Related papers: Non-backtracking operator for Ising model and its …

This paper investigates the principal spectral theory and the asymptotic behavior of the principal spectrum point for a class of time-periodic cooperative systems with nonlocal dispersal operators, incorporating both coupled and uncoupled…

We propose an efficient algorithm to solve inverse problems in the presence of binary clustered datasets. We consider the paradigmatic Hopfield model in a teacher student scenario, where this situation is found in the retrieval phase. This…

When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that…

Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…

Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…

We present a general framework for incorporating non-reciprocal interactions into the Ising model with Glauber dynamics, without requiring multiple species. We then focus on a model with vision-cone type interactions. We solve it in a fully…

The Ising model was originally developed to model magnetisation of solids in statistical physics. As a network of binary variables with the probability of becoming 'active' depending only on direct neighbours, the Ising model appears…

We consider the problem of recovering equations of motion from multivariate time series of oscillators interacting on sparse networks. We reconstruct the network from an initial guess which can include expert knowledge about the system such…

Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for machine learning study of…

The spectrum of the nonbacktracking matrix associated to a network is known to contain fundamental information regarding percolation properties of the network. Indeed, the inverse of its leading eigenvalue is often used as an estimate for…

We study a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins. We study the properties of this family of models as the relative weight of the two kinds…

Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

The output of spectral clustering is a collection of eigenvalues and eigenvectors that encode important connectivity information about a graph or a manifold. This connectivity information is often not cleanly represented in the eigenvectors…

We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…

The nonbacktracking matrix, and the related nonbacktracking centrality (NBC) play a crucial role in models of percolation-type processes on networks, such as non-recurrent epidemics. Here we study the localization of NBC in infinite sparse…

Since the invention of the solid-state transistor, the overwhelming majority of computers followed the von Neumann architecture that strictly separates logic operations and memory. Today, there is a revived interest in alternative…

Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…