4 papers
Fractal and Regular Geometry of Deep Neural Networks
Simmaco Di Lillo, Domenico Marinucci, Michele Salvi +1
We study the geometric properties of random neural networks by investigating the boundary volumes of their excursion sets for different activation functions, as the depth increases…
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…
Neural reproducing kernel Banach spaces and representer theorems for deep networks
Francesca Bartolucci, Ernesto De Vito, Lorenzo Rosasco +1
Characterizing the function spaces defined by neural networks helps understanding the corresponding learning models and their inductive bias. While in some limits neural networks c…
Spectral complexity of deep neural networks
Simmaco Di Lillo, Domenico Marinucci, Michele Salvi +1
It is well-known that randomly initialized, push-forward, fully-connected neural networks weakly converge to isotropic Gaussian processes, in the limit where the width of all layer…