4 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…
Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows
Alex Massucco, Leonardo Del Grande, Marcello Carioni +2
In recent years, transformer architectures have revolutionized the field of language processing, opening the door to previously unforeseen possibilities. However, from a theoretica…
Exact Sparse Representation Recovery in Signal Demixing and Group BLASSO
Marcello Carioni, Leonardo Del Grande
In this short article we present the theory of sparse representations recovery in convex regularized optimization problems introduced in (Carioni and Del Grande, arXiv:2311.08072,…
A General Theory for Exact Sparse Representation Recovery in Convex Optimization
Marcello Carioni, Leonardo Del Grande
In this paper, we investigate the recovery of the sparse representation of data in general infinite-dimensional optimization problems regularized by convex functionals. We show tha…