23 citations · 89 across the 18 of their papers we have counts for
6 papers · 1 filter
From entropic constraints to reinforced processes: a probabilistic origin of multiscale measures
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
We study multiscale measures, defined by a hierarchy of partial Gibbs equilibria, from variational and probabilistic perspectives. We first show that they are the unique solutions…
Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation
Jean Barbier, Francesco Camilli, Minh-Toan Nguyen +2
For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models cap…
Information-theoretic reduction of deep neural networks to linear models in the overparametrized proportional regime
Francesco Camilli, Daria Tieplova, Eleonora Bergamin +1
We rigorously analyse fully-trained neural networks of arbitrary depth in the Bayesian optimal setting in the so-called proportional scaling regime where the number of training sam…
Statistical mechanics of extensive-width Bayesian neural networks near interpolation
Jean Barbier, Francesco Camilli, Minh-Toan Nguyen +2
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features m…
Limit theorems for the non-convex multispecies Curie-Weiss model
Francesco Camilli, Emanuele Mingione, Godwin Osabutey
We study the thermodynamic properties of the generalized non-convex multispecies Curie-Weiss model, where interactions among different types of particles (forming the species) are…
Optimal generalisation and learning transition in extensive-width shallow neural networks near interpolation
Jean Barbier, Francesco Camilli, Minh-Toan Nguyen +2
We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width and input dimension are large and proportional. We prov…