5 papers
From plans to maps: Nonlocal regularization of optimal transport
Marcello Carioni, Leonardo Del Grande, José A. Iglesias +1
We introduce a nonlocal regularization of optimal transport that bridges Kantorovich and Monge formulations. The regularization penalizes oscillations through an interaction kernel…
Towards sparse optimization over convex loops: Equivalence of Square Root Velocity distance and Wasserstein-Fisher-Rao
Giacomo Cristinelli, José A. Iglesias
The Wasserstein-Fisher-Rao (WFR) distance on has recently been shown to coincide with a classical elastic distance between -immersions in the theory of Riemannian sh…
Vector-Valued Reproducing Kernel Banach Spaces for Neural Networks and Operators
Sven Dummer, Tjeerd Jan Heeringa, José A. Iglesias
Recently, there has been growing interest in characterizing the function spaces underlying neural networks. While shallow and deep scalar-valued neural networks have been linked to…
Nonlocal perimeters and variations: Extremality and decomposability for finite and infinite horizons
Marcello Carioni, Leonardo Del Grande, José A. Iglesias +1
We analyze the extremality and decomposability properties with respect to two types of nonlocal perimeters available in the literature, the Gagliardo perimeter based on the eponymo…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…