3 papers
math.CO2025
Lower bounds on the minimal dispersion of point sets via cover-free families
MatÄj Trödler, Jan Volec, Jan VybÃral
We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of points from and cover-free families from the extremal set…
cs.LG2025
Nonlocal techniques for the analysis of deep ReLU neural network approximations
Cornelia Schneider, Mario Ullrich, Jan Vybiral
Recently, Daubechies, DeVore, Foucart, Hanin, and Petrova introduced a system of piece-wise linear functions, which can be easily reproduced by artificial neural networks with the…
math.NA2024
A tight lower bound on the minimal dispersion
MatÄj Trödler, Jan Volec, Jan VybÃral
We give a new lower bound for the minimal dispersion of a point set in the unit cube and its inverse function in the high dimension regime. This is done by considering only a very…