Generalization Error of GAN from the Discriminator's Perspective
This work addresses a fundamental issue in machine learning for researchers and practitioners using GANs, providing theoretical insights into generalization and memorization, but it is incremental as it builds on existing GAN frameworks.
The paper tackles the problem of understanding the generalization ability of GANs, particularly their vulnerability to memorization, by analyzing a simplified model and showing that with early stopping, the generalization error measured by the Wasserstein metric avoids the curse of dimensionality, though memorization eventually occurs.
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.