT/XgBqoYHNOESlVvwKqVb9DyGPtfRpMO/mKMsck9izDfAJc6B+HUSAts8bwH/xHvbZsreDhRSkeJqxvjHbDw9hnlXuJTazGxKg01HdguMqcxlv9gDGD1GR0xRtwND4p9ZCvd0/gctgZ8zmv/0HofcwbGDOYNrpLi+yKh16Ae70nceRUR51vwD9i2+LTvjTk1WuS4xSFTCvd1dCm1ycZ2Ia/D3tQzqzeHN3eWrtI1yoKrSKt0jzaoAiVP6BW9o/fJfLKcrCZrcehMYphzhX57ko2fJIb8xw==
    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
    AAAErHicnVPNbtNAEJ6UACX8NIVLJS4WaVGCqmidAylISJXKAQ4VbZq0leIost1NcOo4lu2Elig8AC/AgRMIDgjBI3Dhwgtw6CMgjkXiwoFvx0kQP0klbNk78+3MN9/O7lq+64SREEeJmVPJ02fOzp5Lnb9w8dJcev7ydtjpBras2B23E+xaZihdx5OVyIlcuesH0mxbrtyx9tfU/E5PBqHT8crRoS9rbbPpOQ3HNiNA9fTCWr3vtAbaHW0967pZJ7esYWjlcvV0RuQLxRVd6Bob4lZhZBQ1PS/4ydDw2ejMJz6QQXvUIZu61CZJHkWwXTIpxFslnQT5wGrUpxYQkwJ4DsdIGlAK+V3gElEm0H38m/CqQ9SDr3hDZrBRycUXIFOjJfFZvBHH4pN4K76IHxO5+syh9BxitOJc6dfnni5sfT8xq40xooe/sqZqjqhBK6zVgXafEbUKO87vPX52vHW7tNS/Ll6Kr9D/QhyJj1iB1/tmv96UpefMfhc5cRcDWOtDBQ/AJ4EoT/XgBqoYHNOESlVvwKqVb9DyGPtfRpMO/mKMsck9izDfAJc6B+HUSAts8bwH/xHvbZsreDhRSkeJqxvjHbDw9hnlXuJTazGxKg01HdguMqcxlv9gDGD1GR0xRtwND4p9ZCvd0/gctgZ8zmv/0HofcwbGDOYNrpLi+yKh16Ae70nceRUR51vwD9i2+LTvjTk1WuS4xSFTCvd1dCm1ycZ2Ia/D3tQzqzeHN3eWrtI1yoKrSKt0jzaoAiVP6BW9o/fJfLKcrCZrcehMYphzhX57ko2fJIb8xw==
    AAAErHicnVPNbtNAEJ6UACX8NIVLJS4WaVGCqmidAylISJXKAQ4VbZq0leIost1NcOo4lu2Elig8AC/AgRMIDgjBI3Dhwgtw6CMgjkXiwoFvx0kQP0klbNk78+3MN9/O7lq+64SREEeJmVPJ02fOzp5Lnb9w8dJcev7ydtjpBras2B23E+xaZihdx5OVyIlcuesH0mxbrtyx9tfU/E5PBqHT8crRoS9rbbPpOQ3HNiNA9fTCWr3vtAbaHW0967pZJ7esYWjlcvV0RuQLxRVd6Bob4lZhZBQ1PS/4ydDw2ejMJz6QQXvUIZu61CZJHkWwXTIpxFslnQT5wGrUpxYQkwJ4DsdIGlAK+V3gElEm0H38m/CqQ9SDr3hDZrBRycUXIFOjJfFZvBHH4pN4K76IHxO5+syh9BxitOJc6dfnni5sfT8xq40xooe/sqZqjqhBK6zVgXafEbUKO87vPX52vHW7tNS/Ll6Kr9D/QhyJj1iB1/tmv96UpefMfhc5cRcDWOtDBQ/AJ4EoT/XgBqoYHNOESlVvwKqVb9DyGPtfRpMO/mKMsck9izDfAJc6B+HUSAts8bwH/xHvbZsreDhRSkeJqxvjHbDw9hnlXuJTazGxKg01HdguMqcxlv9gDGD1GR0xRtwND4p9ZCvd0/gctgZ8zmv/0HofcwbGDOYNrpLi+yKh16Ae70nceRUR51vwD9i2+LTvjTk1WuS4xSFTCvd1dCm1ycZ2Ia/D3tQzqzeHN3eWrtI1yoKrSKt0jzaoAiVP6BW9o/fJfLKcrCZrcehMYphzhX57ko2fJIb8xw==
    AAAErHicnVPNbtNAEJ6UACX8NIVLJS4WaVGCqmidAylISJXKAQ4VbZq0leIost1NcOo4lu2Elig8AC/AgRMIDgjBI3Dhwgtw6CMgjkXiwoFvx0kQP0klbNk78+3MN9/O7lq+64SREEeJmVPJ02fOzp5Lnb9w8dJcev7ydtjpBras2B23E+xaZihdx5OVyIlcuesH0mxbrtyx9tfU/E5PBqHT8crRoS9rbbPpOQ3HNiNA9fTCWr3vtAbaHW0967pZJ7esYWjlcvV0RuQLxRVd6Bob4lZhZBQ1PS/4ydDw2ejMJz6QQXvUIZu61CZJHkWwXTIpxFslnQT5wGrUpxYQkwJ4DsdIGlAK+V3gElEm0H38m/CqQ9SDr3hDZrBRycUXIFOjJfFZvBHH4pN4K76IHxO5+syh9BxitOJc6dfnni5sfT8xq40xooe/sqZqjqhBK6zVgXafEbUKO87vPX52vHW7tNS/Ll6Kr9D/QhyJj1iB1/tmv96UpefMfhc5cRcDWOtDBQ/AJ4EoT/XgBqoYHNOESlVvwKqVb9DyGPtfRpMO/mKMsck9izDfAJc6B+HUSAts8bwH/xHvbZsreDhRSkeJqxvjHbDw9hnlXuJTazGxKg01HdguMqcxlv9gDGD1GR0xRtwND4p9ZCvd0/gctgZ8zmv/0HofcwbGDOYNrpLi+yKh16Ae70nceRUR51vwD9i2+LTvjTk1WuS4xSFTCvd1dCm1ycZ2Ia/D3tQzqzeHN3eWrtI1yoKrSKt0jzaoAiVP6BW9o/fJfLKcrCZrcehMYphzhX57ko2fJIb8xw==
    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
    lmm
    (Z) =
    P
    i2L1, j2L2
    Zij
    Cij
    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

    View Slide

  15. The OTMANN Distance
    :Non-assignment penalty
    n
    n 層数の違いに対応したペナルティ
    :Structural penalty
    n ,
    n 経路長を用いて接続の違いを表現したペナルティ
    n は6パターンの経路長の平均値を意味する
    15
    nas
    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
    str
    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
    nas
    (Z) =
    P
    i2L1
    (lm(i)
    P
    j2L2
    Zij
    ) +
    P
    j2L2
    (lm( j)
    P
    i2L1
    Zij
    )
    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
    AAAFPHicnVPNbtNAEB6XACVAm8IFicuKtCjlJ1pHiBakokpwAAlE/1u1riLb3SSb2o5lO6HF8gvwAhw4gYQE4h164cILcOidC6o4FcGFA7NjNxW0CRJr2Z75duabb2d3Ld+RYcT5rjZwInfy1OnBM/mz584PDRdGLiyFrXZgi0W75bSCFcsMhSM9sRjJyBErfiBM13LEsrV5X80vd0QQypa3EG37Yt01656sSduMEKoW3hl+Q1ZjwzWjRuDGnhkmSWl1nE0xI2y71VgyQ3qMpm3TiR8nVT1hJcctyXF2M4tpHompJGwVc5vJOLveL0gRNQ+Jji2WEVULRV6uTEzqXGdk8DuVA2OC6WVOowjZmGmNaDtgwAa0wIY2uCDAgwhtB0wI8VkDHTj4iK1DDE1ETAjQkxQjIIE85rcRFxhlIrqJ3zp6axnqoa94Q2KwsZKDb4CZDMb4Z/6e7/NP/AP/yn/15IqJQ+nZxr+V5gq/Ovzi0vzPf2a5+I+gcZjVV3MENZgkrRK1+4SoVdhpfuf5y/35u3Nj8VX+hu+h/td8l3/EFXid7/bbWTH3itgfYE7axQCtJ5mCp8gnEFGe6sE1rGJQTB1VqnoJqVa+ATe62P8ymrB1hDHFevcswvkacqlzEPaNtJAtnffQf0Z761IFD0+U0jFH1Y3uDlj4xIRSL/FVazFxVQxrSrQdzOzHuPAXY4BWTOgBY0Td8FCxj9lKdz8+SVZC53z9GK2PcM7AfxHnDaqSp/siUK8BHdqTtPMqIs230N8i26LTvtHlZDBKcaMZUx7v68GlZL2NpUpZR3tWL07fzm7uIFyGK1BCrgmYhocwA4tga0PaLW1Ku5fbyX3J7eW+paEDWpZzEf4YuR+/AX00Mw4=
    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
    str
    (Z) =
    P
    i2L1, j2L2
    Zij
    Cij
    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
    Cij = 1/6
    P
    s2{sp,lp,rw}
    P
    t2{ip,op}
    | s
    t
    (i) s
    t
    ( j)|
    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
    Cij
    AAAEmHicnVNNb9NAEJ0UAyV8tIULgotFWoQQitY5kMIpUpGgB0SbNmmlOopsdxOcOrZlO6Elyh/gxA0BJ5A4IP4DFy78AQ79CYhjkbhw4O3YCeIjQWIt2zNvZ968nd21Q8+NEyEOczPHtOMnTs6eyp8+c/bc3PzC+Xoc9CJH1pzAC6Jt24ql5/qylriJJ7fDSFpd25Nb9t6Kmt/qyyh2A38zOQhlo2u1fbflOlYCqL7SHLidYXO+IIql8rIhDJ0Ncas0Msq6URQ8CpSNtWAh955M2qWAHOpRlyT5lMD2yKIYzw4ZJCgE1qABdYBYFMFzOUbSkPLI7wGXiLKA7uHbhreToT58xRszg4NKHt4ImTotiU/irTgSH8U78Vl8n8g1YA6l5wB/O82VYXPuycWNb//M6uKf0MOfWVM1J9SiZdbqQnvIiFqFk+b3Hz872rhdXRpcFa/FF+h/JQ7FB6zA73913qzL6ktmv4OctIsRrPuZggfgk0CUp3pwHVVMjmlDpao3ZNXKN+nGGPtfRov2/2BMsck9SzDfApc6B/HUSBts6bwP/xHvbZcr+DhRSkeVq5vjHbDxDBjlXuJVa7GwKh01XdgeMqcxbv7GGMEaMDpiTLgbPhSHyFa6p/G5bA35nDf+onUVcyb+BcybXCXP90VCr0l93pO08yoizbfh77Nt82nfHXPqtMhxixlTHvd1dCn1yUa9VDRgrxuFys3s5s7SZbpC18BVpgrdozWqQUmHntJzeqFd0iraXW01DZ3JZTkX6JehVX8ANtr3Vg==
    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

    View Slide

  16. The OTMANN Distance
    Theorem 1|OTMANNは擬距離である
    n OTMANNは擬距離であることをAppendix A.2にて証明
    n (OTMANNを含む)擬距離の性質:
    - 非負性:
    - 対称性:
    - 三角不等式:
    - ※通常の距離と異なり とは限らない
    n 異なる構造であってもOTMANNがゼロとなるケースが存在
    16
    d(G1, G2
    ) 0
    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
    d(G1, G2
    ) = d(G2, G1
    )
    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
    d(G1, G3
    )  d(G1, G2
    ) + d(G2, G3
    )
    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
    AAAFBnicnVNNa9RQFL1TR1vHj7a6EdwEp5WqpbyMi1ZXBQV1IbbTT2iGIcm8aWMzSUzSsTVkL/4BF64UXIjgTtyJ4MY/INifIC4ruBHxvJtMpR8zBV9Icu9595573n3vWYHrRLEQ24W+Y8XjJ/oHTpZOnT5zdnBo+Nxi5G+EtlywfdcPly0zkq7jyYXYiV25HITSbFmuXLLWb6n5pbYMI8f35uOtQNZa5qrnNB3bjAHVh8LGmNEy4zXbdJM7aT3R03FtD3A9vaIZrnykHRVYQeC1/VGVQ+jqQ2UxUZmc0oWusSFuVDrGpKZPCB5lyseMP1z4SAY1yCebNqhFkjyKYbtkUoRnhXQSFACrUUIPgZgUwnM4RlJKJeRvAJeIMoGu47sKbyVHPfiKN2IGG5VcvCEyNRoVX8UbsSO+iLfiu/jdlSthDqVnC38ry5VBffDZhblfR2a18I9p7V9WT80xNWmKtTrQHjCiVmFn+e0nz3fmblZHk8vilfgB/S/FtviMFXjtn/brWVl9wey3kZN1MYR1P1fwAHwSiPJUD66iisExq1Cp6qWsWvkGje9i/8to0uYBxgzr3rMY801wqXMQ9Yy0wJbNe/Af8962uIKHE6V0VLm6sbsDFp6EUe4lXrUWE6vSUNOB7SKzF+P8PsYQVsJohzHmbnhQHCBb6e7F57CV8jmvHaL1HuYM/MuYN7hKie+LhF6D2rwnWedVRJZvwd9k2+LT3tjl1GiE40ZyphLua+dSat2NxcqEDntWL0/r+c0doIt0icbANUnTdJdmaAFKvtGfQn9hoPi0+K74vvghC+0r5Dnnac8ofvoLL7Ygng==
    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
    d(G1, G1
    ) = 0
    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
    AAAEhHicnVM9b9RAEJ0LhgQTSCIaJJoTlyCEULRHQ6CKgAIKRHLJJZHiU2T79o4l/pK9dyRY9wfSUlBQgUSB+A80NPwBivwERBkkGgrejs0hcuSQWMv2zNuZN29nd70kUJkW4rAycco6fWZy6qx9bto+f2Fmdnoji3upL5t+HMTpludmMlCRbGqlA7mVpNINvUBuerv3zPxmX6aZiqN1vZ/IVuh2I9VRvqsBrezM1sSi4FEdNeqlUaNyxHOVD+RQm2LyqUchSYpIww7IpQzPNtVJUAKsRTk9BeJSCk9xjKQB2cjvAZeIcoHu4tuFt12iEXzDmzGDj0oB3hSZVVoQn8U7cSQ+iffii/hxIlfOHEbPPv5ekSuTnZmDS2vf/5kV4q/pye+ssZo1dWiJtSpoTxgxq/CL/P7zl0drdxoL+VXxRnyF/tfiUHzECqL+N//tqmy8Yvb7yCm6mMJ6VCp4DD4JxHimB9dRxeGYLlSaegNWbXyHbgyx/2V0aW+EscBO7pnGfAdc5hxkYyM9sBXzEfxnvLchV4hwooyOBld3hjvg4ckZ5V7iNWtxsaoqairYATLHMa4fY0xh5Yz+YtTcjQiKE2Qb3eP4FFsDPuetv2h9iDkH/xrmHa5i832R0OtQn/ek6LyJKPI9+Htse3za20POKs1z3HzJZOO61o9fzlFj4+ZiHfaqoCm6TFfoGihu0TI9oBVqQkCbDuiFddG6bS0X13qiUt7vOfpjWHd/Ar4v8nw=
    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
    AAAEu3icnVNNb9NAEJ2UACV8NIULEheLtFBQFa1zSUGqVAkk4IBo06atVEeR7WxSt7Zj2U5osfIHkDhz4AQSB8SRK3Dhwh/g0J+AOBaJCwfejpMgCkkl1rI983bmzdvZXStwnSgW4iAzcSJ78tTpyTO5s+fOX5jKT19cj9qd0JZVu+22w03LjKTr+LIaO7ErN4NQmp7lyg1r946a3+jKMHLa/lq8H8iaZ7Z8p+nYZgyonr/emDM8M962TTe516snem9eOwLc0BY1Uc8XRLFUXtCFrrEhbpUGRlnTi4JHgfpjuT2d+UgGNahNNnXII0k+xbBdMinCs0U6CQqA1SihHSAmhfAcjpHUoxzyO8Alokygu/i24G31UR++4o2YwUYlF2+ITI1mxRfxRhyKz+Kt+Cp+juRKmEPp2cffSnNlUJ96enn1x7FZHv4xbf/OGqs5piYtsFYH2gNG1CrsNL/75Pnh6u3KbHJNvBLfoP+lOBCfsAK/+91+vSIrL5j9LnLSLoawHvYVPAKfBKI81YObqGJwTAsqVb0eq1a+QfND7H8ZTdr7izHFRvcsxnwTXOocRGMjLbCl8z78x7y3HlfwcaKUjgpXN4Y7YOFJGOVe4lVrMbEqDTUd2C4yxzGuHWEMYSWMDhhj7oYPxQGyle5xfA5bPT7ntX9ofYA5A/8C5g2ukuP7IqHXoC7vSdp5FZHmW/D32Lb4tDeGnBrNcNxMnymH+zq4lNpoY71U1GGv6IUlvX9zJ+kKXaU5cJVpie7TMlWh5Bm9o/f0IbuYtbM7WTcNncj0cy7RHyPb+QUtTgQW
    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
    d(G1, G2
    ) = 0 , G1 = G2
    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
    AAAE73icnVNda9RAFL2tq9b1o62+CL4MbitVSpnsy1ZBKCiooNivbQtNWZJ0dhubTWIy3baG/QP+gT4IooIPxf8giC/+AR/6C0R8USr44oNnbraVVruCCUnuPXPPuWcmM24c+KmWcqen91jh+ImTfaeKp8+cPdc/MHh+Lo3WEk9VvSiIkgXXSVXgh6qqfR2ohThRTtMN1Ly7esuMz7dUkvpROKs3Y7XUdBqhX/c9RwOqDSwuj9hNR694TpDdadcyqz0qDgDl9lVxU0hh31d1nfiNFe0kSbQuxCEaig7xRG2gJMfKlXFLWoIDeb28F1SENSb5KlHnmowGe96STcsUkUdr1CRFIWnEATmU4l4kiyTFwJYoo0dAHEqQ+VyjqE1F8NeAK1Q5QFfxbiBb7KAhcqObsoKHTgGeBExBw/Kj3Ja78oN8Iz/Ln0dqZaxh/Gzi6+ZcFdf6n16c+fFPVhNfTSu/WV09a6rTOHv14T1mxMzCy/mtJ1u7Mzemh7Mr8pX8Av8v5Y58jxmEre/e6yk1/YzVb4OTr2KC6EHHwUPoKSAmM2twDV1srmnApenXZtcmt2l0H/tfRYc2/lDMsaPXTGO8Di2zD9KulS7U8vEQ+Tr/2yZ3CLGjjI9p7m7v/wEXd8YoryUeMxcHsxLo6SMOwOymOHtIMUGUMbqnqHk1QjiOwTa+u+n5HLV5ny/9xes9jNn4ljBuc5cinxcFvza1+J/kK28qcr6LfINjl3f78r6moCGuG+ooFXFe9w6lODqYK49ZiKdkacLqnNw+ukSXaQRaFZqguzRJVTh5R5/oK30rPC5sFZ4XXuSlvT0dzgU6cBW2fwE2CRlG
    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
    AAAE73icnVNda9RAFL2tq9b1o62+CL4MbitVSpnsy1ZBKCiooNivbQtNWZJ0dhubTWIy3baG/QP+gT4IooIPxf8giC/+AR/6C0R8USr44oNnbraVVruCCUnuPXPPuWcmM24c+KmWcqen91jh+ImTfaeKp8+cPdc/MHh+Lo3WEk9VvSiIkgXXSVXgh6qqfR2ohThRTtMN1Ly7esuMz7dUkvpROKs3Y7XUdBqhX/c9RwOqDSwuj9hNR694TpDdadcyqz0qDgDl9lVxU0hh31d1nfiNFe0kSbQuxCEaig7xRG2gJMfKlXFLWoIDeb28F1SENSb5KlHnmowGe96STcsUkUdr1CRFIWnEATmU4l4kiyTFwJYoo0dAHEqQ+VyjqE1F8NeAK1Q5QFfxbiBb7KAhcqObsoKHTgGeBExBw/Kj3Ja78oN8Iz/Ln0dqZaxh/Gzi6+ZcFdf6n16c+fFPVhNfTSu/WV09a6rTOHv14T1mxMzCy/mtJ1u7Mzemh7Mr8pX8Av8v5Y58jxmEre/e6yk1/YzVb4OTr2KC6EHHwUPoKSAmM2twDV1srmnApenXZtcmt2l0H/tfRYc2/lDMsaPXTGO8Di2zD9KulS7U8vEQ+Tr/2yZ3CLGjjI9p7m7v/wEXd8YoryUeMxcHsxLo6SMOwOymOHtIMUGUMbqnqHk1QjiOwTa+u+n5HLV5ny/9xes9jNn4ljBuc5cinxcFvza1+J/kK28qcr6LfINjl3f78r6moCGuG+ooFXFe9w6lODqYK49ZiKes0oTVObl9dIku0wi0KjRBd2mSqnDyjj7RV/pWeFzYKjwvvMhLe3s6nAt04Cps/wI2WRlH
    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
    AAAE73icnVNda9RAFL2tq9b1o62+CL4MbitVSpnsy1ZBKCiooNivbQtNWZJ0dhubTWIy3baG/QP+gT4IooIPxf8giC/+AR/6C0R8USr44oNnbraVVruCCUnuPXPPuWcmM24c+KmWcqen91jh+ImTfaeKp8+cPdc/MHh+Lo3WEk9VvSiIkgXXSVXgh6qqfR2ohThRTtMN1Ly7esuMz7dUkvpROKs3Y7XUdBqhX/c9RwOqDSwuj9hNR694TpDdadcyqz0qDgDl9lVxU0hh31d1nfiNFe0kSbQuxCEaig7xRG2gJMfKlXFLWoIDeb28F1SENSb5KlHnmowGe96STcsUkUdr1CRFIWnEATmU4l4kiyTFwJYoo0dAHEqQ+VyjqE1F8NeAK1Q5QFfxbiBb7KAhcqObsoKHTgGeBExBw/Kj3Ja78oN8Iz/Ln0dqZaxh/Gzi6+ZcFdf6n16c+fFPVhNfTSu/WV09a6rTOHv14T1mxMzCy/mtJ1u7Mzemh7Mr8pX8Av8v5Y58jxmEre/e6yk1/YzVb4OTr2KC6EHHwUPoKSAmM2twDV1srmnApenXZtcmt2l0H/tfRYc2/lDMsaPXTGO8Di2zD9KulS7U8vEQ+Tr/2yZ3CLGjjI9p7m7v/wEXd8YoryUeMxcHsxLo6SMOwOymOHtIMUGUMbqnqHk1QjiOwTa+u+n5HLV5ny/9xes9jNn4ljBuc5cinxcFvza1+J/kK28qcr6LfINjl3f78r6moCGuG+ooFXFe9w6lODqYK49ZiKes0oTVObl9dIku0wi0KjRBd2mSqnDyjj7RV/pWeFzYKjwvvMhLe3s6nAt04Cps/wI2WRlH
    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

    View Slide

  17. The OTMANN Distance
    構造は異なるがOTMANN = 0となる例
    17
    0: ip
    (100)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: max-pool, 1
    (32)
    5: fc, 16
    (51)
    6: softmax
    (100)
    7: op
    (100)
    0: ip
    (100)
    1: conv3, 16
    (16)
    2: conv3, 8
    (128)
    3: conv3, 8
    (128)
    4: conv3, 32
    (512)
    5: max-pool, 1
    (32)
    6: fc, 16
    (51)
    7: softmax
    (100)
    8: op
    (100)
    Figure 3: An example of 2 CN
    d = ¯
    d = 0 distance. The OT solu
    mass in each layer in the netwo
    the layer horizontally opposite
    with 0 cost. For layer 2 on the
    mapped to layers 2 and 3 on th
    while the descriptor of these netw
    their functional behaviour is the
    0: ip
    (100)
    1: conv3, 16
    (16)
    2: conv3, 16
    (256)
    3: conv3, 32
    (512)
    4: max-pool, 1
    (32)
    5: fc, 16
    (51)
    6: softmax
    (100)
    7: op
    (100)
    0: ip
    (100)
    1: conv3, 16
    (16)
    2: conv3, 8
    (128)
    3: conv3, 8
    (128)
    4: conv3, 32
    (512)
    5: max-pool, 1
    (32)
    6: fc, 16
    (51)
    7: softmax
    (100)
    8: op
    (100)
    Figure 3: An example of 2 CNNs which have
    d = ¯
    d = 0 distance. The OT solution matches the
    mass in each layer in the network on the left to
    the layer horizontally opposite to it on the right
    with 0 cost. For layer 2 on the left, its mass is
    mapped to layers 2 and 3 on the left. However,
    while the descriptor of these networks is different,
    their functional behaviour is the same.
    A.2 Distance Properties of OTMANN

    View Slide

  18. NASBOT
    カーネルの設計
    n 次式で定義されるnegative exponentiated distanceを
    カーネルとして採用:
    - LaplacianカーネルやGaussカーネルに類似したカーネル
    n はOTMANN, は正規化されたOTMANN
    n 著名なカーネルのように正定値性を満たすかは未確認
    n 予備実験では固有値が負になるケースはなかったとのこと
    18
     = ↵ exp( d) + ¯
    ↵ exp( ¯ ¯
    d)
    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
    d
    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
    AAAEk3icnVNNb9NAEJ0UAyV8tAUhIXGxSIsQQtE6B1LgUkEPcKho0qatVEeV7WyCqWNbthNarPwBuII4cAKJA+I/cOHCH+DQn4A4FokLB96OnSA+EiTWsj3zdubN29ldO/TcOBHioDB1RDt67Pj0ieLJU6fPzMzOnd2Ig17kyIYTeEG0ZVux9FxfNhI38eRWGEmra3ty0969o+Y3+zKK3cBfT/ZD2exaHd9tu46VAKq1dmZLolypLhrC0NkQNypDo6obZcGjRPlYDeYK78mkFgXkUI+6JMmnBLZHFsV4tskgQSGwJqX0EIhFETyXYyQNqIj8HnCJKAvoLr4deNs56sNXvDEzOKjk4Y2QqdOC+CTeikPxUbwTn8X3sVwpcyg9+/jbWa4Md2aeXFj79s+sLv4JPfiZNVFzQm1aZK0utIeMqFU4WX7/8YvDtZv1hfSyeC2+QP8rcSA+YAV+/6vzpibrL5l9GTlZFyNYK7mC++CTQJSnenAVVUyO6UClqjdg1co36doI+19Gi/b+YMyw8T1LMN8GlzoH8cRIG2zZvA//Ee9tlyv4OFFKR52rm6MdsPGkjHIv8aq1WFiVjpoubA+ZkxjXf2OMYKWMDhkT7oYPxSGyle5JfC5bAz7nzb9ovYc5E/8S5k2uUuT7IqHXpD7vSdZ5FZHl2/D32Lb5tLdGnDrNc9x8zlTEfR1eSn28sVEpG7BrRmnpen5zp+kiXaIr4KrSEt2lVWpAiaSn9Iyea+e1W9ptbTkLnSrkOefol6Gt/ADnRvUb
    ¯
    d
    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
    AAAEmXicnVNNb9NAEJ0UAyV8tIULUi8WaRFCKFrnQAqnIjgUJESbtE2lOqpsZ5OaOrZlO6HFyh/gxgmJnkDigPgPXLjwBzj0JyCOReLCgbdjJ4iPBIm1bM+8nXnzdnbXDj03ToQ4Kkyd0E6eOj19pnj23PkLM7NzFzfjoBc5csMJvCDasq1Yeq4vNxI38eRWGEmra3uyYe/dVfONvoxiN/DXk4NQNrtWx3fbrmMlgBqmbUVpa7AzWxLlSnXJEIbOhrhVGRpV3SgLHiXKx2owV3hPJrUoIId61CVJPiWwPbIoxrNNBgkKgTUppcdALIrguRwjaUBF5PeAS0RZQPfw7cDbzlEfvuKNmcFBJQ9vhEydFsUn8VYci4/infgsvo/lSplD6TnA385yZbgz8+xy/ds/s7r4J7T7M2ui5oTatMRaXWgPGVGrcLL8/tMXx/XbtcX0qngtvkD/K3EkPmAFfv+r82ZN1g6Z/R5ysi5GsB7mCh6BTwJRnurBdVQxOaYDlaregFUr36QbI+x/GS3a/4Mxw8b3LMF8G1zqHMQTI22wZfM+/Ce8t12u4ONEKR01rm6OdsDGkzLKvcSr1mJhVTpqurA9ZE5iXP+NMYKVMjpkTLgbPhSHyFa6J/G5bA34nDf/ovU+5kz8S5g3uUqR74uEXpP6vCdZ51VElm/D32fb5tPeGnHqtMBxCzlTEfd1eCn18cZmpWzAXjNKyzfzmztN83SFroGrSsu0Qqu0wXvznF7SoTav3dFWtAdZ6FQhz7lEvwyt/gN43/fg
    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

    View Slide

  19. NASBOT
    進化計算による獲得関数の最適化
    1. 獲得関数値が高い個体ほど選択確率を高くなるように設定し,
    親個体をランダムに 個選ぶ
    2. 選んだ個体に以下の操作のいずれかをランダムに適用し,
    子個体を生成
    3. 子個体の獲得関数値を評価し,全て親個体グループに追加
    19
    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
    Operation Description
    dec_single Pick a layer at random and decrease the number of units by 1/8.
    dec_en_masse Pick several layers at random and decrease the number of units by 1/8 for all of them.
    inc_single Pick a layer at random and increase the number of units by 1/8.
    inc_en_masse Pick several layers at random and increase the number of units by 1/8 for all of them.
    dup_path Pick a random path u1, . . . , uk
    , duplicate u2, . . . , uk 1
    and connect them to u1
    and uk
    .
    remove_layer Pick a layer at random and remove it. Connect the layer’s parents to its children if necessary.
    skip Randomly pick layers u, v where u is topologically before v. Add (u, v) to E.
    swap_label Randomly pick a layer and change its label.
    wedge_layer Randomly remove an edge (u, v) from E. Create a new layer w and add (u, w), (w, v) to E.
    Table 2: Descriptions of modifiers to transform one network to another. The first four change the number of
    units in the layers but do not change the architecture, while the last five change the architecture.

    View Slide

  20. NASBOT
    NASBOTの柔軟性
    n NASBOTの枠組みを拡張することでDropoutの確率やバッチ
    正規化のパラメータも層ごとに最適化可能
    n 学習率などのハイパーパラメータも既存のカーネルを使用し
    同時にBOで最適化可能
    n 今回は構造最適化に限定して実験
    20

    View Slide

  21. Experiments|Settings
    比較手法
    n ランダムサーチ(NASBOTの獲得関数の値を一様乱数で決定)
    n 獲得関数の最適化と同じスキームの進化計算法
    n TreeBO(順伝播構造を探索するBO)
    データセットとモデル
    n 回帰(MLP):Blog, Indoor, Slice, Naval, Protein, News
    - 訓練:検証:テスト = 60%:20%:20%
    n 分類(CNN):CIFAR-10
    - 訓練:検証:テスト = 40,000:10,000:10,000
    21

    View Slide

  22. Experiments|Settings
    計算資源
    n 全ての手法で非同期並列処理を使用
    - 概ね70 ~ 120個の構造を評価する実験設定
    n Blog, Indoor, Slice, Naval, Protein:Geforce 970 2枚 × 8時間
    n News: Geforce 980 4枚 × 6時間
    n CIFAR-10:K80 4枚 × 10時間
    SGDによるNNの学習
    n 回帰:学習率10-5,バッチサイズ256,更新回数20K回
    n 分類:初期学習率10-2,バッチサイズ32,更新回数60K回
    22

    View Slide

  23. Experiments|Results
    検証精度の最良値の推移(5試行)
    23
    Time (hours)
    0 2 4 6 8
    Cross Validation MSE
    0.7
    0.8
    0.9
    1
    1.1
    1.2
    Blog Feedback, #workers = 2
    Time (hours)
    0 2 4 6 8
    Cross Validation MSE
    0.1
    0.15
    0.2
    0.25
    Indoor Location, #workers = 2
    Time (hours)
    0 2 4 6 8
    Cross Validation MSE
    0.6
    0.7
    0.8
    0.9
    1
    Slice Localisation, #workers = 2
    Time (hours)
    0 2 4 6 8
    Cross Validation MSE
    10 -2
    10 -1
    Naval Propulsion, #workers = 2
    Time (hours)
    0 2 4 6 8
    Cross Validation MSE
    0.84
    0.86
    0.88
    0.9
    0.92
    0.94
    0.96
    0.98
    Protein, #workers = 2
    Time (hours)
    0 1 2 3 4 5 6
    Cross Validation MSE
    0.7
    0.8
    0.9
    1
    1.1
    News, #workers = 4
    Time (hours)
    0 2 4 6 8 10
    Cross Validation Error
    0.12
    0.13
    0.14
    0.15
    0.16
    0.17
    Cifar10, #workers = 4
    EA
    RAND
    TreeBO
    NASBOT
    Figure 2: Cross validation results: In all figures, the x axis is time. The y axis is the mean squared error
    (MSE) in the first 6 figures and the classification error in the last. Lower is better in all cases. The title of each
    figure states the dataset and the number of parallel workers (GPUs). All figures were averaged over at least 5
    independent runs of each method. Error bars indicate one standard error.
    increasing or decreasing the number of computational units in a layer, by adding or deleting layers,

    View Slide

  24. Experiments|Results
    検証精度が最良であるモデルのテスト精度(5試行)
    24
    Method
    Blog
    (60K, 281)
    Indoor
    (21K, 529)
    Slice
    (54K, 385)
    Naval
    (12K, 17)
    Protein
    (46K, 9)
    News
    (40K, 61)
    Cifar10
    (60K, 1K)
    Cifar10
    150K iters
    RAND
    0.780
    ± 0.034
    0.115
    ±0.023
    0.758
    ± 0.041
    0.0103
    ± 0.002
    0.948
    ± 0.024
    0.762
    ±0.013
    0.1342
    ± 0.002
    0.0914
    ± 0.008
    EA
    0.806
    ± 0.040
    0.147
    ± 0.010
    0.733
    ± 0.041
    0.0079
    ±0.004
    1.010
    ± 0.038
    0.758
    ±0.038
    0.1411
    ± 0.002
    0.0915
    ± 0.010
    TreeBO
    0.928
    ± 0.053
    0.168
    ± 0.023
    0.759
    ± 0.079
    0.0102
    ± 0.002
    0.998
    ± 0.007
    0.866
    ± 0.085
    0.1533
    ± 0.004
    0.1121
    ± 0.004
    NASBOT
    0.731
    ±0.029
    0.117
    ±0.008
    0.615
    ±0.044
    0.0075
    ±0.002
    0.902
    ±0.033
    0.752
    ±0.024
    0.1209
    ±0.003
    0.0869
    ±0.004
    Table 3: The first row gives the number of samples N and the dimensionality D of each dataset in the form
    (N, D). The subsequent rows show the regression MSE or classification error (lower is better) on the test set
    for each method. The last column is for Cifar10 where we took the best models found by each method in 24K
    iterations and trained it for 120K iterations. When we trained the VGG-19 architecture using our training
    procedure, we got test errors 0.1718 (60K iterations) and 0.1018 (150K iterations).
    Experimental Set up: Each method is executed in an asynchronously parallel set up of 2-4 GPUs,
    That is, it can evaluate multiple models in parallel, with each model on a single GPU. When the

    View Slide

  25. Experiments|Results
    学習する構造を決定するまでに要する時間
    NASBOTでの探索結果
    n すべてのデータセットで他の手法と同等以上のスコア
    n CIFAR-10で他の構造探索に比べてスコアが劣るのは探索空間
    が広いことが原因と考えている
    - VGG-19(テストエラー10.18%)よりは良い構造を発見できている
    25
    手法 構造の決定に要する時間 [sec]
    NASBOT 46.13
    ランダムサーチ(RAND) 26.43
    進化計算(EA) 0.19
    TreeBO 7.83

    View Slide

  26. Experiments|Results
    NASBOTが得たベスト構造(Indoorデータセット)
    26
    #0 ip, 64, (28891)
    #1 crelu, 144, (144)
    #2 softplus, 576, (82944)
    #6 logistic, 256, (69632)
    #9 linear, 256, (14445)
    #3 leaky-relu, 72, (41472)
    #4 logistic, 128, (73728)
    #5 elu, 64, (4608)
    #7 logistic, 256, (16384)
    #8 linear, 256, (14445)
    #10 op, 512, (28891)
    #0 ip, 64, (542390)
    #1 elu, 128, (128)
    #2 elu, 256, (32768)
    #3 logistic, 512, (131072)
    #27 logistic, 512, (393216)
    #29 linear, 512, (542390)
    #4 crelu, 512, (262144)
    #5 logistic, 512, (262144)
    #6 logistic, 512, (262144)
    #7 crelu, 512, (262144)
    #8 elu, 512, (262144)
    #9 crelu, 512, (262144)
    #10 tanh, 512, (262144)
    #11 elu, 512, (262144)
    #23 tanh, 324, (259200)
    #12 softplus, 64, (32768)
    #13 tanh, 512, (262144)
    #16 logistic, 72, (9216)
    #14 softplus, 512, (262144)
    #15 softplus, 64, (32768)
    #17 relu, 128, (8192) #18 logistic, 128, (9216)
    #19 tanh, 576, (73728) #20 relu, 128, (16384)
    #21 leaky-relu, 576, (331776) #22 relu, 288, (36864)
    #26 leaky-relu, 512, (589824)
    #24 tanh, 648, (209952)
    #25 leaky-relu, 576, (373248)
    #28 logistic, 512, (262144)
    #30 op, 512, (542390)
    #0 ip, 64, (423488)
    #1 elu, 128, (128)
    #2 elu, 256, (32768)
    #3 linear, 512, (211744)
    #25 tanh, 576, (700416)
    #4 logistic, 512, (131072)
    #21 tanh, 512, (262144)
    #27 op, 512, (423488)
    #5 logistic, 512, (262144)
    #6 logistic, 512, (262144)
    #7 leaky-relu, 512, (262144)
    #8 leaky-relu, 512, (262144)
    #9 leaky-relu, 576, (294912)
    #10 tanh, 64, (32768)
    #11 leaky-relu, 512, (262144)
    #12 tanh, 512, (294912)
    #20 crelu, 256, (81920)
    #13 tanh, 512, (262144)
    #14 tanh, 64, (32768)
    #15 relu, 64, (32768)
    #16 relu, 64, (4096)
    #17 relu, 128, (16384)
    #18 logistic, 256, (32768)
    #19 logistic, 256, (32768)
    #22 crelu, 512, (131072)
    #23 elu, 504, (258048)
    #24 tanh, 576, (290304)
    #26 linear, 512, (211744)
    #0 ip, 64, (206092)
    #1 relu, 112, (112)
    #2 relu, 112, (112)
    #3 relu, 112, (112)
    #4 relu, 224, (25088)
    #20 logistic, 512, (417792)
    #5 logistic, 448, (50176)
    #8 linear, 512, (103046)
    #6 logistic, 392, (87808)
    #7 logistic, 441, (98784)
    #9 logistic, 496, (416640)
    #10 leaky-relu, 62, (27342)
    #22 op, 512, (206092)
    #11 leaky-relu, 496, (246016)
    #12 logistic, 512, (253952)
    #19 logistic, 256, (192512)
    #13 tanh, 128, (7936)
    #14 leaky-relu, 64, (31744)
    #18 softplus, 256, (159744)
    #21 linear, 512, (103046)
    #17 softplus, 128, (32768)
    #15 tanh, 64, (4096)
    #16 tanh, 128, (8192)
    Figure 12: Optimal network architectures found with NASBOTon Indoor data.
    どのデータセットでも
    複数の出力層・長いスキップ結合
    を持つ構造がベスト構造

    View Slide

  27. Conclusion
    NASBOT
    n NNの構造探索のためのBOフレームワークNASBOTを提案
    n NASBOTは他の手法よりも良いMLP・CNNの構造を発見
    OTMANN
    n この論文における重要な貢献はOTMANN
    n BO以外の手法への応用も考えられる
    27

    View Slide

  28. Appendix|他の手法で獲得した構造
    EAで獲得したベスト構造(Indoor データセット)
    28
    Figure 12: Optimal network architectures found with NASBOTon Indoor data.
    #0 ip, 64, (232665)
    #1 relu, 128, (128)
    #2 relu, 256, (32768)
    #3 logistic, 512, (131072)
    #14 crelu, 512, (262144)
    #4 logistic, 512, (262144)
    #5 elu, 512, (262144)
    #6 elu, 512, (262144)
    #13 crelu, 256, (196608)
    #7 tanh, 576, (294912)
    #8 tanh, 64, (36864)
    #9 softplus, 64, (4096)
    #10 softplus, 128, (8192)
    #11 logistic, 128, (16384)
    #12 logistic, 256, (32768)
    #15 tanh, 512, (262144)
    #16 tanh, 512, (262144)
    #17 linear, 512, (232665)
    #18 op, 512, (232665)
    #0 ip, 64, (9121)
    #1 leaky-relu, 128, (128)
    #2 leaky-relu, 128, (128)
    #3 leaky-relu, 224, (28672)
    #4 crelu, 126, (16128)
    #5 logistic, 64, (14336)
    #9 linear, 256, (9121)
    #6 logistic, 72, (4608)
    #7 crelu, 126, (9072)
    #8 crelu, 144, (18144)
    #10 op, 256, (9121)
    #0 ip, 64, (12209)
    #1 relu, 144, (144)
    #2 relu, 252, (36288)
    #7 linear, 256, (12209)
    #3 tanh, 72, (18144)
    #6 logistic, 144, (54720)
    #4 tanh, 64, (4608)
    #5 leaky-relu, 128, (8192)
    #8 op, 256, (12209)
    #0 ip, 64, (30336)
    #1 softplus, 128, (128)
    #2 softplus, 128, (128)
    #3 softplus, 256, (32768)
    #4 softplus, 256, (32768)
    #5 crelu, 160, (40960)
    #8 tanh, 64, (20480)
    #6 softplus, 64, (10240)
    #7 softplus, 64, (4096)
    #12 elu, 128, (24576)
    #9 crelu, 64, (4096)
    #10 tanh, 128, (8192)
    #11 tanh, 128, (16384)
    #13 elu, 112, (14336)
    #14 elu, 256, (28672)
    #15 elu, 256, (65536)
    #16 linear, 256, (30336)
    #17 op, 256, (30336)
    Figure 13: Optimal network architectures found with EA on Indoor data.

    View Slide

  29. Appendix|他の手法で獲得した構造
    RANDで獲得したベスト構造(Indoor データセット)
    29
    #0 ip, 64, (7795)
    #1 relu, 128, (128)
    #2 relu, 256, (32768)
    #7 linear, 256, (7795)
    #3 logistic, 64, (16384)
    #4 logistic, 64, (4096)
    #5 crelu, 128, (8192)
    #6 crelu, 128, (16384)
    #8 op, 256, (7795)
    #0 ip, 64, (133952)
    #1 crelu, 128, (128)
    #2 crelu, 256, (32768)
    #3 crelu, 512, (131072)
    #4 crelu, 64, (32768)
    #5 crelu, 64, (4096)
    #6 crelu, 64, (4096)
    #19 tanh, 256, (81920)
    #7 logistic, 64, (4096)
    #8 logistic, 64, (4096)
    #9 logistic, 64, (4096)
    #10 logistic, 128, (8192)
    #11 logistic, 128, (16384)
    #12 logistic, 128, (16384)
    #13 leaky-relu, 128, (16384)
    #14 leaky-relu, 128, (16384)
    #15 leaky-relu, 128, (16384)
    #16 leaky-relu, 256, (32768)
    #17 leaky-relu, 256, (65536)
    #18 leaky-relu, 256, (65536)
    #20 tanh, 256, (65536)
    #21 tanh, 256, (65536)
    #22 tanh, 512, (131072)
    #23 tanh, 512, (262144)
    #24 tanh, 512, (262144)
    #25 linear, 512, (133952)
    #26 op, 512, (133952)
    #0 ip, 64, (68428)
    #1 relu, 128, (128) #2 relu, 128, (128)
    #3 relu, 256, (32768) #4 leaky-relu, 64, (8192)
    #10 linear, 512, (22809)
    #5 leaky-relu, 512, (131072)
    #11 leaky-relu, 64, (20480)
    #13 tanh, 128, (49152)
    #6 tanh, 128, (8192)
    #7 logistic, 512, (262144) #8 softplus, 256, (32768)
    #9 leaky-relu, 64, (32768)
    #18 op, 512, (68428)
    #12 tanh, 128, (8192)
    #14 softplus, 256, (32768)
    #15 softplus, 256, (65536)
    #16 linear, 512, (22809)
    #17 linear, 512, (22809)
    #0 ip, 64, (68006)
    #1 crelu, 128, (128)
    #2 crelu, 256, (32768)
    #15 linear, 512, (22668)
    #3 elu, 512, (131072)
    #4 logistic, 512, (262144)
    #5 leaky-relu, 64, (32768)
    #6 leaky-relu, 64, (32768) #7 leaky-relu, 64, (4096)
    #8 tanh, 144, (9216) #9 tanh, 144, (9216)
    #10 linear, 512, (22668)
    #11 softplus, 288, (41472)
    #12 softplus, 288, (41472)
    #16 op, 512, (68006)
    #13 softplus, 288, (82944)
    #14 linear, 512, (22668)
    Figure 14: Optimal network architectures found with RAND on Indoor data.

    View Slide

  30. Appendix|他の手法で獲得した構造
    TreeBOで獲得したベスト構造(Indoor データセット)
    30
    Figure 14: Optimal network architectures found with RAND on Indoor data.
    #0 ip, 64, (19993)
    #1 relu, 256, (256)
    #2 logistic, 512, (131072)
    #3 elu, 56, (28672)
    #4 elu, 128, (7168)
    #5 tanh, 256, (32768)
    #6 linear, 256, (19993)
    #7 op, 512, (19993)
    #0 ip, 64, (15146)
    #1 leaky-relu, 128, (128)
    #2 leaky-relu, 216, (27648)
    #3 leaky-relu, 256, (55296)
    #4 softplus, 164, (41984)
    #5 tanh, 81, (13284)
    #6 relu, 162, (13122)
    #7 linear, 256, (15146)
    #8 op, 256, (15146)
    #0 ip, 64, (100)
    #1 softplus, 128, (128)
    #2 linear, 256, (100)
    #3 op, 256, (100)
    #0 ip, 64, (632)
    #1 leaky-relu, 56, (56)
    #2 crelu, 112, (6272)
    #3 linear, 256, (632)
    #4 op, 256, (632)
    Figure 15: Optimal network architectures found with TreeBO on Indoor data.

    View Slide