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1 1,a),3,b) Application of Saliency Extraction Methods to Neural Networks in Shogi Taichi Nakayashiki 1,a) Tomoyuki Kaneko,3,b) Abstract: Computer shogi programs defeated human experts and it has been said that they outperform human experts. On the other hand, although prediction of the best move and winning percentage was successful to a certain degree, the method is not established yet to explain the reason why they are predicted so by computer shogi programs themselves. If computer shogi programs were able to explain the reason to users by itself, they could be used to support human players and be very useful. In this paper, we applied saliency extraction methods which were devised in image classification to neural networks in a computer shogi program. In order to compare variations in its implementation, we compared the difference between visualization methods of the result of saliency extraction methods, which visualize pixels where the neural network paid attention, because some methods can be conceivable. 1. *1 1 Graduate School of Arts and Sciences, The University of Tokyo Interfaculty Initiative in Information Studies, the University of Tokyo 3 JST, PRESTO a) tnakayashiki@g.ecc.u-tokyo.ac.jp b) kaneko@acm.org *1 HUMAN VS COMPUTER (Accessed: ) [1], [] Information Processing Society of Japan - 1 -

2 [1], []. AlphaZero 4 TPU 7 elmo 90 8 [3] AlphaZero 1 TPU TPU 64 [3] AlphaZero elmo AlphaZero [3] [4]AlphaZero [3].3 Saliency Map [5] Smooth- Grad [6].3.1 Saliency Map [5], [6] Saliency Map [5] c C x 0 S c (x 0 ) c 1 x 0 S c (x 0 ) w, b S c (x 0 ) w T c x + b w S c x 0 w = S c x w RGB w w x [5] w Saliency Map 1 back-propagation.3. SmoothGrad Saliency Map [6] [6] SmoothGrad x c S c (x) M c (x) := S c (x)/ x ˆM c (x) := 1 n x0 n M c (x + N (0, σ )) 1 N (0, σ ) 0 σ Saliency Map [6] 3. Saliency Map SmoothGrad 018 Information Processing Society of Japan - -

3 The 3rd Game Programming Workshop 018 1: Table 1 Constant values multiplied by the neural network input [7] 19 Residual Block Pooling [7] Generative Adversarial Networks (GAN) [8] AlphaZero [3] Residual Block [9] Residual Block ( 1 ) 19 ( ) ReLU ( 3 ) 19 ( 4 ) ReLU ( 5 ) 16 Residual Block Global Average Pooling [10] 19 1 Value 1: Apery 703 Apery 61 1 Fig. 1 First player to move. An example where game result is affected by a little difference in the position. The difference between the left position and the right position is the gold piece at 7h and at 7g. The evaluated value by Apery of the left position was 703. The evaluated value by Apery of the right position was 61. Apery used one minute to evaluate these positions. [11] Apery * Apery Apery depth 3. Saliency Map SmoothGrad SmoothGrad SmoothGrad Saliency Map Saliency Map SmoothGrad * Information Processing Society of Japan - 3 -

[5] 9 9 3.3 1 [1] 4. 4.1 Saliency Map SmoothGrad SmoothGrad n = 10, σ = 0.

smoothgrad smoothgrad (abs) : Saliency Map SmoothGrad [1] 1 Saliency Map

The left column is the result of Saliency Map, and the right column is the

0 600 0 400 The upper row is the result of summation of gradients at each pixel.

4 [5] [1] Saliency Map SmoothGrad SmoothGrad n = 10, σ = Saliency Map SmoothGrad saliency map saliency map (abs) smoothgrad smoothgrad (abs) : Saliency Map SmoothGrad [1] 1 Saliency Map SmoothGrad Fig. An example of Saliency Map and SmoothGrad. The left column is the result of Saliency Map, and the right column is the result of SmoothGrad The upper row is the result of summation of gradients at each pixel. The lower row is the result of summation of absolute gradients at each pixel. Saliency Map SmoothGrad SmoothGrad 0. SmoothGrad 018 Information Processing Society of Japan - 4 -

saliency map saliency map (abs) 0 smoothgrad smoothgrad

3 An example of Saliency Map and SmoothGrad.

This progression is supported by the fact that there are a

0 4 400 3 Saliency Map highlighted these pieces and also

Value Saliency Map SmoothGrad : Value Table Fig.

the most important piece pointed out with each method

5 saliency map saliency map (abs) 0 smoothgrad smoothgrad (abs) 3: Saliency Map SmoothGrad [11] 1 Saliency Map Fig. 3 An example of Saliency Map and SmoothGrad. This position was taken from book [11]. First player to move. The expected progression is Pe-d, Pc-d, P*c. This progression is supported by the fact that there are a pawn at e and a rook at h, so these pieces are important Saliency Map highlighted these pieces and also highlighted a rook at 8f. 4. Value Saliency Map SmoothGrad : Value Table Fig. 4 The mean value of the difference obtained by removing the most important piece pointed out with each method Saliency Map 83.6 SmoothGrad : An example position of checkmate with dropping pieces. Value Value 0 floodgate 016 Saliency Map Value Information Processing Society of Japan - 5 -

and the right one is drawn with max value of gradients at each pixel. 3: L Table 3 The L distance for results of each method. L 0.844 0.78 0.

6 5: Fig. 5 A comparison for visualization methods. The left one is drawn with summation of gradients at each pixel, the middle one is drawn with summation of absolute gradients at each pixel, and the right one is drawn with max value of gradients at each pixel. 3: L Table 3 The L distance for results of each method. L [5] RGB SmoothGrad [6] [6] [5] floodgate 9 9 [0, 1] L x x i = (x i min x)/(max x min x) Saliency Map Saliency Map Information Processing Society of Japan - 6 -

1 7 35 6 6 4 35 5. Saliency Map SmoothGrad Value Saliency Map 3 JSPS 16H097 JST [1] Vol. 53, No. 11, pp. 55 53 (01).

, Sifre, L., Ku- 3 4 4 3 6: 1978 11 36 1 16 1 3 7 4 35 Fig.

First row represents the position at 16th move. Second row represents the position at 1th move.

, Lillicrap, T. P., Simonyan, K. and Hassabis, D.

7 Saliency Map SmoothGrad Value Saliency Map 3 JSPS 16H097 JST [1] Vol. 53, No. 11, pp (01). [] GPW016 pp (016). [3] Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Ku : Fig. 6 A game played by Azuma Kazuo and Tanigawa Koji at November, The game ended in 36 plies. First row represents the position at 16th move. Second row represents the position at 1th move. Third row represents the position at 7th move. Fourth row represents the position at 35th move. maran, D., Graepel, T., Lillicrap, T. P., Simonyan, K. and Hassabis, D.: Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm, CoRR, Vol. abs/ (online), available from (017). [4] Vol. 48, No. 11, pp (7). [5] Simonyan, K., Vedaldi, A. and Zisserman, A.: 018 Information Processing Society of Japan - 7 -

8 Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps, CoRR, Vol. abs/ (online), available from (013). [6] Smilkov, D., Thorat, N., Kim, B., Viégas, F. B. and Wattenberg, M.: SmoothGrad: removing noise by adding noise, CoRR, Vol. abs/ (online), available from (017). [7] Wan, S. and Kaneko, T.: Building Evaluation Functions for Chess and Shogi with Uniformity Regularization Networks, IEEE Conference on Computational Intelligence and Games, CIG 018 (018). [8] Goodfellow, I. J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A. C. and Bengio, Y.: Generative Adversarial Networks, CoRR, Vol. abs/ (online), available from (014). [9] He, K., Zhang, X., Ren, S. and Sun, J.: Deep Residual Learning for Image Recognition, 016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 016, Las Vegas, NV, USA, June 7-30, 016, IEEE Computer Society, pp (online), DOI: /CVPR (016). [10] Lin, M., Chen, Q. and Yan, S.: Network In Network, CoRR, Vol. abs/ (online), available from (013). [11] : (). [1] 46 (0). 018 Information Processing Society of Japan - 8 -

Q [4] 2. [3] [5] ϵ- Q Q CO CO [4] Q Q [1] i = X ln n i + C (1) n i i n n i i i n i = n X i i C exploration exploitation [4] Q Q Q ϵ 1 ϵ 3. [3] [5] [4]

Q [4] 2. [3] [5] ϵ- Q Q CO CO [4] Q Q [1] i = X ln n i + C (1) n i i n n i i i n i = n X i i C exploration exploitation [4] Q Q Q ϵ 1 ϵ 3. [3] [5] [4] 1,a) 2,3,b) Q ϵ- 3 4 Q greedy 3 ϵ- 4 ϵ- Comparation of Methods for Choosing Actions in Werewolf Game Agents Tianhe Wang 1,a) Tomoyuki Kaneko 2,3,b) Abstract: Werewolf, also known as Mafia, is a kind of