Related papers: How glassy are neural networks?
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…
The optimal capacity of a diluted Blume-Emery-Griffiths neural network is studied as a function of the pattern activity and the embedding stability using the Gardner entropy approach. Annealed dilution is considered, cutting some of the…
We present extensive simulations of a quantum version of the Hopfield Neural Network to explore its emergent behavior. The system is a network of $N$ qubits oscillating at a given $\Omega$ frequency and which are coupled via Lindblad jump…
Purpose of this paper is to face up to P-spin glass and Gaussian P-spin model, i.e. spin glasses with polynomial interactions of degree P > 2. We consider the replica symmetry and first step of replica simmetry breaking assumptions and we…
Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…
Using the Hopfield model as a benchmark case, the present work focuses on the investigation of partially annealed associative neural networks, wherein neural dynamics is coupled to slowly evolving patterns within the…
Statistical mechanics of spin glasses is one of the main strands toward a comprehension of information processing by neural networks and learning machines. Tackling this approach, at the fairly standard replica symmetric level of…
This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable…
This thesis is an attempt to provide a new outlook on complex systems, as well as some physical answers for certain models, taking a computational approach. We have focused on disordered systems, addressing two traditional problems in three…
A model for studying the ultrametricity of the energy landscape in a disordered heteropolymer is presented. It is treated as a simplified model of a protein molecule in which amino acid residues are modeled as point masses. Pairwise…
Aim of this paper is to give an extensive treatment of bipartite mean field spin systems, ordered and disordered: at first, bipartite ferromagnets are investigated, achieving an explicit expression for the free energy trough a new minimax…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
Two-phase flow in porous media is a ubiquitous phenomenon that has been studied for well over a century. However, we still lack a successful theory that predicts flow on a macroscopic length scale (the so-called Darcy scale) on the basis of…
We study a fully connected Hopfield-type associative memory network with online activity-dependent synaptic plasticity, where neural states and synaptic couplings coevolve during retrieval. Using the generating-functional formalism, we…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard…