89 citations · 525 across the 28 of their papers we have counts for
32 papers
On the determinant in Bray-Moore's TAP complexity formula
David Belius, Francesco Concetti, Giuseppe Genovese
In the computation of the TAP complexity, originally carried out by Bray and Moore, a fundamental step is to calculate the determinant of a random Hessian. As the replica method do…
Transformation of the Gibbs measure of the cubic NLS and fractional NLS under an approximated Birkhoff map
Giuseppe Genovese, Renato Lucà, Riccardo Montalto
We study the Gibbs measure associated to the periodic cubic nonlinear Schrödinger equation. We establish a change of variable formula for this measure under the first step of the B…
Pattern reconstruction with restricted Boltzmann machines
Giuseppe Genovese
Restricted Boltzmann machines are energy models made of a visible and a hidden layer. We identify an effective energy function describing the zero-temperature landscape on the visi…
Universal approximation of credit portfolio losses using Restricted Boltzmann Machines
Giuseppe Genovese, Ashkan Nikeghbali, Nicola Serra +1
We introduce a new portfolio credit risk model based on Restricted Boltzmann Machines (RBMs), which are stochastic neural networks capable of universal approximation of loss distri…
A remark on the spherical bipartite spin glass
Giuseppe Genovese
Auffinger and Chen proved a variational formula for the free energy of the spherical bipartite spin glass in terms of a global minimum over the overlaps. We show that a different o…
Quasi-invariance of Gaussian measures for the periodic Benjamin-Ono-BBM equation
Giuseppe Genovese, Renato Lucá, Nikolay Tzvetkov
The BBM equation is a Hamiltonian PDE which revealed to be a very interesting test-model to study the transformation property of Gaussian measures along the flow. In this paper we…
Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs
Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov
We show that introducing an exponential cut-off on a suitable Sobolev norm facilitates the proof of quasi-invariance of Gaussian measures with respect to Hamiltonian PDE flows and…
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov
The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian…
Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines
Giuseppe Genovese
We study the free energy of a most used deep architecture for restricted Boltzmann machines, where the layers are disposed in series. Assuming independent Gaussian distributed rand…
Legendre Equivalences of Spherical Boltzmann Machines
Giuseppe Genovese, Daniele Tantari
We study either fully visible and restricted Boltzmann machines with sub-Gaussian random weights and spherical or Gaussian priors. We prove the free energies of the spherical and G…
Long time behaviour of a local perturbation in the isotropic XY chain under periodic forcing
Livia Corsi, Giuseppe Genovese
We study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic problem can be mapped into a highly resonant Flo…
Invariant measures for the periodic derivative nonlinear Schrödinger equation
Giuseppe Genovese, Renato Lucà, Daniele Valeri
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in and we show these mea…
Overlap synchronisation in multipartite random energy models
Giuseppe Genovese, Daniele Tantari
In a multipartite random energy model, made of a number of coupled GREMs, we determine the joint law of the overlaps in terms of the ones of the single GREMs. This provides the sim…
Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priors
Adriano Barra, Giuseppe Genovese, Peter Sollich +1
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence…
Phase transitions in Restricted Boltzmann Machines with generic priors
Adriano Barra, Giuseppe Genovese, Peter Sollich +1
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis o…
Periodic Driving at High Frequencies of an Impurity in the Isotropic XY Chain
Livia Corsi, Giuseppe Genovese
We study the isotropic XY chain with a transverse magnetic field acting on a single site and analyse the long time behaviour of the time-dependent state of the system when a period…
Local Central Limit Theorem for a Random Walk Perturbed in One Point
Giuseppe Genovese, Renato Lucà
We consider a symmetric random walk on the -dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central…
Singular behavior of the leading Lyapunov exponent of a product of random matrices
Giuseppe Genovese, Giambattista Giacomin, Rafael Leon Greenblatt
We consider a certain infinite product of random matrices appearing in the solution of some and dimensional disordered models in statistical mechanics, which…
Non-Convex Multipartite Ferromagnets
Giuseppe Genovese, Daniele Tantari
We investigate a multipartite ferromagnetic model without self-interactions between spins of the same party, so that the Hamiltonian is not a definite quadratic form of the magneti…
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
Giuseppe Genovese, Renato Lucà, Daniele Valeri
We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite s…
Legendre Duality of Spherical and Gaussian Spin Glasses
Giuseppe Genovese, Daniele Tantari
The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin…
On the Dynamics of XY Spin Chains with Impurities
Giuseppe Genovese
We provide a theoretical set up for studying the dynamics in quantum spin chain models with inhomogeneous two-body interaction. We frame in our formalism models that can be mapped…
Random Walk on Lattice with an Antisymmetric Perturbation in One Point
Giuseppe Genovese, Renato Lucà
We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactl…
How glassy are neural networks?
Adriano Barra, Giuseppe Genovese, Francesco Guerra +1
In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one o…