Relativistic GAN

In a ground-breaking paper, “The Relativistic Discriminator: A Key Element Missing from Standard GAN” by Alexia Jolicoeur-Martineau, it is argued that standard GAN, as described in Ian Goodfellow’s first paper, is missing a fundamental property: training the generator should not only increase the probability that fake data is real, but also decrease the probability that real data is real.

Relativistic approaches in GANs

Relativistic GANs are not completely new, as the WGAN, the Wasserstein GAN with gradient penalty (WGAN-GP), and the LSGAN already have a relativistic discriminator. These approaches are classified as such because this possibly explains why they are more standard GANs. Fortunately, the standard GANs can also be modified to become relativistic.

Giving this property to the discriminator makes the standard GAN relativistic. As we will show, the discriminator of any GAN loss can be made to be relativistic. Interestingly, IPM-based GANs (WGAN, WGAN-GP, and so on) already have a relativistic discriminator. This explains in part why such approaches are generally much more stable than standard GAN; relativism improves image quality and training stability.

As described in Alexia’s paper, GANs like the WGAN and LSGAN are based on integral probability metrics (IPMS). IPMs are a class of divergences such that: