3 papers
math.DS2026
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…
math.DS2026
Tracking Finite-Time Lyapunov Exponents to Robustify Neural ODEs
Tobias Wöhrer, Christian Kuehn
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth…
math.AP2024
Global stability for McKean-Vlasov equations on large networks
Christian Kuehn, Tobias Wöhrer
We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide…