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2017-07-12 NN論文を肴に酒を飲む会 #3 @ TFUG
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Wasserstein GAN Tfug2017 07-12
1.
Wasserstein GAN 2017-07-12 NN
#3 @ TFUG
2.
Yuta Kashino (
) BakFoo, Inc. CEO Astro Physics /Observational Cosmology Zope / Python Realtime Data Platform for Enterprise / Prototyping
3.
Yuta Kashino (
) arXiv stat.ML, stat.TH, cs.CV, cs.CL, cs.LG math-ph, astro-ph - PyCon2016 - PyCon2017 Edward - 2017 8 TFUG @yutakashino https://www.slideshare.net/yutakashino/pyconjp2016
4.
Wasserstein GAN
5.
… - WGAN: GAN - -
DCGAN - -
6.
Generative Adversarial Networks
7.
GAN 1 - Generative
Adversarial Networks - Ian Goodfelow - Bengio , Theano/Pyleran2 - Google Brain - 2016 NIPIS Tutorial - : The GAN Zoo https://goo.gl/uC8xn2 https://github.com/hindupuravinash/the-gan-zoo
8.
GAN 2 - GAN
… - Meow Generator - HDCGAN, WGAN, LSGAN… https://ajolicoeur.wordpress.com/cats/ https://github.com/hindupuravinash/the-gan-zoo
9.
Vanila GAN - Generator
Discriminator min/max - G D - MLP https://goo.gl/vHUpqG https://goo.gl/7u4zS6
10.
DCGAN - - CNN - G
/D - Pool/ Full Batch Norm, Leaky ReLU Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks https://arxiv.org/abs/1511.06434 https://goo.gl/8EmZgT
11.
GAN - G/D JS - - - - -
12.
Wasserstein GAN
13.
WGAN 1 - /
/ - / - - - - - (
14.
WGAN 2 - - Read-through:
Wasserstein GAN - Wasserstein GAN and the Kantorovich-Rubinstein Duality - https://goo.gl/7ywVwc https://goo.gl/40eCbR
15.
WGAN GAN Descriminator/Critic W 1.
W ( 1, 2) 2. W ( 3) 3. W 4.
16.
WGAN
17.
1. WGAN:
18.
4 - Total Variation(TV) -
Kullback-Leibler (KL) divergence - Jenson-Shannon (JS) divergence - Earth Mover (EM) / Wasserstein (Pr, Pg) = sup A |Pr(A) Pg(A)| KL(PrkPg) = Z x log ✓ Pr(x) Pg(x) ◆ Pr(x) dx JS(Pr, Pg) = 1 2 KL(PrkPm) + 1 2 KL(PgkPm) M = Pr/2 + Pg/2M W(Pr, Pg) = inf 2⇧(Pr,Pg) E(x,y)⇠ ⇥ kx yk ⇤
19.
4 - W - JS -
KL - TV KL(P0kP✓) = KL(P✓kP0) = ( +1 if ✓ 6= 0 , 0 if ✓ = 0 , (P0, P✓) = ( 1 if ✓ 6= 0 , 0 if ✓ = 0 . JS(P0, P✓) = ( log 2 if ✓ 6= 0 , 0 if ✓ = 0 , W(P0, P✓) = |✓| U[0, 1] https://goo.gl/40eCbR
20.
3 1 - 1: W -
2: W W - 1, 2 W GAN Loss
21.
3 2 3: Kantorovich-Rubinstein -
W - W max w2W Ex⇠Pr [fw(x)] Ex⇠P✓ [fw(x)] sup kfkLK Ex⇠Pr [f(x)] Ex⇠P✓ [f(x)] = K · W(Pr, P✓) r✓W(Pr, P✓) = r✓(Ex⇠Pr [fw(x)] Ez⇠Z[fw(g✓(z))]) = Ez⇠Z[r✓fw(g✓(z))]
22.
W/EM 1 - - W(Pr, Pg)
= inf 2⇧(Pr,Pg) E(x,y)⇠ ⇥ kx yk ⇤ scypy.optimize.linprog γ https://goo.gl/7ywVwc https://goo.gl/7ywVwc
23.
W/EM 2 : Kantorovich-Rubinstein - W(Pr,
Pg) = inf 2⇧(Pr,Pg) E(x,y)⇠ ⇥ kx yk ⇤ W(Pr, Pg) = sup kfkL1 Ex⇠Pr [f(x)] Ex⇠Pg [f(x)]
24.
3 2( ) 3:
Kantorovich-Rubinstein - W - W max w2W Ex⇠Pr [fw(x)] Ex⇠P✓ [fw(x)] sup kfkLK Ex⇠Pr [f(x)] Ex⇠P✓ [f(x)] = K · W(Pr, P✓) r✓W(Pr, P✓) = r✓(Ex⇠Pr [fw(x)] Ez⇠Z[fw(g✓(z))]) = Ez⇠Z[r✓fw(g✓(z))]
25.
2. WGAN:
26.
r✓W(Pr, P✓) =
r✓(Ex⇠Pr [fw(x)] Ez⇠Z[fw(g✓(z))]) = Ez⇠Z[r✓fw(g✓(z))]
27.
PyTorch https://goo.gl/unktzn
28.
3. WGAN:
29.
- WGAN
30.
- W DCGAN JS WGAN W
31.
DCGAN WGAN DCGAN
32.
BatchNorm OK BatchNorm WGAN BatchNorm DCGAN
33.
OK MLP WGAN MLP DCGAN
34.
35.
- - - WGAN - GAN
G D Improved Training of Wasserstein GANs https://arxiv.org/abs/1704.00028 Do GANs actually learn the distribution? An empirical study https://arxiv.org/abs/1706.08224
36.
WGAN GAN Descriminator/Critic W 1.
W ( 1, 2) 2. W ( 3) 3. W 4.
37.
Questions kashino@bakfoo.com @yutakashino
38.
BakFoo, Inc. NHK NMAPS:
+
39.
BakFoo, Inc. PyConJP 2015 Python
40.
BakFoo, Inc.
41.
BakFoo, Inc. : SNS
+
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