2 citations · 3 across the 5 of their papers we have counts for
5 papers
Universal Approximation Constraints of Narrow ResNets: The Tunnel Effect
Christian Kuehn, Sara-Viola Kuntz, Tobias Wöhrer
We analyze the universal approximation constraints of narrow Residual Neural Networks (ResNets) both theoretically and numerically. For deep neural networks without input space aug…
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…
The Influence of the Memory Capacity of Neural DDEs on the Universal Approximation Property
Christian Kuehn, Sara-Viola Kuntz
Neural Ordinary Differential Equations (Neural ODEs), which are the continuous-time analog of Residual Neural Networks (ResNets), have gained significant attention in recent years.…
Analysis of the Geometric Structure of Neural Networks and Neural ODEs via Morse Functions
Christian Kuehn, Sara-Viola Kuntz
Besides classical feed-forward neural networks such as multilayer perceptrons, also neural ordinary differential equations (neural ODEs) have gained particular interest in recent y…
Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems
Samuel Jelbart, Christian Kuehn, Sara-Viola Kuntz
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.…