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math.PR2026
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…
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…