相关论文: Memristive Networks: from Graph Theory to Statisti…

These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…

In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…

In deep learning, neural networks serve as noisy channels between input data and its representation. This perspective naturally relates deep learning with the pursuit of constructing channels with optimal performance in information…

This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution.…

A lecture notes style review of the non-equilibrium statistical mechanics of recurrent neural networks with discrete and continuous neurons (e.g. Ising, graded-response, coupled-oscillators). To be published in the Handbook of Biological…

Physically motivated stochastic dynamics are often used to sample from high-dimensional distributions. However such dynamics often get stuck in specific regions of their state space and mix very slowly to the desired stationary state. This…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…

Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…

Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…

We represent the Ising model of statistical physics by normal factor graphs in the primal and in the dual domains. By analogy with Kirchhoff's voltage and current laws, we show that in the primal normal factor graphs, the dependency among…

Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…

We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement…

This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized…

This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…

Accurately identifying the underlying graph structures of multi-agent systems remains a difficult challenge. Our work introduces a novel machine learning-based solution that leverages the attention mechanism to predict future states of…

We study the dynamics of the processes in the small-world networks with a power-law degree distribution where every node is considered to be in one of the two available statuses. We present an algorithm for generation of such network and…