# Analysis of Kinetic Models for Label Switching and Stochastic Gradient Descent

arXiv: https://arxiv.org/abs/2207.00389 · HTML: https://mlsanity.com/paper/2207.00389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations](https://mlsanity.com/paper/1811.01558/) (2018)
- [Stochastic gradient descent with noise of machine learning type. Part I: Discrete time analysis](https://mlsanity.com/paper/2105.01650/) (2021)
- [Analysis of Stochastic Gradient Descent in Continuous Time](https://mlsanity.com/paper/2004.07177/) (2020)
- [Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation](https://mlsanity.com/paper/1902.00635/) (2019)
- [The convergence of the Stochastic Gradient Descent (SGD) : a self-contained proof](https://mlsanity.com/paper/2103.14350/) (2021)

## Abstract (arXiv)

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.