生成对抗网络训练的随机微分方程逼近及其长期行为

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2023-10-02 DOI:10.1017/jpr.2023.57

Haoyang Cao, Xin Guo

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引用次数: 0

摘要

摘要本文利用随机微分方程分析了生成式对抗网络(GANs)的训练过程。首先建立了随机梯度算法下GANs训练的SDE近似，并进行了精确的误差界分析。然后，它通过在适当条件下的SDE近似的不变度量来描述GAN训练的长期行为。这项工作为GAN训练奠定了理论基础，并为研究GAN的演化和稳定性提供了分析工具。

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

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.

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.