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Wasserstein GAN Tfug2017 07-12
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Wasserstein GAN 2017-07-12 NN #3 @ TFUG
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Transcript of Wasserstein GAN Tfug2017 07-12
Wasserstein GAN2017-07-12 NN #3 @ TFUG
Yuta Kashino ( )
BakFoo, Inc. CEO Astro Physics /Observational Cosmology Zope / Python Realtime Data Platform for Enterprise / Prototyping
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
Wasserstein GAN
…- WGAN: GAN
-
- DCGAN
-
-
Generative Adversarial Networks
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
GAN 2- GAN …
- Meow Generator - HDCGAN, WGAN, LSGAN…
https://ajolicoeur.wordpress.com/cats/
https://github.com/hindupuravinash/the-gan-zoo
Vanila GAN- Generator Discriminator min/max
- G D
- MLPhttps://goo.gl/vHUpqG https://goo.gl/7u4zS6
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
GAN- G/D JS
-
-
-
-
-
Wasserstein GAN
WGAN 1- / /
- /
-
-
-
-
- (
WGAN 2-
- Read-through: Wasserstein GAN - Wasserstein GAN and the Kantorovich-Rubinstein Duality
- https://goo.gl/7ywVwc
https://goo.gl/40eCbR
WGANGAN Descriminator/Critic W
1. W
( 1, 2)
2. W
( 3)
3. W
4.
WGAN
1. WGAN:
4- Total Variation(TV)
- Kullback-Leibler (KL) divergence
- Jenson-Shannon (JS) divergence
- Earth Mover (EM) / Wasserstein
�(Pr, Pg) = supA
|Pr(A)� Pg(A)|
KL(P
r
kPg
) =
Z
x
log
✓P
r
(x)
P
g
(x)
◆P
r
(x) dx
JS(Pr, Pg) =1
2KL(PrkPm) +
1
2KL(PgkPm)
M = Pr/2 + Pg/2M
W (Pr
, P
g
) = inf�2⇧(Pr,Pg)
E(x,y)⇠�
⇥kx� yk
⇤
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
3 1- 1:
W
- 2:
W
W
- 1, 2
W GAN Loss
3 23: Kantorovich-Rubinstein
- W
- W
max
w2WEx⇠Pr [fw(x)]� E
x⇠P✓ [fw(x)] sup
kfkLK
Ex⇠Pr [f(x)]� E
x⇠P✓ [f(x)]
= K ·W (P
r
, P
✓
)
r✓
W (Pr
, P
✓
) = r✓
(Ex⇠Pr [fw(x)]� E
z⇠Z
[fw
(g✓
(z))])
= �Ez⇠Z
[r✓
f
w
(g✓
(z))]
W/EM 1
-
-
W (Pr
, P
g
) = inf�2⇧(Pr,Pg)
E(x,y)⇠�
⇥kx� yk
⇤
scypy.optimize.linprog
γ
https://goo.gl/7ywVwc
https://goo.gl/7ywVwc
W/EM 2: Kantorovich-Rubinstein
-
W (Pr
, P
g
) = inf�2⇧(Pr,Pg)
E(x,y)⇠�
⇥kx� yk
⇤
W (Pr
, P
g
) = supkfkL1
Ex⇠Pr [f(x)]� E
x⇠Pg [f(x)]
3 2( )3: Kantorovich-Rubinstein
- W
- W
max
w2WEx⇠Pr [fw(x)]� E
x⇠P✓ [fw(x)] sup
kfkLK
Ex⇠Pr [f(x)]� E
x⇠P✓ [f(x)]
= K ·W (P
r
, P
✓
)
r✓
W (Pr
, P
✓
) = r✓
(Ex⇠Pr [fw(x)]� E
z⇠Z
[fw
(g✓
(z))])
= �Ez⇠Z
[r✓
f
w
(g✓
(z))]
2. WGAN:
r✓
W (Pr
, P
✓
) = r✓
(Ex⇠Pr [fw(x)]� E
z⇠Z
[fw
(g✓
(z))])
= �Ez⇠Z
[r✓
f
w
(g✓
(z))]
PyTorchhttps://goo.gl/unktzn
3. WGAN:
- WGAN
- W
DCGAN JS
WGAN W
DCGAN
WGAN
DCGAN
BatchNorm OK
BatchNorm WGAN
BatchNorm DCGAN
OK
MLP WGAN
MLP DCGAN
-
-
- 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
WGAN
GAN Descriminator/Critic W
1. W
( 1, 2)
2. W
( 3)
3. W
4.
BakFoo, Inc.NHK NMAPS: +
BakFoo, Inc.PyConJP 2015
Python
BakFoo, Inc.: SNS +
