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Neural Networkを可視化してみる(数学カフェ忘年会 LT資料)

Neural Networkを可視化してみる(数学カフェ忘年会 LT資料)
Christopher Olahさんのブログ
"Neural Networks, Manifolds, and Topology"
http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/
にインスピレーションを受け、Pythonで実装、検証してみたものです。

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Neural Networkを可視化してみる(数学カフェ忘年会 LT資料)

  1. 1. Neural Network 2016/12/11(Sun) LT @kenmatsu4
  2. 2. Twitter
  3. 3. Neural Network 0 0 1 0 x2 x783 x784 x1 x0 z10u10 z1u1 z2u1 z9u9 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 z(l+1) = f(u(l+1) ) softmax y = softmax(z(L) ) … 0.01 … 0.02 0.92 0.03
  4. 4. u(l+1) = W(l+1) z(l) + b(l+1) z(1) = x (l = 1, 2, · · · , L 1, L) x2 x783 x784 x1 x0 z10u10 z1u1 z2u1 z9u9 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 z(l+1) = f(u(l+1) ) Neural NetworkNeural Network (1) = x W, b M 1 N 1 N M 1 N z(l+1) = f(u(l+1) ) y = softmax(z(L) ) softmaxk(z(L) ) = exp(u (L) k ) PK j=1 exp(u (L) j )
  5. 5. f(u) = 1 1 + exp( u) f(u) = tanh(u) tanh ReLu f(u) = max(0, u)
  6. 6. u(l+1) = W(l+1) z(l) + b(l+1) z(l+1) = f(u(l+1) ) z(1) = x x2 x783 x784 x1 x0 z10u10 z1u1 z2u1 z9u9 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 z100 0 u1000 z999u999 u1 z1 u2 z2 z0 Neural Network (1) = x z(l+1) = f(u(l+1) ) bW M 1 N 1 N M 1 N W, b y = softmax(z(L) ) (l = 1, 2, · · · , L 1, L) softmaxk(z(L) ) = exp(u (L) k ) PK j=1 exp(u (L) j ) L(w) = NY n=1 KY k=1 (yk(x, w))
  7. 7. x = ✓ x1 x2 ◆ W(1) = w (1) 11 w (1) 12 w (1) 21 w (1) 22 ! W(2) = w (2) 11 w (2) 12 w (2) 21 w (2) 22 ! b(1) = b (1) 1 b (1) 2 ! b(2) = b (2) 1 b (2) 2 ! https://github.com/matsuken92/Qiita_Contents/blob/master/General/mathcafe_20161212.ipynb
  8. 8. x = ✓ x1 x2 ◆ W(1) = w (1) 11 w (1) 12 w (1) 21 w (1) 22 ! W(2) = w (2) 11 w (2) 12 w (2) 21 w (2) 22 ! b(1) = b (1) 1 b (1) 2 ! b(2) = b (2) 1 b (2) 2 ! ✔ https://github.com/matsuken92/Qiita_Contents/blob/master/General/mathcafe_20161212.ipynb
  9. 9. http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/ https://github.com/matsuken92/Qiita_Contents/blob/master/ General/mathcafe_20161212.ipynb Chainer MNIST https://github.com/matsuken92/Qiita_Contents/blob/master/ chainer-MNIST/chainer-MNIST_forPubs.ipynb

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