Seminario

Understanding Neural Networks with Reproducing Kernel Banach Spaces

Seminario periodico del Dipartimento di Matematica
18 maggio 2022
Orario di inizio 
16:30
PovoZero - Via Sommarive 14, Povo (Trento)
Aula Seminari "-1"
Destinatari: 
Comunità universitaria
Comunità studentesca UniTrento
Partecipazione: 
Online
Email per prenotazione: 
Referente: 
Prof. Gian Paolo Leonardi
Contatti: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
Speaker: 
Ernesto De Vito (Università di Genova)

Abstract: Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. The talk is devoted to show how the theory of reproducing kernel Banach spaces can be used to characterize the function spaces corresponding to neural networks. In particular, I will show a representer theorem for a class of reproducing kernel Banach spaces, which includes one hidden layer neural networks of possibly infinite width. Furthermore, I will prove that, for a suitable class of ReLU activation func-tions, the norm in the corresponding reproducing kernel Banach space can be characterized in terms of the inverse Radon transform of a bounded real measure. The talk is based on joint work with F. Bartolucci, L. Rosasco and S. Vigogna.