3 papers
math.PR2026
Stochastic Flows with Strong Shear - Part I: Strong Completeness and Set Attractors
Dennis Chemnitz, Maximilian Engel, Michael Scheutzow
We study strong completeness and the existence of a set attractor for the stochastic flows induced by a class of two-dimensional stochastic differential equations resembling a plan…
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…