4 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…
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…
Quantitative CLTs in Deep Neural Networks
Stefano Favaro, Boris Hanin, Domenico Marinucci +2
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant . Und…