# The Theory of Generative Adversarial Networks

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### Room: Drago-Adeje

In Generative Adversarial Networks (GANs), two machines learn together about a probability distribution P by pursuing competing goals. On the one hand, the generator transforms vectors of random noise into samples that resemble the distribution P, according to the scores of the discriminator. On the other hand, the discriminator distinguishes between real samples drawn from P and fake samples synthesized by the generator. After training ends, the generator estimates an implicit generative model of the distribution P, and the discriminator estimates the energy landscape of the data. Recent efforts have established connections between GAN training and f-divergence minimization, optimal transport, and energy-based learning. However, our theoretical understanding of GANs remains on its infancy, and many fascinating questions cry for an answer. How can we better understand the optimization dynamics of GANs? How can we evaluate the quality of a GAN? How to stabilize training of GANs? How to capture parameter uncertainty in the GAN framework, i.e. what is the analogue to the Bayesian neural network in the GAN setting?In this workshop, we will foster interesting discussions to ask ourselves these and many other questions.Speakers:

- Dougal Sutherland
- Ferenc Huszár
- Emily Denton
- David Pfau
- Olivier Bousquet
- David Duvenaud
- Arthur Szlam
- Fernando Perez-Cruz

09:20- 09:30

**Introduction**

09:30- 10:00

**Two-Sample Tests, Integral Probability Metrics, and GAN Objective**Dougal J. Sutherland, Gatsby unit, UCL

10:00- 10:30

**Connecting GANs, Actor-Critic Methods and Multilevel Optimization**David Pfau, Deepmind

10:30- 11:00

**AdaGAN: Boosting Generative Models**Olivier Bousquet, Google

11:30- 12:00

**Image Superresolution: from mean squared error to variational inference with GANs**Ferenc Huszár, Twitter Cortex

12:00- 12:30

**Generator-Aware Discriminators for Stable GAN Training**David Duvenaud, Toronto

12:30- 13:00

**Semi-Supervised Learning with Context-Conditional Generative Adversarial Networks**Emily Denton, NYU

18:00- 18:30

**Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Play**Arthur Szlam, Facebook

18:30- 19:00

**On Generative Adversarial Networks and Density Estimation**Fernando Perez-Cruz, Stevens Institute of Technology

19:00- 20:00

**Brainstorming and discussion**

# Abstracts

**Two-Sample Tests, Integral Probability Metrics, and GAN Objective**

#### Abstract

One of the major failure patterns of typical GAN models is when the generator collapses to a single point considered highly realistic by the current discriminator, after which the learning problem becomes stuck. To help avoid this issue, we can replace the discriminator with a function that looks at an entire sample set at a time, so that no single point becomes attractive to the generator. Doing so brings us into the well-studied realm of two-sample testing. This talk will discuss several different techniques for two-sample testing and their application in GAN settings, including classifier-based two sample tests which correspond to the traditional GAN, the maximum mean discrepancy, and Wasserstein distances. We will also discuss the use of these types of distances as tools to diagnose convergence of generative models and discover ways in which their samples differ from the reference distribution.

**Connecting GANs, Actor-Critic Methods and Multilevel Optimization**

#### Abstract

Generative Adversarial Networks pose a challenging optimization problem due to the multiple loss functions which must be optimized simultaneously. The GAN game can be framed as a bilevel optimization problem, like many other problems currently of interest to the deep learning community. We show that there is a close connection between GANs and actor-critic methods for continuous control such as deep deterministic policy gradients, and suggest that generic optimization tricks may help stabilize both classes of models. Towards this goal, we introduce unrolled GANs, an algorithm for GAN training which approximates gradients with respect to the optimal discriminator by backpropagating through several steps of SGD.

**AdaGAN: Boosting Generative Models**

#### Abstract

Generative Adversarial Networks (GAN) (Goodfellow et al., 2014) are an effective method for training generative models of complex data such as natural images. However, they are notoriously hard to train and can suffer from the problem of missing modes where the model is not able to produce examples in certain regions of the space. We propose an iterative procedure, called AdaGAN, where at every step we add a new component into a mixture model by running a GAN algorithm on a reweighted sample. This is inspired by boosting algorithms, where many potentially weak individual predictors are greedily aggregated to form a strong composite predictor. We prove that such an incremental procedure leads to convergence to the true distribution in a finite number of steps if each step is optimal, and convergence at an exponential rate otherwise. We also illustrate experimentally that this procedure addresses the problem of missing modes.

**Image Superresolution: from mean squared error to variational inference with GANs**

#### Abstract

Like many other problems, convolutional neural networks have achieved state of the art performance in photo-realistic image superresolution. The main limitation of early methods was that they minimise mean square reconstruction error, which is known to be a poor proxy to perceptual quality. Newer methods, based on generative adversarial networks produce significantly more perceptually accurate results. This talk is about understanding why GANs work so well for image superresolution and what they really do. I will first show how GANs can be used to approximate MAP inference in the SR problem, and then show how a simple stochastic extension of existing methods can be shown to perform variational inference. In the second half of the talk I'm going to talk about a generalisation of this idea: using implicit models in variational inference.

**Generator-Aware Discriminators for Stable GAN Training**

#### Abstract

The alternating optimization of generator and discriminator produces sometimes unfavorable training dynamics. In particular, as the generator changes, the discriminator forgets how to discriminate against previously-seen generators. We examine the idea of training a single universal discriminator, who takes as an extra argument the weights of the generator network. We also explore a similar idea for training variational recognition networks when integrating over the generator weights.

**Semi-Supervised Learning with Context-Conditional Generative Adversarial Networks**

#### Abstract

The main focus of this talk will be on a simple semi-supervised learning approach for images based on in-painting using an adversarial loss. Images with random patches removed are presented to a generator whose task is to fill in the hole, based on the surrounding pixels. The in-painted images are then presented to a discriminator network that judges if they are real (unaltered training images) or not. This task acts as a regularizer for standard supervised training of the discriminator. Using our approach we are able to directly train large VGG-style discriminator networks in a semi-supervised fashion, obtaining competitive results on STL-10 and PASCAL datasets.

**Intrinsic Motivation and Automatic Curricula via Asymmetric Self-Play**

#### Abstract

I will discuss how an agent can learn to manipulate its environment by proposing itself tasks to complete. In tabular, in Markovian environments that are reversible or resetable, with an appropriate choice of reward function, the agent learns to transition from any state to any other as efficiently as possible. I will further discuss our experiments showing that in more complex environments that this unsupervised training can reduce the number of episodes needed to learn extrinsic tasks. Joint work with Sainbayar Sukhbaatar, Ilya Kostrikov, and Rob Fergus.

**On Generative Adversarial Networks and Density Estimation**

#### Abstract

Generative adversarial networks (GANs) propose an alternative approach for density estimation that relies on a discriminative network's output to lead a generativenetwork's density model. They seem to be able to tackle density estimation in high dimensional spaces with limited number of training samples. In this paper, we analyze the accuracy of GANs in estimating the underlying density of the training samples. We focus on both the asymptotically analysis and an empirical study with a state-of-the-art GAN implementation. For the former, we show a limitation in the proof of convergence in (Goodfellow et al., 2014) that might prevent the GAN density estimation from converging to the true density as the number of samples increases. For the latter, we advocate for a two-sample test as the proper test for measuring GANs performance, since it is a simple test would tell us if two set of samples come from the same distribution.