BRGANS: STABILIZING GANS' TRAINING PROCESS WITH BROWNIAN MOTION CONTROL

Abstract

The training process of generative adversarial networks (GANs) is unstable and does not converge globally. In this paper, we propose a universal higher-order noise-based controller called Brownian Motion Controller (BMC) that is invariant to GANs' frameworks so that the training process of GANs is stabilized. Specifically, starting with the prototypical case of Dirac-GANs, we design a BMC and propose Dirac-BrGANs, which retrieve exactly the same but reachable optimal equilibrium regardless of GANs' framework. The optimal equilibrium of our Dirac-BrGANs' training system is globally unique and always exists. Furthermore, we give theoretical proof that the training process of Dirac-BrGANs achieves exponential stability almost surely for any arbitrary initial value and derive bounds for the rate of convergence. Then we extend our BMC to normal GANs and propose BrGANs. We provide numerical experiments showing that our BrGANs effectively stabilize GANs' training process and obtain state-of-theart performance in terms of FID and inception score compared to other stabilizing methods.

1. INTRODUCTION

Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) are popular deep learning based generative architecture. Given a multi-dimensional input dataset with unknown P real , GANs can obtain an estimated P model and produce new entries that are as close to indistinguishable as possible from the input entries. For example, GANs can be used to generate images that look real to the human eyes (Wang et al., 2017) . A GAN's architecture consists of two neural networks: a generator and a discriminator. The generator creates new elements that resemble the entries from the input dataset as closely as possible. The discriminator, on the other hand, aims to distinguish the (counterfeit) entries produced by the generator from the original members of the input dataset. The GAN's two networks can be modeled as a minimax problem; they compete against one another while striving to reach a Nash-equilibrium, an optimal solution where the generator can produce fake entries that are, from the point of view of the discriminator, in all respects indistinguishable from real ones. 2017a) is able to push GANs to converge to local Nash equilibrium using a two-time scale update rule (TTUR). Many previous methods (Mescheder et al., 2018; Arjovsky & Bottou, 2017; Nagarajan & Kolter, 2017; Kodali et al., 2017) have investigated the causes of such instabilities and attempted to reduce them by introducing various changes to the GAN's architecture. However, as Mescheder et al. (2018) show in their study, where they analyze the convergence behavior of several GANs models, despite bringing significant improvements, GANs and its variations are still far from achieving stability in the general case. To accomplish this goal, in our work, we design a Brownian Motion Control (BMC) using control theory and propose a universal model, BrGANs, to stabilize GANs' training process. We start with the prototypical Dirac-GAN (Mescheder et al., 2018 ) and analyze its system of training dynamics. 1



Unfortunately, training GANs often suffers from instabilities. Previously, theoretical analysis has been conducted on GAN's training process. Fedus et al. (2018) argue that the traditional view of considering training GANs as minimizing the divergence of real distribution and model distribution is too restrictive and thus leads to instability. Arora et al. (2018) show that GANs training process does not lead generator to the desired distribution. Farnia & Ozdaglar (2020) suggest that current training methods of GANs do not always have Nash equilibrium, and Heusel et al. (

