[Paper Review] Generative Adversarial Networks

Ian Goodfellow, Jean Pouget-Abadie+6 more|arXiv (Cornell University)|Jun 10, 2014

Generative Adversarial Networks and Image Synthesis4,518 citations

TL;DR

This paper introduces the Generative Adversarial Nets framework, training a generator and a discriminator in a minimax game to model data distributions without Markov chains, and demonstrates qualitative and quantitative results on several datasets.

ABSTRACT

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Motivation & Objective

• Motivate a new generative modeling approach that avoids intractable likelihoods and Markov chains.
• Propose a two-player game where a generator learns to produce data indistinguishable from real samples by fooling a discriminator.
• Establish theoretical conditions under which the generator can recover the true data distribution in the non-parametric limit.
• demonstrate the framework empirically on standard image datasets to assess sample quality and learning dynamics.

Proposed method

• Define a generator G(z; θ_g) mapping noise z to data space and a discriminator D(x; θ_d) predicting data vs. model origin.
• Formulate a minimax objective V(D,G) = E_x~pdata[log D(x)] + E_z~pz[log(1 − D(G(z)))] and train D to maximize while G minimizes.
• Alternate between k steps of updating D and one step of updating G to keep D near its optimum as G changes.
• Use backpropagation to train both networks; no Markov chains or explicit inference required.
• Provide theoretical analysis showing the global optimum occurs when pg = pdata and analyze convergence of the training procedure.

Experimental results

Research questions

• RQ1 Under what conditions can a generative model learn the true data distribution using an adversarial training setup?
• RQ2 How should D and G be updated during training to ensure stable convergence?
• RQ3 What is the theoretical relationship between the minimax objective and divergences between pdata and pg?
• RQ4 How does the GAN framework perform empirically on standard image datasets in terms of sample quality and likelihood estimates?

Key findings

• The global optimum of the game is reached if and only if the generator distribution pg equals the data distribution pdata.
• The fixed-point discriminator D* becomes pdata/(pdata+pg) and, at convergence, the generator can reproduce pdata.
• Empirically, adversarial nets generate samples on MNIST, Toronto Face Database, and CIFAR-10 that are competitive with other deep generative models.
• Parzen-window estimates of test-log-likelihood show competitive performance for adversarial nets on MNIST and TFD (Table 1).
• The model avoids the need for Markov chains during training and sampling, enabling direct backpropagation-based optimization.