The document discusses generative adversarial networks (GANs). It begins with an introduction to GANs, describing their concept and training process. It then reviews a seminal GAN paper, discussing its mathematical formulation of GAN training as a minimax game and theoretical results showing global optimality can be achieved. The document concludes by outlining the configuration, implementation, and flowchart for a GAN experiment.

1. What is this? Gum? It's GAN.
ISL Lab Seminar
Hansol Kang
: Intuition & Mathematical proof

2. Contents
Introduction
Paper review
Configuration
Experiment
Summary
2018-07-17
2

3. "Generative adversarial nets."
Introduction
• Ian Goodfellow
2018-07-17
3
GAN
Oh, you are GANfather
Nope. I’m GANdalfDCGAN
F-GAN
InfoGAN
Unrolled
GAN
LSGAN
BEGAN
DiscoGAN
CycleGAN
…

4. Introduction
• Concept of GAN
2018-07-17
4
VsD
GF1
F1
F1
F1
FakeR1

5. Introduction
• Concept of GAN
2018-07-17
5
VsD
G
Fake?R1
@
F1

6. Introduction
• Process of Training
2018-07-17
6
D
GNoise
Real(Kurt Cobain)
Fake(Not Kurt Cobain)
…
Latent code
Dataset
*
*
Train D
Train G

7. Introduction
• Process of Training
2018-07-17
7
D
GNoise
Real(Kurt Cobain)
Fake(Not Kurt Cobain)
…
Latent code
Dataset
*
Train D
Train G

8. Introduction
• Process of Training
2018-07-17
8
D
GNoise
Real(Kurt Cobain)
Fake(Not Kurt Cobain)
…
Latent code
Dataset
*
Train D
Train G
Train D
Train G
: Supervised (Real or Fake)
: Unsupervised

9. Introduction
• Final Goal
2018-07-17
9
x
)(xpdata
x
)(xpg
“Generative Adversarial Networks”
Goal Method
GNoise
Latent code
Kurt Cobain

10. Paper review
• Adversarial nets
2018-07-17
10
)))]((1[log()]([log),(maxmin )(~)(~ zGDExDEGDV zpzxpx
DG zdata

Smart D
)))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata
Real case
Fake case
1
)))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata

0
should be 0
should be 0
1
Log(x)
cf.
Stupid D
)))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata
Real case
Fake case
0
)))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata

1
should be negative infinity
should be negative infinity
D perspective,
it should be maximum.

11. Paper review
• Adversarial nets
2018-07-17
11
)))]((1[log()]([log),(maxmin )(~)(~ zGDExDEGDV zpzxpx
DG zdata

Generator
)))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata

1
should be negative infinity
1
Log(x)
cf.
G perspective,
it should be minimum.
Smart G
Stupid G )))]((1[log()]([log )(~)(~ zGDExDE zpzxpx zdata

0
should be 0

12. Paper review
• Adversarial nets
2018-07-17
12
Algorithm 1

13. Paper review
• Theoretical Results
2018-07-17
13
1) Global Optimality of
)()(
)(
)(*
xpxp
xp
xD
gdata
data
G


 
z
z
x
data dzzGDzpdxxDxp )))((1log()())(log()(
datag pp 
),( DGV
        zGDExDEDGV zdata pzpx  1loglog),( ~~
 
x
g
x
data dxxDxpdxxDxp ))(1log()())(log()(
)(zGx 
 
x
gdata dxxDxpxDxp ))(1log()())(log()(
Proposition 1. For G fixed, the optimal discriminator D is
Proof. The training criterion for the discriminator D, given any generator G, is to maximize the quantity
x
)(xpdata

14. Paper review
• Theoretical Results cont.
2018-07-17
14
1) Global Optimality of datag pp 
 
x
gdata dxxDxpxDxp ))(1log()())(log()(
yxDbxpaxp gdata  )(,)(,)(
)1log(log ybya 
ba
a
y


)()(
)(
)(
xpxp
xp
xD
gdata
data


))(1log()())(log()( xDxpxDxp gdata x
dx Maximize
Substitute

15. Paper review
• Theoretical Results cont.
2018-07-17
15
1) Global Optimality of datag pp 
),(max)( DGVGC
D

    ))((1log)(log *
~
*
~ zGDExDE GpzGpx zdata

    )(1log)(log *
~
*
~ xDExDE GpxGpx gdata





















)()(
)(
log
)()(
)(
log ~~
xpxp
xp
E
xpxp
xp
E
gdata
g
px
gdata
data
px gdata

16. Paper review
• Theoretical Results cont.
2018-07-17
16
1) Global Optimality of datag pp 
Theorem 1. The global minimum of the virtual training criterion C(G) is achieved if and only if At that point, C(G) achieves the
value –log4
datag pp 
Proof.
   ))(1log()(log)( *
~
*
~ xDExDEGC GpxGpx gdata













 )
2
1
1log(
2
1
log EE 4log
4
1
log 




















)()(
)(
log
)()(
)(
log4log4log)( ~~
xpxp
xp
E
xpxp
xp
EGC
gdata
g
px
gdata
data
px gdata
 



x gdata
g
g
x gdata
data
data
xpxp
xp
xp
xpxp
xp
xp
)()(
)(
log)(
)()(
)(
log)(2log2log4log

17. Paper review
• Theoretical Results cont.
2018-07-17
17
1) Global Optimality of datag pp 
 



x gdata
g
g
x gdata
data
data
xpxp
xp
xp
xpxp
xp
xp
)()(
)(
log)(
)()(
)(
log)(2log2log4log
 



x gdata
g
g
x gdata
data
data
xpxp
xp
xp
xpxp
xp
xp
2
)()(
)(
log)(
2
)()(
)(
log)(4log





 





 

2
)()(
||)(
2
)()(
||)(4log
xpxp
xpKL
xpxp
xpKL
gdata
g
gdata
data
 )(||)(24log xpxpJSD gdata 4log,0  thenJSDif
Kullback–Leibler divergence

i iQ
iP
iPQPKL
)(
)(
log)()||(
Jensen–Shannon divergence
   MQKLMPKLQPJSD ||
2
1
||
2
1
)||( 
cf.

18. Paper review
• Theoretical Results cont.
2018-07-17
18
2) Convergence of Algorithm
Proposition 2. If G and D have enough capacity, and at each step of Algorithm 1, the discriminator is allowed to reach its optimum given G, and
is updated so as to improve the criterion
gp
then converges togp datap
   ))(1log()(log *
~
*
~ xDExDE GpxGpx gdata


19. Paper review
• Theoretical Results cont.
2018-07-17
19
2) Convergence of Algorithm
Proof.
The subderivatives of a supremum of convex functions include the derivative of the function at the point where the maximum is attained.
is convex in),( DpU g gpNote that
if and is convex in)(sup)( xfxf A  )(xf
x for every , then )(suparg)( xfiffxf A   
This is equivalent to computing a gradient descent update for at optimal D given the corresponding Ggp
g?g=data? ),(sup)( DpUxf gA 
is convex in with a unique global optima as proven in Thm 1, therefore with sufficiently small updates of , converges to ,
concluding proof.
gp),(sup DpU gD gp gp datap
as a functions of as done in the above criterion.),(),( DpUDGV gConsider gp
• 실수 b가 집합 A의 모든 원소들보다 크거나 같을때
즉, a≤b 이면 b를 집합 A의 상계(Upper bound)라 한다. 단, a∈A
• 집합 A의 상계들의 집합을 U라 하면 U의 최소원소를 집합 A의 상한이라 하고 supA라 쓴다.
supremum
cf.
(http://mathnmath.tistory.com/27)
Convex function
)()1()())1(( yftxtfyttxf 
]1,0[:t
cf.
“No line segment lies below the graph at any point.”

20. Paper review
• Experiment
2018-07-17
20

21. Configuration
• Deep Learning Framework
2018-07-17
21
Written in : Python
Interface : PythonNov. 2010
Written in : C++
Interface : Python, MATLAB, C++Dec. 2013
Written in : C, Lua
Interface : C, LuaJul. 2014
Written in : Python
Interface : Python, RMar. 2015
Written in : C++, Python, CUDA
Interface : Python, C/C++, Java, Go, R, JuliaNov. 2015
Written in :
Interface : Python, C++Apr. 2017
Written in : Python, C, CUDA
Interface : PythonOct. 2016
**
DL4J(Java)
Chainer(Python)
MXNet(C++, Python, Julia, MATLAB, JavaScript, Go, R, Scala, Perl)
CNTK(Python, C++),
TF Learn(Python)
TF-Slim(Python)
Etc.
Recommend to choose these framework

22. Configuration
• Language
2018-07-17
22
R
Py
JS
Java
C
Lua Julia SwiftElimination :

23. Configuration
• Development Tool
2018-07-17
23
: Cell based execution
: Intellisense
: Intellisense
: Management of python env.
: GitHub
: AI tool package
: Startup file
: Intellisense
: Cell based execution
: Management of python env.
: Extension program
: Insane extension program
: Intellisense
: Environment setting

24. Configuration
• CM(Configuration Management) Tool
2018-07-17
24
GitHub
Everywhere
Collaborate on code
Version management
Markdown(.md)
Integration with development tools.
★★★
★★★☆
★★★★
Very personal opinion

25. Configuration
• CM(Configuration Management) Tool
2018-07-17
25

26. Configuration
• CM(Configuration Management) Tool
2018-07-17
26
<- Revision history
VS 2017 ->

27. Configuration
• CM(Configuration Management) Tool
2018-07-17
27

28. Experiment
• Flowchart
2018-07-17
28
Data Fake Image
Train D
Train G
i<ep?
end
Y
N

29. Experiment
• Flowchart
2018-07-17
29
Data Fake Image
Train D
Train G
i<ep?
end
Y
N
Discriminator
Data Noise
Generator
Results
*
0
1

30. Experiment
• Flowchart
2018-07-17
30
Data Fake Image
Train D
Train G
i<ep?
end
Y
N
Noise
Generator
Discriminator
Results
*
1
Discriminator
Data Noise
Generator
Results
*
0
1

31. Experiment
• Implementation
2018-07-17
31
Import
Parameter
Data load
Range
Discriminator
Generator
GPU
Optimizer
Train the D
Train the G
(https://github.com/rivergang/PyTorch_GAN)

32. Experiment
• Implementation(Import, Parameter, Data load)
2018-07-17
32

33. Experiment
• Implementation(Range, Discriminator, Generator)
2018-07-17
33

34. Experiment
• Implementation (GPU, Optimizer)
2018-07-17
34

35. Experiment
• Implementation (Train the D)
2018-07-17
35
Images(batch=100)
…
28
28
100
Reshape(28*28*1->784)
7
8
4
7
8
4…
7
8
4
100
1
0
0
Noise(z)
Label
1 0
Real Fake

36. Experiment
• Implementation (Train the D) - cont.
2018-07-17
36
1
0
0
Noise(z)
Label
1 0
Real Fake
G (z)
Generate
D(Fakes)
D(Images)
Discriminate
Loss
Real
Loss
Fake
Loss
Reshape(28*28*1->784)
7
8
4
7
8
4…
7
8
4
100

37. Experiment
• Implementation (Train the D) - cont.
2018-07-17
37
D(Fakes)
D(Images)
Discriminate
Loss
Real
Loss
Fake
Total
Loss
Loss
Update

38. Experiment
• Implementation(Train the G)
2018-07-17
38
1
0
0
Noise(z) Label
1
Real
G (z)
Generate
D(Fakes)
Discriminate
Loss
g
Loss
Update

39. Experiment
• Result#1 (MNIST)
2018-07-17
39
Real
1 10 30
100 200 400

40. Experiment
• Result#2 (FashionMNIST)
2018-07-17
40
Real
1 10 30
100 200 400

41. Experiment
• Result#3 (CIFAR10)
2018-07-17
41
Real
1 10 30
100 200 400

42. Summary
2018-07-17
42
• Generative Adversarial Network is composed the generator model and the discriminator.
• When training the discriminator, the parameters of the generator should be fixed and vice versa.
• The global minimum of the training criterion is achieved if and only if .
• The generative distribution converges to the data distribution.
datag pp  Global optimality
Convergence of algorithm

43. Future work & Reference
2018-07-17
43
• DCGAN (based Conv. layer, optimal training network)
• AE, VAE (encoder & decoder)
• InfoGAN (meaning of latent vector)
• Unrolled GAN (problem of instability)
• LSGAN (Loss)
• Wasserstein GAN (Wasserstein distance)
• BEGAN (equilibrium concept)
• Pix2Pix (mapping)
• Disco GAN (cross domain relation)
• Cycle GAN (cross domain relation)
• f-GAN
• Energy based GAN
• U-Net
• ResNet
• …

44. &

45. Reference
2018-07-17
45
[1] Goodfellow, Ian, et al. "Generative adversarial nets." Advances in neural information processing systems. 2014.
[2] Wang, Su. "Generative Adversarial Networks (GAN) A Gentle Introduction."
[2] 초짜 대학원생의 입장에서 이해하는 Generative Adversarial Networks (https://jaejunyoo.blogspot.com/)
[3] 1시간만에 GAN(Generative Adversarial Network) 완전 정복하기 (https://www.slideshare.net/NaverEngineering/1-gangenerative-
adversarial-network)
[4] 프레임워크 비교(https://deeplearning4j.org/kr/compare-dl4j-torch7-pylearn)
[5] AI 개발에AI 개발에 가장 적합한 5가지 프로그래밍 언어
(http://www.itworld.co.kr/news/109189#csidxf9226c7578dd101b41d03bfedfec05e)
[6] Git는 머꼬? GitHub는 또 머지?(https://www.slideshare.net/ianychoi/git-github-46020592)
[7] svn 능력자를 위한 git 개념 가이드(https://www.slideshare.net/einsub/svn-git-17386752)

46. Appendix
• What is Pythonic?
2018-07-17
46
(http://devdoggo.netlify.com/post/python/python_techniques/)

47. Appendix
• [gæ n] or [gʌn]
2018-07-17
47