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math.PR2026
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…
math.PR2026
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…
math.PR2026
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…