5 papers · 1 filter
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…
Some vector-valued examples of noncentral moderate deviation results
Claudio Macci, Barbara Pacchiarotti
The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probab…
Large and moderate deviations for Gaussian neural networks
Claudio Macci, Barbara Pacchiarotti, Giovanni Luca Torrisi
We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more…
Asymptotic results for compound sums in separable Banach spaces
Claudio Macci, Barbara Pacchiarotti
We prove large and moderate deviation results for sequences of compound sums, where the summands are i.i.d. random variables taking values in a separable Banach space. We establish…