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論文紹介:Efficient Architecture Search by Network Transformation [Cai et al., AAAI-2018]

論文紹介:Efficient Architecture Search by Network Transformation [Cai et al., AAAI-2018]

2018/05/08の論文紹介ゼミで使用した資料です.

文献情報:
H. Cai, T. Chen, W. Zhang, Y. Yu, and J. Wang, “Efficient Architecture Search by Network Transformation,” in Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), 2018.
https://arxiv.org/abs/1707.04873

S.Shota

May 08, 2018
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  1. 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 白川研究室 修士2年 斉藤 翔汰 2018年5月8日 H. Cai,

    T. Chen, W. Zhang, Y. Yu, and J. Wan Efficient Architecture Search by Network Transformation Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), 2018.
  2. 概要 2 • Net2Net:もとの学習済みNeural Network (NN)の構造を拡大して再学習する手法 • 重み継承(パラメータ共有)付き構造探索 • NAS:NNの構造を出力するRNNを用意し,

    強化学習(REINFORCE)で構造学習する手法 Net2Net + Neural Architecture Search 提案手法を構成する技術 [Chen et al., 2016] [Zoph & Le, 2017]
  3. Table 3: Test error rate (%) comparison with state-of-the-art architectures.

    Model Depth Params C10+ human designed ResNet (He et al. 2016a) ResNet (stochastic depth) (Huang et al. 2017) Wide ResNet (Zagoruyko and Komodakis 2016) Wide ResNet (Zagoruyko and Komodakis 2016) ResNet (pre-activation) (He et al. 2016b) DenseNet (L = 40, k = 12) (Huang et al. 2017) DenseNet-BC (L = 100, k = 12) (Huang et al. 2017) DenseNet-BC (L = 190, k = 40) (Huang et al. 2017) 110 1202 16 28 1001 40 100 190 1.7M 10.2M 11.0M 36.5M 10.2M 1.0M 0.8M 25.6M 6.61 4.91 4.81 4.17 4.62 5.24 4.51 3.46 auto designed Large-Scale Evolution (250 GPUs)(Real et al. 2017) NAS (predicting strides, 800 GPUs) (Zoph and Le 2017) NAS (max pooling, 800 GPUs) (Zoph and Le 2017) NAS (post-processing, 800 GPUs) (Zoph and Le 2017) EAS (plain CNN, 5 GPUs) - 20 39 39 20 5.4M 2.5M 7.1M 37.4M 23.4M 5.40 6.01 4.47 3.65 4.23 action. The result is reported in Figure 5, which shows that the RL based meta-controller can effectively focus on the right search direction, while the random search cannot (left plot), and thus find high performance architectures more ef- ficiently than random search. Explore DenseNet Architecture Space 概要 3 • 5GPUs × 4日で,NAS (800GPUs)やLarge- Scale Evolution(250GPUs, 進化計算) [Real et al., 2017] に匹敵する構造を発見 Model human designed ResNet (He et al. 2016a) ResNet (stochastic depth) (Huang et al. 2017) Wide ResNet (Zagoruyko and Komodakis 20 Wide ResNet (Zagoruyko and Komodakis 20 ResNet (pre-activation) (He et al. 2016b) DenseNet (L = 40, k = 12) (Huang et al. 201 DenseNet-BC (L = 100, k = 12) (Huang et a DenseNet-BC (L = 190, k = 40) (Huang et a auto designed Large-Scale Evolution (250 GPUs)(Real et al NAS (predicting strides, 800 GPUs) (Zoph an NAS (max pooling, 800 GPUs) (Zoph and Le NAS (post-processing, 800 GPUs) (Zoph and EAS (plain CNN, 5 GPUs) Figure 5: Comparison between RL based meta-controller and random search on C10+. Table 4: Test error rate (%) results of exploring DenseNet architecture space with EAS. Model Depth Params C10 C10+ DenseNet (L = 100, k = 24) 100 27.2M 5.83 3.74 DenseNet-BC (L = 250, k = 24) 250 15.3M 5.19 3.62 DenseNet-BC (L = 190, k = 40) 190 25.6M - 3.46 NAS (post-processing) 39 37.4M - 3.65 EAS (DenseNet on C10) 70 8.6M 4.66 - EAS (DenseNet on C10+) 76 10.7M - 3.44 actio the R right plot) ficie Exp We spac the s bottl and plyin achi best havi error 3.46 less In th ward スキップ 結合なし スキップ 結合あり
  4. Introduction 4 • NASやLarge-Scale Evolutionなどは数百の GPUを要する(計算コストの弱点) • 人間がチューニングする際には,成功した 構造をもとにして少しずつ変えていくはず •

    計算コストの制約があるのに,成功した 構造・重みを捨てるのは無駄! 成功した構造と重みを再利用すれば 効率的に構造探索ができるはず
  5. Introduction 5 • ネットワーク変換:レイヤーの挿入, ユニット数の増加,スキップ結合の追加など • この論文ではスキップ結合なしのCNNと DenseNet[Huang et al.,

    2017]を基にした空間を探索 • どのようなネットワーク変換操作を取るべきかを 強化学習で探索 ネットワーク変換+ 強化学習でパラメータ空間を探索 Efficient Architecture Search (EAS)
  6. Related Work and Background 6 1990 ~ 2000 Neuro-Evolution 2010

    ~ 2016 Bayesian Optimization 2016 ~ 強化学習ベースの手法 進化計算で構造や重みを最適化 目的関数をガウス過程によって 推定し,ある基準に従って探索 構造を探索するエージェントを考え, 強化学習で方策を更新 NAS以外にQ-Learningを用いた手法 [Baker et al., 2017] が存在 現在
  7. • NASの枠組み:Recurrent NN + REINFORCE Related Work and Background 7

    Child Network 1 (CNN) … Child Network N (CNN) Meta-Controller (RNN) ①RNNが学習した生成確率P に基づいて構造を複数サンプル Reward 1 (Accuracy) Reward N (Accuracy) … ②NNを学習して 評価値を算出 ③評価値をもとに勾配を計算 ④勾配を使ってControllerの パラメータを更新 m: Child Networkの個数,T:ハイパーパラメータの個数 r✓ J ( ✓ ) ⇡ 1 m m X k= 1 T X t= 1 ( R( T ) k b ) r✓ log P ( a( t ) | a( t 1):1 ; ✓ )
  8. Related Work and Background 8 • Net2Netの枠組み:出力を保つ構造変換 z x y

    a b z y y’ b x a Original Network Transformed Network (Wider) Net2WiderNet Operator ②重みをコピー ③重みを1/2 ①コピー元のユニット をランダム選択 変換後も出力zは変わらない function-preserving transformation ④変換後のネットワークを学習
  9. Related Work and Background 9 • もうひとつのNet2Net:Net2DeeperNet z x y

    a b z y’ b x’ a Original Network Transformed Network (Deeper) Net2DeeperNet Operator ①コピー元の層を ランダム選択 変換後も出力zは変わらない ③変換後のネットワークを学習 y x ②新しい重みを 単位行列で初期化
  10. Architecture Search by Net Transformation 10 • 提案手法の概要: Encoder Network

    Network Transformation Bi-LSTM Bi-LSTM Bi-LSTM Bi-LSTM CONV(32,3,1) POOL(2,2) CONV(64,5,1) POOL(2,2) FC(64) Net2Wider Actor Network ... Layer Embedding Update the network Multiple Actor Networks Network Transformation Layer Embedding Layer Embedding Layer Embedding Layer Embedding Net2Deeper Actor Network Figure 1: Overview of the RL based meta-controller in EAS, which consists of an encoder network for encoding the ar- chitecture and multiple separate actor networks for taking network transformation actions. Encoder Network Net2Wider Actor Probability of Widening the Layer Sigmoid Classifier Sigmoid Classifier Sigmoid Classifier Decision of Widening the Layer Bi-LSTM Bi-LSTM Block Index Layer Index Filter Size Stride Parameters of New Layer if Applicable (CNN as example) <START> Initial State Encoder Network Net2Deeper Actor Bi-LSTM ①層の情報を全結合NNで低次元特徴に変換 ②Bi-directional LSTMで構造全体をEncoding ③出力にSigmoidを適用し,ユニットを増やすか決定 ④Decoder Netを用いて,追加する層の構造を決定
  11. Actor Networks (Net2Wider Actor) 11 • Net2WiderNetをCNNに適用 • つまり,出力チャネル数を大きくしていく •

    記号の定義: • 層目のカーネル • 層目のフィルタの幅・高さ: , • 層目の入力・出力チャネル数: , • Net2Widerで拡張したカーネル: • ただし K l = ( kl w , kl h , fl i , fl o ) <latexit 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  12. Gl( j) = 8 > > < > > :

    j 1  j  fl o random sample from { 1 , . . . , fl o } fl o < j  ˆ fl o <latexit 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  13. Actor Networks (Net2Wider Actor) 13 • 出力を等しくする(function-preserving) ため,出力側の重みに補正を入れる • 層目のカーネルを

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sha1_base64="3YUxI/u2fXd0LNb5BOXPU7nrhTM=">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</latexit> インデックスが重複した数で割る ˆ K l +1 = ( kl +1 w , kl +1 h , ˆ fl +1 i = ˆ fl o , fl +1 o ) <latexit 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sha1_base64="tFOUvvHfoY7BfoY5KfY+uPU2DFg=">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</latexit> ˆ K l +1 [ x , y , j , k ] = K l +1 [ x , y , Gl ( j ), k ] #{ z | Gl ( z ) = Gl ( j )} <latexit 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  14. Actor Networks (Net2Wider Actor) 14 • Net2Wider Actorでは,Bi-directional LSTMの出力に直接sigmoid関数を適用 •

    出力チャネルを増加させるかどうか • 「増加」の場合は Net2WiderNetを実行 • 次の離散レベルへ 出力チャネル数を変更 • 例:32個→64個 Encoder Network Net2Wider Actor Probability of Widening the Layer Sigmoid Classifier Sigmoid Classifier Sigmoid Classifier Decision of Widening the Layer Bi-LSTM Bi-LSTM Figure 2: Net2Wider actor, which uses a shared sigmoid classifier to simultaneously determine whether to widen each layer based on its hidden state given by the encoder network.
  15. Actor Networks (Net2Deeper Actor) 15 • Net2Deeper ActorではRNNを用いて 挿入する層の情報を出力 •

    畳み込み層をどこに挿入するか,フィルタサイズ・ ストライドの大きさをどうするか • グローバル平均プーリングや 全結合層の後に挿入する 場合は全結合層に限定 • 挿入された層の重みは 単位行列で初期化 Block Index Layer Index Filter Size Stride Parameters of New Layer if Applicable (CNN as example) <START> Initial State Encoder Network Net2Deeper Actor Bi-LSTM Figure 3: Net2Deeper actor, which uses a recurrent network to sequentially determine where to insert the new layer and corresponding parameters for the new layer based on the fi- nal hidden state of the encoder network given the input ar- chitecture.
  16. Function-preserving Transformation for DenseNet 16 • スキップ結合を持つネットワーク構造でも function-preservingを実現する方法を考案 • DenseBlockの中にNet2Wider

    or Deeperを適用 Convolutional Networks ng Liu∗ University s.tsinghua.edu.cn Laurens van der Maaten Facebook AI Research [email protected] Q. Weinberger ll University cornell.edu n n o e - r s L t r e s - t - - x0 x1 H1 x2 H2 H3 H4 x3 x4 Figure 1: A 5-layer dense block with a growth rate of k = 4. Each layer takes all preceding feature-maps as input. Convolution Pooling n lo Convolution Pooling Pooling in Convolution n ut P i tion o n lo n lo Figure 2: A deep DenseNet with three dense blocks. The layers between two adjacent blocks are referred to as transition layers and change feature-map sizes via convolution and pooling. ResNets can improve its performance provided the depth is sufficient [41]. FractalNets also achieve competitive results on several datasets using a wide network structure [17]. Instead of drawing representational power from ex- tremely deep or wide architectures, DenseNets exploit the potential of the network through feature reuse, yielding con- densed models that are easy to train and highly parameter- efficient. Concatenating feature-maps learned by different layers increases variation in the input of subsequent layers and improves efficiency. This constitutes a major difference between DenseNets and ResNets. Compared to Inception networks [35, 36], which also concatenate features from dif- ferent layers, DenseNets are simpler and more efficient. An advantage of ResNets is that the gradient can flow di- rectly through the identity function from later layers to the earlier layers. However, the identity function and the output of Hℓ are combined by summation, which may impede the information flow in the network. Dense connectivity. To further improve the information flow between layers we propose a different connectivity pattern: we introduce direct connections from any layer to all subsequent layers. Figure 1 illustrates the layout of the resulting DenseNet schematically. Consequently, the ℓth layer receives the feature-maps of all preceding layers, x0, . . . , xℓ−1, as input: 密な結合を 持つブロック DenseNetの構成図[Huang et al., 2017]より ダウンサンプリング 前層までの出力 を 全て結合して次の層 に入力: Ol = Fl ([O0, O1, . . . , Ol 1 ]) <latexit 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  17. Function-preserving Transformation for DenseNet 17 • 層目にNet2WiderNetが行われたときの 層目( )の入力は次の関数 で決定:

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  18. Function-preserving Transformation for DenseNet 18 • 層目にNet2DeeperNetが行われたときの 層目( )の入力は次となる: •

    追加された層の重み は次で初期化: l <latexit sha1_base64="pOirDeeeiq8P2ig2ydrOUtP4KSo=">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</latexit> <latexit 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sha1_base64="ekjuI+6Z4ceYYi60DGC2RVwaYcg=">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</latexit> <latexit 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sha1_base64="ekjuI+6Z4ceYYi60DGC2RVwaYcg=">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</latexit> フィルタサイズ が3x3の場合 • nはチャネルのインデックス(ランダムに指定) • 選ばれたチャネル以外は全てゼロ行列で初期化 Onew = ˆ F([O0, . . . , Ol]) <latexit sha1_base64="EpQn93M0UPk8+0Vvwv8u+RZNl7Y=">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</latexit> <latexit 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sha1_base64="EpQn93M0UPk8+0Vvwv8u+RZNl7Y=">AAAE1nicnVPPaxNBFH6tUWv80VQvgpfFtFKlhEk92ApKURE9SH+3gU4Iu5tJsmZ/sTtNW5f1JoInbx48KQiK/4MXL568ifZPEI8VvHjwm9m0UmsiOMvuvvfNe9/75s2MFbpOLBnbHhg8lDt85OjQsfzxEydPDRdGTq/EwXpki2U7cIOoYpmxcB1fLEtHuqISRsL0LFesWu2ban61I6LYCfwluRWKqmc2fafh2KYEVCvcmK0l3DNlK/ISX2ykqXHN4C1TJrdTY9zgrhWZdttAEEsnDF4PZDyhPDc1eJTNXawViqw0OT3FLk8bB41yielRpO6YC0YG3hGnOgVk0zp5JMgnCdslk2I8a1QmRiGwKiV0H4hJETxHxwhKKY/8deACUSbQNr5NeGtd1IeveGPNYKOSizdCpkFj7BN7w3bYB/aWfWU/e3IlmkPp2cLfynJFWBt+cnbxxz+zPPwltX5n9dUsqUFTWqsD7aFG1CrsLL/z4NnO4tWFseQCe8m+Qf8Lts3eYwV+57v9al4sPNfst5CTdTGCda+rYBZ8AojyVA8uoQrXMU2oVPVSrVr5nCb2sP9lNGnzAGOG9e6ZxHwDXOocxH0jLbBl8z78Db23nq7g40QpHQu6Ot/bAQtPolHdS7xqLSZWZaCmA9tFZj/GpT8YI1iJRncZpe6GD8UhspXufnyOtlJ9zqt/0XoXcxz/Iua5rpLX90VAL6eO3pOs8yoiy7fgb2rb0qe9vsdp0KiOG+0y5XFfdy+l0dtYmSyVWak8z4oz17s3d4jO0XkaB9cVmqE7NEfLUPKaPtJn+pKr5B7mHuUeZ6GDA92cM7Rv5J7+AtQODtk=</latexit> <latexit sha1_base64="EpQn93M0UPk8+0Vvwv8u+RZNl7Y=">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</latexit> ただし
  19. Experiments and Results 19 • 探索する構造は2種類 • Conv層,プーリング層,全結合層で構成される スキップ結合なしのCNN •

    DenseNetをベースとしたスキップ結合ありのCNN • GeForce1080 GPUを5枚使用して実験 • NAS(800GPUs)と比べると,計算量に対して 強い制約を設けた状況
  20. Experiments and Results (Image Datasets) 20 実験で使用したデータセット 名前 訓練 /

    検証 / テスト / 前処理など クラス数 ドメイン CIFAR-10 (C10) 45,000 / 5,000 / 10,000 / 標準化(平均0,分散1にスケール) データ拡張(C10+と表記), 10 一般画像 分類 SVHN 68,257 / 5,000 / 26,032 / 正規化(255で割る) ベスト構造の学習:68,257 + 531,131 10 表札数字 分類 < Back to Alex Krizhevsky's home page The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million tiny images dataset. They were collected by Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The CIFAR-10 dataset The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly-selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. Here are the classes in the dataset, as well as 10 random images from each: airplane automobile bird cat deer dog frog horse "3BOE$*'"3EBUBTFUT IUUQTXXXDTUPSPOUPFEVdLSJ[DJGBSIUNM < Back to Alex Krizhevsky's home page The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million t Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The CIFAR-10 dataset The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 c 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, e exactly 1000 randomly-selected images from each class. The training random order, but some training batches may contain more images fr training batches contain exactly 5000 images from each class. Here are the classes in the dataset, as well as 10 random images fro airplane automobile bird cat deer dog frog horse ship truck $*'"3BOE$*'"3EBUBTFUT < Back to Alex Krizhevsky's home page The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million tiny images dataset. They were collected by Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The CIFAR-10 dataset The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly-selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. Here are the classes in the dataset, as well as 10 random images from each: airplane automobile bird cat deer dog frog horse ship truck "3BOE$*'"3EBUBTFUT IUUQTXXXDTUPSPOUPFEVdLSJ[DJGBSIUNM < Back to Alex Krizhevsky's home page The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million ti Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The CIFAR-10 dataset The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 c 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, e exactly 1000 randomly-selected images from each class. The training random order, but some training batches may contain more images fr training batches contain exactly 5000 images from each class. Here are the classes in the dataset, as well as 10 random images fro airplane automobile bird cat deer dog frog horse ship truck The classes are completely mutually exclusive. There is no overlap b includes sedans, SUVs, things of that sort. "Truck" includes only big t These are the original, variable-resolution, color house- bounding boxes, as shown in the examples images abov illustration purposes. The bounding box information are directly on the images in the dataset.) Each tar.gz file co together with a digitStruct.mat file, which can be loaded contains a struct called digitStruct with the same length element in digitStruct has the following fields: name wh corresponding image. bbox which is a struct array that c digit bounding box in the image. Eg: digitStruct(300 digit bounding box in the 300th image. Format 2: Cropped Digits: train_32x32.mat, test_32x commercial use only) 5IF4USFFU7JFX)PVTF/VNCFST 47)/ %BUBTFU < Back to Alex Krizhevsky's home page The CIFAR-10 and CIFAR-100 are labeled subsets of the 80 million tiny images dataset. They were collected by Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. The CIFAR-10 dataset The CIFAR-10 dataset consists of 60000 32x32 colour images in 10 classes, with 6000 images per class. There are 50000 training images and 10000 test images. The dataset is divided into five training batches and one test batch, each with 10000 images. The test batch contains exactly 1000 randomly-selected images from each class. The training batches contain the remaining images in random order, but some training batches may contain more images from one class than another. Between them, the training batches contain exactly 5000 images from each class. Here are the classes in the dataset, as well as 10 random images from each: airplane automobile bird cat deer dog frog horse ship truck The classes are completely mutually exclusive. There is no overlap between automobiles and trucks. "Automobile" includes sedans, SUVs, things of that sort. "Truck" includes only big trucks. Neither includes pickup trucks. CIFAR-10*1 SVHN*2 *1:https://www.cs.toronto.edu/~kriz/cifar.html *2:http://ufldl.stanford.edu/housenumbers/
  21. Experiments and Results (Training Details) 21 • 層数・ユニット数:1層・50個 • 埋め込み層の出力:16次元

    • 最適化法:Adam (学習率は小さめ) • サンプル数:10 • 評価値:tan(検証データの精度 × π / 2) • 60%→61%よりも90%→91%のほうが良い評価値 • ベースライン:指数移動平均(係数0.95) Bi-directional LSTM (Encoder Net)
  22. Experiments and Results (Training Details) 22 • 最適化法:Nesterov Momentum •

    初期学習率 ・慣性の強さ:0.02・0.9 • 学習率のスケジュール: • Weight Decay:0.0001 • バッチサイズ:64 • エポック数:20 [Gastaldi 2017]の実装*3より ⌘init <latexit sha1_base64="3hCcBN9fzZoOE9P9BTE6CVZqksE=">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</latexit> <latexit 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sha1_base64="9tWUo8ZgBhxPVGZ42gSrFNSiSTw=">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</latexit> サンプルされたCNN *3:https://github.com/xgastaldi/shake-shake/blob/master/train.lua#L206-L213
  23. Experiments and Results (Explore Plain CNN Architecture Space) 23 •

    フィルタサイズ:1×1,3×3,5×5 • チャネル数:最小16〜最大512 16×(1, 2, 4, 6, 8, 16, 20, 24, 28, 32) • ストライド:1 • 全結合層のユニット数:最小64〜最大1024 64×(1, 2, 4, 6, 8, 10, 12, 14, 16) • 活性化関数:ReLU • バッチ正規化,Dropout(SVHNのみ,rate 0.2) サンプルされたCNNの具体的な設定
  24. Experiments and Results (Explore Plain CNN Architecture Space) 24 •

    入力する構造 (start point): • 学習を2ステップに分割 1. Net2Deeper 5回,Net2Wider 4回を実行 2. 300個サンプリング,ベストな構造を100エポック学習 1. Net2Deeper 5回,Net2Wider 4回を実行 2. 150個サンプリング,ベストな構造を300エポック学習 Step1 Step2 Table 1: Simple start point network. C(n, f, l) denotes a convolutional layer with n filters, filter size f and stride l; P(f, l, MAX) and P(f, l, AVG) denote a max and an average pooling layer with filter size f and stride l respectively; FC(n) denotes a fully- connected layer with n units; SM(n) denotes a softmax layer with n output units. Model Architecture Validation Accuracy (%) C(16, 3, 1), P(2, 2, MAX), C(32, 3, 1), P(2, 2, MAX), C(64, 3, 1), P(2, 2, MAX), C(128, 3, 1), P(4, 4, AVG), FC(256), SM(10) 87.07 we use ReLU and batch normalization for each convolu- tional or fully-connected layer. For SVHN, we add a dropout layer after each convolutional layer (except the first layer) and use a dropout rate of 0.2 (Huang et al. 2017). Start with Small Network We begin the exploration on C10+, using a small network (see Table 1), which achieves 87.07% accuracy in the held-out validation set, as the start point. Different from (Zoph and Le 2017; Baker et al. 2017), EAS is not restricted to start from empty and can flexibly use any discovered architecture as the new start point. As such, to take the advantage of such flexibility and also re- duce the search space for saving the computational resources and time, we divide the whole architecture search process into two stages where we allow the meta-controller to take 5 steps of Net2Deeper action and 4 steps of Net2Wider action in the first stage. After 300 networks are sampled, we take the network which performs best currently and train it with Table 2: Test error rate (%) comparison with CNNs that use convolutional, fully-connected and pooling layers alone. Model C10+ SVHN human designed Maxout (Goodfellow et al. 2013) NIN (Lin, Chen, and Yan 2013) All-CNN (Springenberg et al. 2014) VGGnet (Simonyan and Zisserman 2015) 9.38 8.81 7.25 7.25 2.47 2.35 - - auto designed MetaQNN (Baker et al. 2017) (depth=7) MetaQNN (Baker et al. 2017) (ensemble) EAS (plain CNN, depth=16) EAS (plain CNN, depth=20) 6.92 - 4.89 4.23 - 2.06 1.83 1.73 space, in the second experiment, we use the top architec- tures discovered in the first experiment, as the start points to explore a larger architecture space on C10+ and SVHN. This experiment on each dataset takes around 2 days on 5 GPUs.
  25. Experiments and Results (Explore Plain CNN Architecture Space) 25 •

    ハンドメイドの構造よりも優れた構造 • C10+のベスト構造の重みを初期化& SVHNを40エポック学習させても良い結果に • 5 GPUs × 2日 of the nth entry in [O0, O1, · · · , O l ], we can set ˆ F (using the special case that knew w = knew h = 3 for illustration) as the following ˆ F [ x, y, n ] = 2 4 0 0 0 0 1 0 0 0 0 3 5 , (5) while all other values in ˆ F are set to be 0. Note that n can be chosen randomly from {1, · · · , f0: l +1 o } for each filter. After all filters in the new layer are set, we can form an equivalent random remapping function for all subsequent layers as is done in Eq. (4) and modify their kernels accordingly. Experiments and Results In line with the previous work (Baker et al. 2017; Zoph and Le 2017; Real et al. 2017), we apply the proposed EAS on image benchmark datasets (CIFAR-10 and SVHN) to ex- plore high performance CNN architectures for the image classification task1. Notice that the performances of the final (87.07) (90.18) (91.78) (92.47) (95.11) 100 epochs training 300 epochs training Figure 4: Progress of two stages architecture search on C10+ in the plain CNN architecture space. ional layer with n filters, filter size f and stride l; P(f, l, MAX) h filter size f and stride l respectively; FC(n) denotes a fully- th n output units. Validation Accuracy (%) MAX), C(64, 3, 1), 56), SM(10) 87.07 Table 2: Test error rate (%) comparison with CNNs that use convolutional, fully-connected and pooling layers alone. Model C10+ SVHN human designed Maxout (Goodfellow et al. 2013) NIN (Lin, Chen, and Yan 2013) All-CNN (Springenberg et al. 2014) VGGnet (Simonyan and Zisserman 2015) 9.38 8.81 7.25 7.25 2.47 2.35 - - auto designed MetaQNN (Baker et al. 2017) (depth=7) MetaQNN (Baker et al. 2017) (ensemble) EAS (plain CNN, depth=16) EAS (plain CNN, depth=20) 6.92 - 4.89 4.23 - 2.06 1.83 1.73
  26. Table 3: Test error rate (%) comparison with state-of-the-art architectures.

    Model Depth Params C10+ human designed ResNet (He et al. 2016a) ResNet (stochastic depth) (Huang et al. 2017) Wide ResNet (Zagoruyko and Komodakis 2016) Wide ResNet (Zagoruyko and Komodakis 2016) ResNet (pre-activation) (He et al. 2016b) DenseNet (L = 40, k = 12) (Huang et al. 2017) DenseNet-BC (L = 100, k = 12) (Huang et al. 2017) DenseNet-BC (L = 190, k = 40) (Huang et al. 2017) 110 1202 16 28 1001 40 100 190 1.7M 10.2M 11.0M 36.5M 10.2M 1.0M 0.8M 25.6M 6.61 4.91 4.81 4.17 4.62 5.24 4.51 3.46 auto designed Large-Scale Evolution (250 GPUs)(Real et al. 2017) NAS (predicting strides, 800 GPUs) (Zoph and Le 2017) NAS (max pooling, 800 GPUs) (Zoph and Le 2017) NAS (post-processing, 800 GPUs) (Zoph and Le 2017) EAS (plain CNN, 5 GPUs) - 20 39 39 20 5.4M 2.5M 7.1M 37.4M 23.4M 5.40 6.01 4.47 3.65 4.23 Experiments and Results (Further Explore Larger Architecture Space) 26 • 先程の実験で得られたベスト構造を入力と して再度学習(5GPUs × 2日) Q学習ベースの手法 MetaQNNよりも深い構造を 探索することが可能 スキップ結合付きの 構造に匹敵する性能 ional layer with n filters, filter size f and stride l; P(f, l, MAX) h filter size f and stride l respectively; FC(n) denotes a fully- th n output units. Validation Accuracy (%) MAX), C(64, 3, 1), 56), SM(10) 87.07 Table 2: Test error rate (%) comparison with CNNs that use convolutional, fully-connected and pooling layers alone. Model C10+ SVHN human designed Maxout (Goodfellow et al. 2013) NIN (Lin, Chen, and Yan 2013) All-CNN (Springenberg et al. 2014) VGGnet (Simonyan and Zisserman 2015) 9.38 8.81 7.25 7.25 2.47 2.35 - - auto designed MetaQNN (Baker et al. 2017) (depth=7) MetaQNN (Baker et al. 2017) (ensemble) EAS (plain CNN, depth=16) EAS (plain CNN, depth=20) 6.92 - 4.89 4.23 - 2.06 1.83 1.73 space, in the second experiment, we use the top architec- tures discovered in the first experiment, as the start points to explore a larger architecture space on C10+ and SVHN. This experiment on each dataset takes around 2 days on 5 GPUs. The summarized results of comparing with human- designed and automatically designed architectures that use a similar design scheme (plain CNN), are reported in Table 2, where we can find that the top model designed by EAS on the plain CNN architecture space outperforms all similar models by a large margin. Specifically, comparing to human- designed models, the test error rate drops from 7.25% to
  27. Experiments and Results (Comparison Between RL and Random Search) 27

    • ランダムにネットワーク変換を施す探索方法 も考えられる(Random Search) • Table 1の構造を入力としてNet2Deeper 5回, Net2Wider 4回を実行した結果と比較 • EASのほうが 効率的に探索可能
  28. Experiments and Results (Explore DenseNet Architecture Space) 28 • DenseNet-BCを入力にして構造探索

    • DenseBlock + 特徴マップを縮小 (Bottleneck) + チャネル数を削減 (Compression) • 合計40(=L)層,DenseBlock内のConv層における 出力チャネル数40(=k; Growth rate) • Bottleneck以外の層の出力チャネル数: 40, 44, 48, 52, 56, 60, 64 human designed Wide ResNet (Zagoruyko and Komodakis 2016) ResNet (pre-activation) (He et al. 2016b) DenseNet (L = 40, k = 12) (Huang et al. 2017) DenseNet-BC (L = 100, k = 12) (Huang et al. 2017) DenseNet-BC (L = 190, k = 40) (Huang et al. 2017) 28 1001 40 100 190 36.5M 10.2M 1.0M 0.8M 25.6M 4.17 4.62 5.24 4.51 3.46 auto designed Large-Scale Evolution (250 GPUs)(Real et al. 2017) NAS (predicting strides, 800 GPUs) (Zoph and Le 2017) NAS (max pooling, 800 GPUs) (Zoph and Le 2017) NAS (post-processing, 800 GPUs) (Zoph and Le 2017) EAS (plain CNN, 5 GPUs) - 20 39 39 20 5.4M 2.5M 7.1M 37.4M 23.4M 5.40 6.01 4.47 3.65 4.23 Figure 5: Comparison between RL based meta-controller and random search on C10+. Table 4: Test error rate (%) results of exploring DenseNet architecture space with EAS. Model Depth Params C10 C10+ DenseNet (L = 100, k = 24) 100 27.2M 5.83 3.74 DenseNet-BC (L = 250, k = 24) 250 15.3M 5.19 3.62 DenseNet-BC (L = 190, k = 40) 190 25.6M - 3.46 NAS (post-processing) 39 37.4M - 3.65 EAS (DenseNet on C10) 70 8.6M 4.66 - EAS (DenseNet on C10+) 76 10.7M - 3.44 action. The result is reported in Figure 5, which the RL based meta-controller can effectively fo right search direction, while the random search c plot), and thus find high performance architectur ficiently than random search. Explore DenseNet Architecture Space We also apply EAS to explore the DenseNet a space. We use the DenseNet-BC (L = 40, k the start point. The growth rate, i.e. the width o bottleneck layer is chosen from {40, 44, 48, 52, 5 and the result is reported in Table 4. We find plying EAS to explore the DenseNet architecture achieve a test error rate of 4.66% on C10, bett best result, i.e. 5.19% given by the original Dens having 43.79% less parameters. On C10+, we ac error rate of 3.44%, also outperforming the best 3.46% given by the original DenseNet while havi less parameters. Conclusion In this paper, we presented EAS, a new fram パラメータ数削減& 性能向上
  29. 参考文献 30 • [Chen et al. 2016] T. Chen, I.

    Goodfellow, and J. Shlens, “Net2Net: Accelerating Learning via Knowledge Transfer,” in Proceedings of 4th International Conference on Learning Representations (ICLR’16), 2016. • [Zoph & Le, 2017] B. Zoph and Q. V Le, “Neural Architecture Search with Reinforcement Learning,” in Proceedings of 5th International Conference on Learning Representations (ICLR'17), 2017. • [Real et al., 2017] E. Real, S. Moore, A. Selle, S. Saxena, Y. L. Suematsu, J. Tan, Q. Le, and A. Kurakin, “Large-Scale Evolution of Image Classifiers,” in Proceedings of the 34th International Conference on Machine Learning, vol. PMLR 70, pp. 2902–2911, Mar. 2017. • [Huang et al., 2017] G. Huang, Z. Liu, L. v. d. Maaten, and K. Q. Weinberger, “Densely Connected Convolutional Networks,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 2261–2269. • [Baker et al., 2017] B. Baker, O. Gupta, N. Naik, and R. Raskar, “Designing Neural Network Architectures Using Reinforcement Learning,” in Proceedings of 5th International Conference on Learning Representations (ICLR’17), 2017. • [Gastaldi 2017] X. Gastaldi, “Shake-Shake regularization,” Preprint arXiv 1705.07485v2, May 2017.