Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent

TL;DR

This paper introduces a new analytical framework for kinetic models involving label switching, connecting particle systems and stochastic gradient descent, with insights into their evolution and stationary states.

Contribution

It provides a novel approach to analyze kinetic models for label switching and their relation to stochastic gradient descent in a continuous-time setting.

Findings

Analytical results on the evolution of particle systems with label switching.

Numerical simulations illustrating the stationary states.

Insights into the connection between kinetic models and machine learning algorithms.

Abstract

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.