相关论文: Non-backtracking operator for Ising model and its …

Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…

In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network…

We consider Hopfield networks, where neurons interact pair-wise by Hebbian couplings built over $i$. a set of definite patterns (ground truths), $ii$. a sample of labeled examples (supervised setting), $iii$. a sample of unlabeled examples…

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the…

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…

This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…

In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristic (attribute) of nodes (or edges) of networks. Each isospectral compression (when a…

We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties of the so-called Koopman operator, our approach can be regarded as a natural extension of classic linear…

We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval…

We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…

A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…

There have been two separate lines of work on estimating Ising models: (1) estimating them from multiple independent samples under minimal assumptions about the model's interaction matrix; and (2) estimating them from one sample in…

Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the…

The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…

Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph…

We perform a stationary state replica analysis for a layered network of Ising spin neurons, with recurrent Hebbian interactions within each layer, in combination with strictly feed-forward Hebbian interactions between successive layers.…

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present…

We consider the problem of sampling from the Ising model when the underlying interaction matrix has eigenvalues lying within an interval of length $\gamma$. Recent work in this setting has shown various algorithmic results that apply…

We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…