Stabilizing GANs' Training with Brownian Motion Controller

TL;DR

This paper introduces a Brownian Motion Controller (BMC) based on control theory to stabilize GAN training, achieving faster convergence and improved performance across different GAN architectures.

Contribution

The paper proposes a novel higher-order noise-based controller, BMC, for stabilizing GAN training, with theoretical guarantees and practical effectiveness demonstrated on StyleGANv2-ada.

Findings

BMC ensures global exponential stability in Dirac-GANs.

BMC accelerates convergence and reduces oscillations in GAN training.

BMC improves FID scores in practical GAN training scenarios.

Abstract

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we examine the stability of GANs from the perspective of control theory and propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC). Starting with the prototypical case of Dirac-GANs, we design a BMC to retrieve precisely the same but reachable optimal equilibrium. We theoretically prove that the training process of DiracGANs-BMC is globally exponential stable and derive bounds on the rate of convergence. Then we extend our BMC to normal GANs and provide implementation instructions on GANs-BMC. Our experiments show that our GANs-BMC effectively stabilizes GANs' training under StyleGANv2-ada frameworks with a faster rate of convergence, a smaller range of oscillation, and better performance in terms of FID score.