Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent
This provides a theoretical framework connecting label switching models to stochastic gradient descent, which could benefit researchers in machine learning and physics.
The authors developed a novel approach to analyze kinetic models for label switching in particle systems, showing that stochastic gradient descent can be understood as a time-continuous variant in this framework. They provided analytical and numerical results for evolution in external potentials.
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.