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Generalization error of GAN from the discriminator’s perspective

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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 stop**, 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.

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Notes

  1. Technically, Fig. 1 curve \(\textcircled {1}\) concerns the \(W_2\) loss, but it is reasonable to believe that training on \(W_1\) or any \(W_p\) loss cannot escape from the curse of dimensionality either.

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Authors and Affiliations

  1. Program in Applied and Computational Mathematics, Princeton University, Princeton, USA

    Hongkang Yang & Weinan E

  2. Department of Mathematics, Princeton University, Princeton, USA

    Weinan E

  3. Bei**g Institute of Big Data Research, Bei**g, China

    Weinan E

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  1. Hongkang Yang
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Yang, H., E, W. Generalization error of GAN from the discriminator’s perspective. Res Math Sci 9, 8 (2022). https://doi.org/10.1007/s40687-021-00306-y

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