30 citations · 239 across the 25 of their papers we have counts for
25 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…
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…
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…
Ferromagnetic Ising Model on multiregular random graphs
Diego Alberici, Pierluigi Contucci, Emanuele Mingione +1
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings an…
Central limit theorem for the overlaps on the Nishimori line
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
The overlap distribution of the Sherrington-Kirkpatrick model on the Nishimori line has been proved to be self averaging for large volumes. Here we study the joint distribution of…
Limit theorems for the cubic mean-field Ising model
Pierluigi Contucci, Emanuele Mingione, Godwin Osabutey
We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They…
On the convergence to the non-equilibrium steady state of a Langevin dynamics with widely separated time scales and different temperatures
Diego Alberici, Nicolas Macris, Emanuele Mingione
We study the solution of the two-temperatures Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and…
An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model…
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…
Stationarization and Multithermalization in spin glasses
Pierluigi Contucci, Federico Corberi, Jorge Kurchan +1
We develop further the study of a system in contact with a multibath having different temperatures at widely separated timescales. We consider those systems that do not thermalize…
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…
Deep Boltzmann machines: rigorous results at arbitrary depth
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A class of deep Boltzmann machines is considered in the simplified framework of a quenched system with Gaussian noise and independent entries. The quenched pressure of a -layers…
Annealing and replica-symmetry in Deep Boltzmann Machines
Diego Alberici, Adriano Barra, Pierluigi Contucci +1
In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interac…
Equilibrium and Dynamics of a Multi-Bath Sherrington-Kirkpatrick Model
Pierluigi Contucci, Jorge Kurchan, Emanuele Mingione
In this paper we study the equilibrium statistical mechanical as well as the dynamical properties of a Sherrington and Kirkpatrick model in a multi-bath setting introduced in [4].…
A Multi-Scale Spin-Glass Mean-Field Model
Pierluigi Contucci, Emanuele Mingione
In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied. The pressure per particle in the thermodynamical limit is proved to obey a v…
Two populations mean-field monomer-dimer model
Diego Alberici, Emanuele Mingione
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit…
Mean-Field Monomer-Dimer models. A review
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A collection of rigorous results for a class of mean-field monomer-dimer models is presented. It includes a Gaussian representation for the partition function that is shown to cons…
Aggregation models on hypergraphs
Diego Alberici, Pierluigi Contucci, Emanuele Mingione +1
Following a newly introduced approach by Rasetti and Merelli we investigate the possibility to extract topological information about the space where interacting systems are modelle…
Limit theorems for monomer-dimer mean-field models with attractive potential
Diego Alberici, Pierluigi Contucci, Micaela Fedele +1
The number of monomers, in a monomer-dimer mean-field model with an attractive potential, fluctuates according to the central limit theorem when the parameters are outside the crit…
A mean-field monomer-dimer model with random monomer activities. Exact solution and rigorous results
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
Independent random monomer activities are considered on a mean-feld monomer-dimer model. Under very general conditions on the randomness the model is shown to have a self-averaging…
A mean-field monomer-dimer model with attractive interaction. The exact solution
Diego Alberici, Pierluigi Contucci, Emanuele Mingione
A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb…
Multi-species mean-field spin-glasses. Rigorous results
Adriano Barra, Pierluigi Contucci, Emanuele Mingione +1
We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the singl…
Factorization properties in d-dimensional spin glasses. Rigorous results and some perspectives
Pierluigi Contucci, Emanuele Mingione, Shannon Starr
In this paper we show that d-dimensional Gaussian spin glass models are strongly stochastically stable, fulfill the Ghirlanda-Guerra identities in distribution and the ultrametrici…