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1 c ILSVRC LeNet 1. 1 convolutional neural network 1980 Fukushima [1] [2] 80 LeCun (back propagation) LeNet [3, 4] LeNet okatani@vision.is.tohoku.ac.jp (simple cell) (complex cell) 2 [2, 5, 6] 1 2 (a) (b) 4 4 (c) (c) 2(a) (b) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
2 1 (a) (b) (c) 2 3 K 3 H H H H K (a) (b) W W (i, j)(i =0,...,W 1, j =0,...,W 1) (i, j) x ij H H (p, q)(p =0,...,H 1 q =0,...,H 1) h pq 1 H 1 H 1 a ij = x i+p,j+qh pq (1) p=0 q= K K K =1 RGB 3 K =3 K =16 K = 256 W W K W W K 3 K x ijk(k = 0,...,K 1) M =3 h pqkm(m =0,...,M 1) (m =0, 1, 2) K H H K 3 (1) K 1 H 1 H 1 a ijm = x i+p,j+q,kh pqkm + b ijm (2) k=0 p=0 q= Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited
3 b ijm 1 b ijm = b m a ijm y ijm = f(a ijm) (3) (rectified linear) f(x) =max(x, 0) y ijm M W W K M W W M 2.3 (i, j) H H H P ij P ij H 2 1 P ij (max pooling) P ij P ij (local contrast normalization) [7] (fully-connected) (softmax) K k(= 1,...,K) a k y k = exp(a k) K j=1 exp(aj) (4) k (conv1) 2 MNIST( mnist/) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
![1000 1 ILSVRC (ImageNet Large Scale Visual Recognition Challenge) 1,000 1,000 6 2012 ILSVRC [9] 5 3 2 3 128](/docs-images/91/105231394/images/4-1.jpg "200,000 1 20 128/ = = 25 conv1 conv2 7 conv1 3 conv2 2015 4 Copyright c by ORSJ.")
4 6 (convolution) (pooling) (fullyconnected) 5 (pool1) (conv2) (pool2) (conv1 conv2) (pool1 pool2) 2.6 [8] x d {(x n, d n),n=1,...,n} x n y(x n) d n ILSVRC (ImageNet Large Scale Visual Recognition Challenge) 1,000 1, ILSVRC [9] , / = = 25 conv1 conv2 7 conv1 3 conv Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited
5 japanese spaniel 2 1, conv1 96 ( ) conv (5 5 48) (a) (c) conv1 conv2 pool5 (d) (f) fc6 fc7 fc8 lion (g) lion papillon bag-of-words bag-of-features BoF [10] lion [11, 12] BoF BoF BoF BoF Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
![8 6 9 (a) conv1 96 7 96 55 55 (b) conv2 256 48 27 27 (c) pool5 256 6 6 (d) fc6 4096 (e) fc7 4096 (f) fc8 1000 (g) fc8 9 5 3 2012 ILSVRC 5 2012 15 2013 11 2014 7 [13] 1 Google](/docs-images/91/105231394/images/6-0.jpg "GoogLeNet[14] Oxford VGG[7] 20 2014 ILSVRC 4.2 [15] 4.3 Poggio M-theory Mallat wavelet scattering network[16] Arora [17] [18] [19] 3 CC BY BY-SA 2.0 https://www.flickr.")
6 8 6 9 (a) conv (b) conv (c) pool (d) fc (e) fc (f) fc (g) fc ILSVRC [13] 1 Google GoogLeNet[14] Oxford VGG[7] ILSVRC 4.2 [15] 4.3 Poggio M-theory Mallat wavelet scattering network[16] Arora [17] [18] [19] 3 CC BY BY-SA Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited
7 [1] K. Fukushima and S. Miyake, Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position, Pattern Recognition, 15, pp , [2] D. H. Hubel and T. N. Wiesel, Receptive fields, binocular interactions, and functional architecture in the cat s visual cortex, Journal of Physiology, 160, pp , [3] Y. Lecun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard and L. D. Jackel, Backpropagation applied to handwritten zip code recognition, Neural Computation, 1, pp , [4] Y. LeCun, L. Bottou, Y. Bengio and P. Haffner, Gradient-based learning applied to document recognition, In Proceedings of IEEE, 86, pp , [5] D. H. Hubel and T. N. Wiesel, Receptive fields and functional architecture of monkey striate cortex, The Journal of Physiology, 195, pp , [6] P. Berkes and L. Wiskott, Slow feature analysis yields a rich repertoire of compelx cell properties, Journal of Vision, 5, pp , [7] K. Simonyan and A. Zisserman, Very deep convolutional networks for large-scale image recognition, arxiv. [8] G. Hinton, S. Osindero and Y.-W. Teh, A fast learning algorithm for deep belief nets, Neural Computation, 18, pp , [9] A. Krizhevsky, I. Sutskever and G. E. Hinton, ImageNet classification with deep convolutional neural networks, In Proceedings of Neural Information Processing Systems, [10] G. Csurka, C. Dance, L. Fan, J. Willamowski and C. Bray, Visual categorization with bags of keypoints, In Proceedings of European Conference on Conputer Vision, 1, [11] J. J. DiCarlo, D. Zoccolan and N. C. Rust, How does the brain solve visual object recognition? Neuron, 73, pp , [12] N. C. Rust and J. J. DiCarlo, Selectivity and tolerance ( invariance ) both increase as visual information propagates from cortical area v4 to it, The Journal of Neuroscience, 30, pp , [13] O. Russakovsky, J. Deng, H. Su, J. Krause, S. Satheesh, S. Ma, Z. Huang, A. Karpathy, A. Khosla, M. Bernstein, A. C. Berg and L. Fei-Fei, Imagenet large scale visual recognition challenge, 2014, arxiv. [14] C. Szegedy, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke and A. Rabinovich, Going deeper with convolutions, arxiv. [15] D. L. K. Yamins, H. Hong, C. F. Cadieu, E. A. Solomon, D. Seibert and J. J. DiCarlo, Performanceoptimized hierarchical models predict neural responses in higher visual cortex, In Proceedings of the National Academy of Sciences of the United States of America, [16] J. Bruna and S. Mallat, Invariant scattering convolution networks, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, pp , [17] S. Arora, A. Bhaskara, R. Ge and T. Ma, Provable bounds for learning some deep representations, arxiv. [18] M. D. Zeiler and R. Fergus, Visualizing and understanding convolutional networks, In European Conference on Computer Vision, [19] C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow and R. Fergus, Intriguing properties of neural networks, arxiv Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.
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