4 papers · 2 filters
A large deviation principle for a class of weighted means of random variables which converges weakly to the Dickman distribution
Rita Giuliano, Claudio Macci
In this paper we consider a wide class of weighted means of random variables which converge weakly to the Dickman distribution. This is inspired by a result proved in [3]. Then we…
Analysis of multivariate symbol statistics in primitive rational models
Massimiliano Goldwurm, Claudio Macci, Marco Vignati +1
We study the asymptotic behaviour of sequences of multivariate random variables representing the number of occurrences of a given set of symbols in a word of length generated a…
Functional Large Deviations for Wide Deep Neural Networks with Gaussian Initialization and Lipschitz Activations
Claudio Macci, Barbara Pacchiarotti, Katerina Papagiannouli +2
We establish a functional large deviation principle for fully connected multi-layer perceptrons with i.i.d. Gaussian weights (LeCun initialization) and general Lipschitz activation…
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…