Generative adversarial network (GAN) is a minimax game between the generator and discriminator players. While generative models learned by GANs achieve great success in practice, GANs’ approximation, generalization, and optimization properties are still poorly understood. We focus on analyzing these theoretical aspects of GANs, providing both a comprehensive analysis addressing all the three aspects for a simplistic GAN architecture and a more specific analysis addressing only the approximation aspect for general GAN problems.
Generative adversarial network (GAN) is a minimax game between two players: a generator whose goal is to produce real-like samples and a discriminator whose task is to distinguish between the fake samples generated by the generator and the real training samples. While GANs result in state-of-the-art generative models in several benchmark computer vision tasks, their theoretical aspects are still poorly understood. Theoretical studies of GANs aim to address three main questions: 1) Approximation: Which probability distributions can be expressed by a generator function? 2) Generalization: Do the generative models learned by GANs generalize properly to the true distribution of data? 3) Optimization: Are standard gradient methods used to train GANs globally stable? We provide a comprehensive analysis of all the three aspects for a simplistic GAN formulation with linear generator and quadratic discriminator architectures. We also develop a convex analysis framework for specifically analyzing GANs’ approximation properties, which is applicable to a broad class of GAN formulations.
David Tse
Room 264, Packard Building
Electrical Engineering Department
350 Jane Stanford Way
Stanford, CA 94305-9515
dntse@stanford.edu
Helen Niu
Room 310, Packard Building
Electrical Engineering Department
350 Jane Stanford Way
Stanford, CA 94305-9515
Tel: (650) 723-8121
Fax: (650) 723-9251
helen.niu@stanford.edu
