51 citations · 211 across the 29 of their papers we have counts for
6 papers · 1 filter
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…
Approximation Rates for Metaplectic Neural Networks
Ahmed Abdeljawad, Marcello Carioni, Elena Cordero
In this paper we develop quantitative approximation results for shallow neural networks constructed using a dictionary based on metaplectic operators. First, we extend the concept…
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune +1
Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the o…
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…
Atomic Gradient Flows: Gradient Flows on Sparse Representations
Christian Amend, Marcello Carioni, Konstantinos Zemas
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the pro…
A Dual Certificate Approach to Sparsity in Infinite-Width Shallow Neural Networks
Leonardo Del Grande, Christoph Brune, Marcello Carioni
In this paper, we study total variation (TV)-regularized training of infinite-width shallow ReLU neural networks, formulated as a convex optimization problem over measures on the u…