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Stochastic differential equation approximations of generative adversarial network training and its long-run behavior

Part of: Limit theorems Stochastic analysis

Published online by Cambridge University Press:  02 October 2023

Haoyang Cao Open the ORCID record for Haoyang Cao [Opens in a new window]  and
Xin Guo Open the ORCID record for Xin Guo [Opens in a new window]
Haoyang Cao*
Affiliation:
École Polytechnique
Xin Guo*
Affiliation:
University of California, Berkeley
*
*Postal address: Centre de Mathématiques Appliquées, École Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France. Email: haoyang.cao@polytechnique.edu
**Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA 94720, USA. Email: xinguo@berkeley.edu
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Abstract

This paper analyzes the training process of generative adversarial networks (GANs) via stochastic differential equations (SDEs). It first establishes SDE approximations for the training of GANs under stochastic gradient algorithms, with precise error bound analysis. It then describes the long-run behavior of GAN training via the invariant measures of its SDE approximations under proper conditions. This work builds a theoretical foundation for GAN training and provides analytical tools to study its evolution and stability.

Keywords

Generative adversarial networksstochastic gradient algorithmstochastic differential equation

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60F17: Functional limit theorems; invariance principles 60H10: Stochastic ordinary differential equations

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 2 , June 2024 , pp. 465 - 489
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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