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math.AP2026
The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning
Nima Rezaei, Stephan Wojtowytsch
We illustrate in several examples that even neural networks of infinite width (specifically, Barron functions) may encounter substantial obstacles when used as a model class for pr…
math.AP2025
Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs
Oluwatosin Akande, Patrick Dondl, Kanan Gupta +2
We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine le…
math.AP2024
A note on spatially inhomogeneous Cahn-Hilliard energies
Stephan Wojtowytsch
In 2023, Cristoferi, Fonseca and Ganedi proved that Cahn-Hilliard type energies with spatially inhomogeneous potentials converge to the usual (isotropic and homogeneous) perimeter…