Functional Space Analysis of Local GAN Convergence

TL;DR

This paper introduces a novel functional space approach to analyze GAN convergence, representing local dynamics as PDEs, enabling pre-training eigenvalue estimation and insights into stabilization techniques.

Contribution

It proposes analyzing GAN training in functional space via PDEs, allowing eigenvalue-based convergence assessment and optimal data augmentation selection.

Findings

Eigenvalues can be estimated before training from dataset.

Insights into stabilization techniques like gradient penalty and data augmentation.

Method enables a priori selection of data augmentation strategies.

Abstract

Recent work demonstrated the benefits of studying continuous-time dynamics governing the GAN training. However, this dynamics is analyzed in the model parameter space, which results in finite-dimensional dynamical systems. We propose a novel perspective where we study the local dynamics of adversarial training in the general functional space and show how it can be represented as a system of partial differential equations. Thus, the convergence properties can be inferred from the eigenvalues of the resulting differential operator. We show that these eigenvalues can be efficiently estimated from the target dataset before training. Our perspective reveals several insights on the practical tricks commonly used to stabilize GANs, such as gradient penalty, data augmentation, and advanced integration schemes. As an immediate practical benefit, we demonstrate how one can a priori select an optimal data augmentation strategy for a particular generation task.