5 papers
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Simmaco Di Lillo, Leonardo Maini, Domenico Marinucci
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We…
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…
Large deviation principles and functional limit theorems in the deep limit of wide random neural networks
Simmaco Di Lillo, Claudio Macci, Barbara Pacchiarotti
This paper studies large deviation principles and weak convergence, both at the level of finite-dimensional distributions and in functional form, for a class of continuous, isotrop…
Critical Points of Random Neural Networks
Simmaco Di Lillo
This work investigates the expected number of critical points of random neural networks with different activation functions as the depth increases in the infinite-width limit. Unde…
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…