Generative Adversarial Networks

For the Nantes Machine Learning Meetup
By Hugo Mougard
On July, 3

Paper

Title
Generative Adversarial Nets
Authors
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville and Yoshua Bengio
Conference
NIPS 2014
Citations
872

Overview

  • Concept
  • Implementation example
  • Extensions
Concept

What we'll talk about

Generative networks. Trained on unlabelled data. Useful to build priors (ie word2vec).

“What I cannot create, I do not understand.”
Richard Feynman
Concept

Applied to images

Concept

Applied to text

              Busino game camperate spent odea
              In the bankaway of smarling the
              SingersMay , who kill that imvic
              Keray Pents of the same Reagun D
              Manging include a tudancs shat "
              His Zuith Dudget , the Denmbern
              In during the Uitational questio
              Divos from The ’ noth ronkies of
              She like Monday , of macunsuer S
              Solice Norkedin pring in since
              ThiS record ( 31. ) UBS ) and Ch
              It was not the annuas were plogr
              This will be us , the ect of DAN
              These leaded as most-worsd p2 a0
              The time I paidOa South Cubry i
              Dour Fraps higs it was these del
              This year out howneed allowed lo
              Kaulna Seto consficutes to repor
Concept

How it used to be done

  1. Conceive a generator network (CNN, RNN, …)
  2. Craft a problem-dependent loss function
  3. …
  4. Profit?
Concept

GANs

Generative Adversarial Networks use a network instead of a problem-specific loss.

Concept

GANs

Concept

Training

Minimax: train the two networks by maximizing opposite objectives

  1. maximize the efficiency of the discriminator given the data
  2. maximize the errors of the discriminator on generated data
  3. goto 1.
Concept

Discriminator training

$$ \underset{D}{\max} \underset{\mathcal{x \sim P_\mathcal{r}}}{\mathbb{E}} \left[\log\left(D(\mathcal{x})\right)\right] + \underset{\mathcal{\tilde{x} \sim P_\mathcal{g}}}{\mathbb{E}} \left[\log\left(1 - D(\mathcal{\tilde{x}})\right)\right] $$
Concept

Discriminator training

$$ \underset{D}{\max} \color{red}{ \underset{\mathcal{x \sim P_\mathcal{r}}}{\mathbb{E}} \left[\log\left(D(\mathcal{x})\right)\right] } + \underset{\mathcal{\tilde{x} \sim P_\mathcal{g}}}{\mathbb{E}} \left[\log\left(1 - D(\mathcal{\tilde{x}})\right)\right] $$

Maximize the probability $D(\mathcal{x})$ when the input is real data.

Concept

Discriminator training

$$ \underset{D}{\max} \underset{\mathcal{x \sim P_\mathcal{r}}}{\mathbb{E}} \left[\log\left(D(\mathcal{x})\right)\right] + \color{red}{ \underset{\mathcal{\tilde{x} \sim P_\mathcal{g}}}{\mathbb{E}} \left[\log\left(1 - D(\mathcal{\tilde{x}})\right)\right] } $$

Minimize the probability $D(\mathcal{\tilde{x}})$ ($\max$ of $1 - p$) when the input is generated.

Concept

Generator training

$$ \underset{G}{\min} \underset{\mathcal{x \sim P_\mathcal{g}}}{\mathbb{E}} \left[\log\left(1 - D(\mathcal{\tilde{x}})\right)\right] $$

Maximize the probability $D(\mathcal{\tilde{x}})$ ($\max$ of $1 - p$) when the input is generated.

Concept

Convergence

Final formulation

$$ \underset{G}{\min} \underset{D}{\max} \underset{\mathcal{x \sim P_\mathcal{r}}}{\mathbb{E}} \left[\log\left(D(\mathcal{x})\right)\right] + \underset{\mathcal{x \sim P_\mathcal{g}}}{\mathbb{E}} \left[\log\left(1 - D(\mathcal{\tilde{x}})\right)\right] $$

Overview

  • Concept
  • Implementation example
  • Extensions
Implementation example

DCGAN

Title
Unsupervised representation learning with deep convolutional GANs
Authors
Alec Radford, Luke Metz and Soumith Chintala
Conference
ICLR 2015
Citations
415
Implementation example

DCGAN

Let's have a look at the DCGAN Torch code.

Implementation example

DCGAN

Overview

  • Concept
  • Implementation example
  • Extensions
Extensions

Wasserstein GANs

GANs are extremely hard to train. WGANs fix that.

Extensions

Wasserstein GANs

Change the role of the discriminator:

Before
Output a probability of the data being real
After
Output a scalar representing how much the fake data distribution has to change to match the real one.
Extensions

Wasserstein GANs

Extensions

Adversarially Learned Inference

Add an encoder from input to code to be able to query the generator.

Extensions

Adversarially Learned Inference

Extensions

Adversarially Learned Inference

The discriminator now distinguishes between couples $(x, z)$.

Extensions

Invertible Conditional GANs

Extensions

Invertible Conditional GANs

Extensions

Improved Training of WGANs

Minor tweak on WGANs that allowed very easy training of GANs in multiple domains (text, image, …)

Conclusion

  • Very promising paradigm
  • Results in very good priors
  • Becoming easier and easier to train
  • Not limited to images and toy data anymore

Thank you very much for your attention
😍

Discussion time!