![Generative Adversarial Networks
Let D denote the discriminator’s predicted probability of being data
Discriminator’s cost function: cross-entropy loss for task of classifying
real vs. fake images
JD = Ex∼D[− log D(x)] + Ez[− log(1 − D(G(z)))]
One possible cost function for the generator: the opposite of the
discriminator’s
JG = −JD
= const + Ez[log(1 − D(G(z)))]
This is called the minimax formulation, since the generator and
discriminator are playing a zero-sum game against each other:
max
G
min
D
JD
Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 10 / 25](https://image.slidesharecdn.com/lec19-231020020453-c8438837/85/lec19-pdf-10-320.jpg)
![A Better Cost Function
We introduced the minimax cost function for the generator:
JG = Ez[log(1 − D(G(z)))]
One problem with this is saturation.
Recall from our lecture on classification: when the prediction is really
wrong,
“Logistic + squared error” gets a weak gradient signal
“Logistic + cross-entropy” gets a strong gradient signal
Here, if the generated sample is really bad, the discriminator’s
prediction is close to 0, and the generator’s cost is flat.
Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 14 / 25](https://image.slidesharecdn.com/lec19-231020020453-c8438837/85/lec19-pdf-14-320.jpg)
![A Better Cost Function
Original minimax cost:
JG = Ez[log(1 − D(G(z)))]
Modified generator cost:
JG = Ez[− log D(G(z))]
This fixes the saturation problem.
Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 15 / 25](https://image.slidesharecdn.com/lec19-231020020453-c8438837/85/lec19-pdf-15-320.jpg)
lec19.pdf
- 1. CSC321 Lecture 19: Generative Adversarial Networks Roger Grosse Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 1 / 25
- 2. Overview In generative modeling, we’d like to train a network that models a distribution, such as a distribution over images. One way to judge the quality of the model is to sample from it. This field has seen rapid progress: 2009 2015 2018 Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 2 / 25
- 3. Overview Four modern approaches to generative modeling: Generative adversarial networks (today) Reversible architectures (next lecture) Autoregressive models (Lecture 7, and next lecture) Variational autoencoders (CSC412) All four approaches have different pros and cons. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 3 / 25
- 4. Implicit Generative Models Implicit generative models implicitly define a probability distribution Start by sampling the code vector z from a fixed, simple distribution (e.g. spherical Gaussian) The generator network computes a differentiable function G mapping z to an x in data space Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 4 / 25
- 5. Implicit Generative Models A 1-dimensional example: Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 5 / 25
- 6. Implicit Generative Models https://blog.openai.com/generative-models/ Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 6 / 25
- 7. Implicit Generative Models This sort of architecture sounded preposterous to many of us, but amazingly, it works. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 7 / 25
- 8. Generative Adversarial Networks The advantage of implicit generative models: if you have some criterion for evaluating the quality of samples, then you can compute its gradient with respect to the network parameters, and update the network’s parameters to make the sample a little better The idea behind Generative Adversarial Networks (GANs): train two different networks The generator network tries to produce realistic-looking samples The discriminator network tries to figure out whether an image came from the training set or the generator network The generator network tries to fool the discriminator network Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 8 / 25
- 9. Generative Adversarial Networks Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 9 / 25
- 10. Generative Adversarial Networks Let D denote the discriminator’s predicted probability of being data Discriminator’s cost function: cross-entropy loss for task of classifying real vs. fake images JD = Ex∼D[− log D(x)] + Ez[− log(1 − D(G(z)))] One possible cost function for the generator: the opposite of the discriminator’s JG = −JD = const + Ez[log(1 − D(G(z)))] This is called the minimax formulation, since the generator and discriminator are playing a zero-sum game against each other: max G min D JD Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 10 / 25
- 11. Generative Adversarial Networks Updating the discriminator: Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 11 / 25
- 12. Generative Adversarial Networks Updating the generator: Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 12 / 25
- 13. Generative Adversarial Networks Alternating training of the generator and discriminator: Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 13 / 25
- 14. A Better Cost Function We introduced the minimax cost function for the generator: JG = Ez[log(1 − D(G(z)))] One problem with this is saturation. Recall from our lecture on classification: when the prediction is really wrong, “Logistic + squared error” gets a weak gradient signal “Logistic + cross-entropy” gets a strong gradient signal Here, if the generated sample is really bad, the discriminator’s prediction is close to 0, and the generator’s cost is flat. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 14 / 25
- 15. A Better Cost Function Original minimax cost: JG = Ez[log(1 − D(G(z)))] Modified generator cost: JG = Ez[− log D(G(z))] This fixes the saturation problem. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 15 / 25
- 16. Generative Adversarial Networks Since GANs were introduced in 2014, there have been hundreds of papers introducing various architectures and training methods. Most modern architectures are based on the Deep Convolutional GAN (DC-GAN), where the generator and discriminator are both conv nets. GAN Zoo: https://github.com/hindupuravinash/the-gan-zoo Good source of horrible puns (VEEGAN, Checkhov GAN, etc.) Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 16 / 25
- 17. GAN Samples Celebrities: Karras et al., 2017. Progressive growing of GANs for improved quality, stability, and variation Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 17 / 25
- 18. GAN Samples Bedrooms: Karras et al., 2017. Progressive growing of GANs for improved quality, stability, and variation Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 18 / 25
- 19. GAN Samples Objects: Karras et al., 2017. Progressive growing of GANs for improved quality, stability, and variation Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 19 / 25
- 20. GAN Samples GANs revolutionized generative modeling by producing crisp, high-resolution images. The catch: we don’t know how well they’re modeling the distribution. Can’t measure the log-likelihood they assign to held-out data. Could they be memorizing training examples? (E.g., maybe they sometimes produce photos of real celebrities?) We have no way to tell if they are dropping important modes from the distribution. See Wu et al., “On the quantitative analysis of decoder-based generative models” for partial answers to these questions. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 20 / 25
- 21. CycleGAN Style transfer problem: change the style of an image while preserving the content. Data: Two unrelated collections of images, one for each style Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 21 / 25
- 22. CycleGAN If we had paired data (same content in both styles), this would be a supervised learning problem. But this is hard to find. The CycleGAN architecture learns to do it from unpaired data. Train two different generator nets to go from style 1 to style 2, and vice versa. Make sure the generated samples of style 2 are indistinguishable from real images by a discriminator net. Make sure the generators are cycle-consistent: mapping from style 1 to style 2 and back again should give you almost the original image. Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 22 / 25
- 23. CycleGAN Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 23 / 25
- 24. CycleGAN Style transfer between aerial photos and maps: Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 24 / 25
- 25. CycleGAN Style transfer between road scenes and semantic segmentations (labels of every pixel in an image by object category): Roger Grosse CSC321 Lecture 19: Generative Adversarial Networks 25 / 25