Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates

TL;DR

This paper introduces measure-conditional discriminators for GANs that incorporate generated distributions into their input, making the discriminator's optimum stationary and more robust, with applications to statistical distance estimation and transfer learning.

Contribution

It presents a novel discriminator modification that ensures stationarity of the optimum, improving robustness and enabling surrogate modeling of statistical distances.

Findings

Discriminator becomes more robust with the proposed measure-conditional design.

The method can handle multiple target distributions effectively.

It serves as a surrogate for statistical distances like KL divergence.

Abstract

We propose a simple but effective modification of the discriminators, namely measure-conditional discriminators, as a plug-and-play module for different GANs. By taking the generated distributions as part of input so that the target optimum for the discriminator is stationary, the proposed discriminator is more robust than the vanilla one. A variant of the measure-conditional discriminator can also handle multiple target distributions, or act as a surrogate model of statistical distances such as KL divergence with applications to transfer learning.