Related papers: Diluted Generalized Random Energy Model
We study the two-dimensional Edwards-Anderson spin-glass model using a parallel tempering Monte Carlo algorithm. The ground-state energy and entropy are calculated for different bond distributions. In particular, the entropy is obtained by…
We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices.…
The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
For many real spin-glass materials, the Edwards-Anderson model with continuous-symmetry spins is more realistic than the rather better understood Ising variant. In principle, the nature of an occurring spin-glass phase in such systems might…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…
In this paper we study the Random energy model - so called toy model of the spin glass theory - where the underlying distributions are compactly supported. We prove a general theorem on the asymptotics of free energy and obtain formulae in…
We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order…
We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
We introduce "AnnealSGD", a regularized stochastic gradient descent algorithm motivated by an analysis of the energy landscape of a particular class of deep networks with sparse random weights. The loss function of such networks can be…
We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are…
We perform a statistical analysis of deterministic energy-decreasing algorithms on mean-field spin models with complex energy landscape like the Sine model and the Sherrington Kirkpatrick model. We specifically address the following…
Global Autoregressive Models (GAMs) are a recent proposal [Parshakova et al., CoNLL 2019] for exploiting global properties of sequences for data-efficient learning of seq2seq models. In the first phase of training, an Energy-Based model…
Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous…
We consider ground state energies (GSE) of multipartite $p$-spin models. Relying on partially lifted random duality theory (pl RDT) concepts we introduce an analytical mechanism that produces easy to compute lower and upper GSE bounds for…
We address the question of geometrical as well as energetic properties of local excitations in mean field Ising spin glasses. We study analytically the Random Energy Model and numerically a dilute mean field model, first on tree-like…
To provide a novel tool for the investigation of the energy landscape of the Edwards-Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of…