Functional Space Analysis of Local GAN Convergence

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 adversari...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Khrulkov, Valentin, Babenko, Artem, Oseledets, Ivan
Format: Article
Language:English
Subjects:
Convergence
Data augmentation
Eigenvalues
Operators (mathematics)
Partial differential equations
Training
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422