Generalization error of GAN from the discriminator’s perspective

Hongkang Yang, E. Weinan

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Article number8
JournalResearch in Mathematical Sciences
Issue number1
StatePublished - Mar 2022

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics


  • Curse of dimensionality
  • Early stopping
  • Generalization error
  • Probability distribution
  • Wasserstein metric


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