The Bures Metric for Generative Adversarial Networks

TL;DR

This paper introduces a novel diversity matching method using the Bures distance in feature space to mitigate mode collapse in GANs, improving sample diversity and quality without extra hyperparameters.

Contribution

It proposes a simple, hyperparameter-free training approach that uses the Bures distance to match real and fake data diversity in GANs, reducing mode collapse.

Findings

Diversity matching significantly reduces mode collapse.

Improves quality of generated samples.

Method is simple and does not require extra hyperparameters.

Abstract

Generative Adversarial Networks (GANs) are performant generative methods yielding high-quality samples. However, under certain circumstances, the training of GANs can lead to mode collapse or mode dropping, i.e. the generative models not being able to sample from the entire probability distribution. To address this problem, we use the last layer of the discriminator as a feature map to study the distribution of the real and the fake data. During training, we propose to match the real batch diversity to the fake batch diversity by using the Bures distance between covariance matrices in feature space. The computation of the Bures distance can be conveniently done in either feature space or kernel space in terms of the covariance and kernel matrix respectively. We observe that diversity matching reduces mode collapse substantially and has a positive effect on the sample quality. On the practical side, a very simple training procedure, that does not require additional hyperparameter tuning, is proposed and assessed on several datasets.