14 papers
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…
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…