3 papers
math.PR2025
Mixing at the Batchelor Scale for White-In-Time Flows
Robin Chemnitz, Dennis Chemnitz
We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffu…
math.DS2025
A Dynamical Systems Perspective on the Analysis of Neural Networks
Dennis Chemnitz, Maximilian Engel, Christian Kuehn +1
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide var…
cs.LG2024
Characterizing Dynamical Stability of Stochastic Gradient Descent in Overparameterized Learning
Dennis Chemnitz, Maximilian Engel
For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these set…