9 papers
Variational Bounds for Perceptron Learning from Structured Data
Francesco Camilli, Pierluigi Contucci, Federica Gerace +1
We introduce a variational approach to a finite-temperature continuous-spin perceptron trained on a Gaussian mixture. The model allows for a broad class of concave utilities and lo…
On the phase diagram of the multiscale mean-field spin-glass
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione +1
In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging…
From entropic constraints to reinforced processes: a probabilistic origin of multiscale measures
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
We investigate multiscale Gibbs measures from a variational and probabilistic viewpoint, focusing on the structural asymmetry among conditional entropies that characterizes their c…
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…
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…
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…