Related papers: Deep Boltzmann machines: rigorous results at arbit…
We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences…
Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a…
We investigate quantum information processing and manipulations in disordered systems of ultracold atoms and trapped ions. First, we demonstrate generation of entanglement and local realization of quantum gates in a quantum spin glass…
We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero field limit the system exactly realizes the…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational…
We study the expectation value of the logarithm of the partition function of large binary-to-binary lattice-gas Restricted Boltzmann Machines (RBMs) within a replica-symmetric ansatz, averaging over the disorder represented by the…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
A new kinetic model for multiphase flow was presented under the framework of the discrete Boltzmann method (DBM). Significantly different from the previous DBM, a bottom-up approach was adopted in this model. The effects of molecular size…
Many real-world tasks, from associative memory to symbolic reasoning, benefit from discrete, structured representations that standard continuous latent models can struggle to express. We introduce the Gaussian-Multinoulli Restricted…
The characterization of excitations in disordered quantum systems is a central issue in connection with glass physics and many-body localization. Here, we show that quench spectroscopy of a disordered model, as realized from its…
We successfully model the behavior of two-spin systems using neural networks known as conditional Restricted Boltzmann Machines (cRBMs) which encode physical information in the properties of a thermal ensemble akin to an Ising model. The…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…