标签切换和随机梯度下降的动力学模型分析

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2023-01-01 DOI:10.3934/krm.2023005

Martin Burger, Alex Rossi

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引用次数: 1

摘要

在本文中，我们提供了一种新的方法来分析标签切换的动力学模型，该模型用于可以在不同能量景观中在梯度流之间随机切换的粒子系统。除了生物学和物理学中的问题，我们还证明了随机梯度下降，机器学习中最流行的技术，在考虑时间连续变量时，可以在这种情况下被理解。我们的分析集中在外部势集合的演化情况下，为此我们提供了关于演化以及平稳问题的分析和数值结果。

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Analysis of kinetic models for label switching and stochastic gradient descent

In this paper we provide a novel approach to the analysis of kinetic models for label switching, which are used for particle systems that can randomly switch between gradient flows in different energy landscapes. Besides problems in biology and physics, we also demonstrate that stochastic gradient descent, the most popular technique in machine learning, can be understood in this setting, when considering a time-continuous variant.Our analysis is focusing on the case of evolution in a collection of external potentials, for which we provide analytical and numerical results about the evolution as well as the stationary problem.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.