5 papers · 1 filter
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…
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…
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…
The solution of the deep Boltzmann machine on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational…
The multi-species mean-field spin-glass on the Nishimori line
Diego Alberici, Francesco Camilli, Pierluigi Contucci +1
In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions…