3 papers
math.DS2026
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…
math.DS2025
The conditioned Lyapunov spectrum for random dynamical systems
Matheus M. Castro, Dennis Chemnitz, Hugo Chu +3
We establish the existence of a full spectrum of Lyapunov exponents for memoryless random dynamical systems with absorption. To this end, we crucially embed the process conditioned…
cs.LG2025
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…