Generalization Error of GAN from the Discriminator's Perspective

TL;DR

This paper investigates the generalization capabilities of GANs from the discriminator's perspective, showing that early stopping can prevent memorization and improve generalization in high-dimensional settings.

Contribution

It provides a theoretical analysis of GAN generalization, highlighting the role of early stopping and presenting a hardness result for WGAN learning.

Findings

Early stopping helps avoid memorization in GAN training.

Generalization error can escape the curse of dimensionality with early stopping.

WGAN learning is computationally hard in certain settings.

Abstract

The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the memorization phenomenon, the eventual convergence to the empirical distribution. We consider a simplified GAN model with the generator replaced by a density, and analyze how the discriminator contributes to generalization. We show that with early stopping, the generalization error measured by Wasserstein metric escapes from the curse of dimensionality, despite that in the long term, memorization is inevitable. In addition, we present a hardness of learning result for WGAN.