1 citations · 1 across the 2 of their papers we have counts for
4 papers
Approximation in norm and energy with bounded functions for autonomous variational problems
Pierre Bousquet, Carlo Mariconda, Giulia Treu
We study the approximation of finite-energy Sobolev functions by bounded Sobolev functions for integral functionals associated with possibly signed Carathéodory integrands. The app…
Beyond Constant Truncations: The Bounded Sobolev Approximation Gap
Pierre Bousquet, Carlo Mariconda, Giulia Treu
We study the approximation of finite-energy Sobolev functions by bounded Sobolev functions for integral functionals associated with possibly signed Carathéodory integrands. The app…
Born Discrete, Made Smooth: Variational Formulation of Shallow Neural Networks
Matej Benko, Pierre Bousquet, Iwona Chlebicka +1
Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochasti…
Discarding Lavrentiev's Gap in Non-autonomous and Non-Convex Variational Problems
Michał Borowski, Pierre Bousquet, Iwona Chlebicka +2
We establish that the Lavrentiev gap between Sobolev and Lipschitz maps does not occur for a scalar variational problem of the form: \[ \textrm{to minimize} \qquad u \mapsto \int_Ω…