This document provides a friendly introduction to generative adversarial networks (GANs). It explains the general idea of GANs which involve a discriminator and generator playing a game, with the goal of the generator being to generate fake images that cannot be distinguished from real images by the discriminator. The document then walks through building the simplest GAN with a 1-layer neural network discriminator and generator. It explains how to train the GAN by having the discriminator and generator update through backpropagation to minimize their loss functions. Code examples are provided to demonstrate how to implement the GAN.

1. A friendly introduction to
Generative Adversarial Networks
Luis Serrano

2. thispersondoesnotexist.com

3. Python (no packages!)
www.github.com/luisguiserrano/gans

4. General idea

5. Generative Adversarial Networks
DiscriminatorGenerator

6. Generative Adversarial Networks
DiscriminatorGenerator
Nope!

7. Generative Adversarial Networks
DiscriminatorGenerator
Nope!

8. Generative Adversarial Networks
DiscriminatorGenerator
Nope!

9. Generative Adversarial Networks
DiscriminatorGenerator
Nope!

10. Yup!
Generative Adversarial Networks
DiscriminatorGenerator
AHA!! ?

11. DiscriminatorGenerator
Real images
?AHA!!

12. Build the simplest GAN

13. Slanted Land
Slanted people 2x2 screens
1-layer
Neural networks

14. Faces

15. No faces (noise)

16. Tell them apart
Faces
Noise

17. 0.25 0
1 0.75
0.25 1
0.5 0.75
0.75 0.5
0.75 0
1 1
0 0.75
0.75 0
0 0.75
1 0.25
0.25 0.75
1 0
0 1
0.75 0
0.25 0.75
Faces
Noise
10

18. Building the Discriminator

19. Building the discriminator
Faces Noise
1 0
0 1
0.25 1
0.5 0.75
Big
Big
small
small
any
any
any
any

20. Building the discriminator
Faces Noise
1 0
0 1
0.25 1
0.5 0.75
+
+
+
+
--
- -
1*1 + 0*(-1) + 0*(-1) + 1*1
= 2
0.25*1 + 1*(-1) + 0.5*(-1) + 0.75*1
= -0.5Threshold = 1
More than 1: face. Less than 1: no face

21. Discriminator
1 0
0 1
+1
-1
+1
-1
1
-1
Bias
1*1
+0*(-1)
+0*(-1)
+1*1
-1
1σ( ) = 0.73
σ(x) =
1
1 + e−x
1
1
0.73

22. Discriminator
1Bias
0.25*1
+1*(-1)
+0.5*(-1)
+0.75*1
-1
-0.5σ( )
0.25 1
0.5 0.75
= 0.37
+1
-1
+1
-1
-1

23. Building the Generator

24. Building the generator
Faces Noise
1 0
0 1
0.25 1
0.5 0.75
Big
Big
small
small
any
any
any
any

25. Generator
0.85 0.15
0.15 0.85
Bias
1
-1
+1
-1
-1
+1
+1
+1 -1
z
0 1
0.7
+1*0.7 + 1
+1*0.7 + 1
-1*0.7 - 1
-1*0.7 - 1
1.7
-1.7
-1.7
1.7
σ( )
σ( )
σ( )
σ( )
= 0.85
= 0.15
= 0.85
= 0.15

26. The training process:
Error functions

27. Log-loss error function
Label: 1
Prediction: 0.1
Error: large
Label: 1
Prediction: 0.9
Error: small
−ln(0.1) = 2.3
−ln(0.9) = 0.1
Error = -ln(prediction)

28. Log-loss error function
Label: 0
Prediction: 0.1
Error: small
Label: 0
Prediction: 0.9
Error: large −ln(0.1) = 2.3
−ln(0.9) = 0.1
Error = -ln(1 - prediction)

29. Summary
If we want a prediction to be 1:
Log-loss = -ln(prediction)
y = − ln(x)
High error
Low error

30. Summary
If we want a prediction to be 0:
Log-loss = -ln(1-prediction)
y = − ln(1 − x)
High error
Low error

31. The training process:
Backpropagation

32. Backpropagation
Error
Prediction

33. Backpropagation
Error
Prediction
Error plot

34. Training the generator and the discriminator

35. σ
1
Bias
z
σ
σ
σ
σ
1
z
0 1
0.25 1
0.5 0.75
0.68
Want 0
Error = -ln(1-0.68)
Want 1
Error = -ln(0.68)
Generated
image
Bias
Generator Discriminator
−ln (D(G(z))) −ln (1 − D(G(z)))

36. σ
1
Bias
0.44
Error = -ln(0.44)
1 0
0 1
Real image
Want 1
Discriminator
0
z
σ
σ
σ
σBias
1
z
1
Generator
−ln (D(x))

37. Repeat many times…

38. σ
1
Bias
z
σ
σ
σ
σBias
1
z
0 1
Generator Discriminator

39. σ
1
Bias
z
σ
σ
σ
σBias
1
z
0 1
1 0
0 1
Real image
Generator Discriminator

40. After many of these iterations (epochs)

41. σ
1
Bias
z
σ
σ
σ
σBias
1
z
0 1
Generator Discriminator
0.7
0.6
0.8
0
-0.5
2.5
2.8
-3.4
-2.9
-0.3
-0.4
0.4
-0.9

42. z
σ
σ
σ
σBias
1
Generator
z
0 1

43. Math and Code
www.github.com/luisguiserrano/gans

45. Discriminator
1 0
0 1
w1
w2
w4
w3
1
b
Bias
σ
x1
x2
x3
x4
Prediction
D(x) = σ(x1w1+x2w2+x3w3+x4w4 + b)
∂E
∂wi
=
∂E
∂D
⋅
∂D
∂wi
Loss function (error) from images
E = − ln(D(x))
=
−1
D(x)
⋅ σ(
4
∑
j=1
xjwj + b)[1 − σ(
4
∑
j=1
xjwj + b)]xi
=
−1
D(x)
⋅ D(x)[1 − D(x)]xi
Derivatives
∂E
∂b
=
∂E
∂D
⋅
∂D
∂b
= − [1 − D(x)]
= − [1 − D(x)]xi

46. Discriminator
0.25 1
0.5 0.75
w1
w2
w4
w3
1
b
Bias
σ
x1
x2
x3
x4
∂E
∂wi
=
∂E
∂D
⋅
∂D
∂wi
Loss function (error) from noise
E = − ln(1 − D(x))
=
1
1 − D(x)
⋅ σ(
4
∑
j=1
xjwj + b)[1 − σ(
4
∑
j=1
xjwj + b)]xi
=
1
1 − D(x)
⋅ D(x)[1 − D(x)]xi
Derivatives
∂E
∂b
=
∂E
∂D
⋅
∂D
∂b
= D(x)
Prediction
D(x) = σ(x1w1+x2w2+x3w3+x4w4 + b)
= D(x)xi

48. Generator Predictions
G(z) = (G1, G2, G3, G4)
∂E
∂wi
=
∂E
∂D
⋅
∂D
∂G
⋅
∂G
∂z
Loss function (error)
E = − ln(D(G(z))
Derivatives
=
−1
D(G(z))
⋅ σ(
4
∑
j=1
Giwi + b)[1 − σ(
4
∑
j=1
Giwi + b)]G(z) ⋅ σ(wiz + bi)[1 − σ(wiz + bi]z
=
−1
D(G(z))
⋅ D(G(z))[1 − D(G(z))] ⋅ Gi(1 − Gi)z
= (σ(v1z+c1), σ(v2z+c2), σ(v3z+c3), σ(v4z+c4))
D(G(z)) = σ(G1w1 + G2w2 + G3w3 + G4w4 + b)
= − [1 − D(G(z))] ⋅ Gi(1 − Gi)z
Biases
1
z
v1
v2
v4
v3
c1
c2
c4
c3
σ
σ
σ
σ
G1 G2
G3 G4
∂E
∂b
= − [1 − D(G(z))] ⋅ Gi(1 − Gi)

50. Error function plots

52. Acknowledgements

53. With a little help from my friends…
Sahil Juneja
@sjuneja90
Diego Gomez Mosquera
https://medium.com/@diegoalejogm
Alejandro Perdomo
@aperdomoortiz

54. https://medium.com/@diegoalejogm

55. Conclusion

56. https://www.manning.com/books/grokking-machine-learning
Discount code: serranoyt
Grokking Machine
Learning
By Luis G. Serrano

57. Thank you!
@luis_likes_math
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