相关论文: Statistical Mechanics of Recurrent Neural Networks…

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

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…

We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems…

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…

The statistics of correlations are central quantities characterizing the collective dynamics of recurrent neural networks. We derive exact expressions for the statistics of correlations of nonlinear recurrent networks in the limit of a…

Shunting inhibitory cellular neural networks (SICNNs) with continuous as well as discontinuous external inputs are investigated. The descriptions of homoclinic and heteroclinic motions are provided in the functional sense for the…

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…

Lecture notes on elements of nonequilibrium statistical mechanics: (1) a characterization of the nonequilibrium condition, largely by contrast to equilibrium; (2) a retelling of some of the great performances of the more distant past,…

We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we…

We describe the application of tools from statistical mechanics to analyse the dynamics of various classes of supervised learning rules in perceptrons. The character of this paper is mostly that of a cross between a biased non-encyclopedic…

Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…

We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective…

In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant…

In this study, we investigate the continuous time dynamics of Recurrent Neural Networks (RNNs), focusing on systems with nonlinear activation functions. The objective of this work is to identify conditions under which RNNs exhibit perpetual…

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…

A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics

Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…

The fluctuating dynamics of a network about its stable, noise-free steady state are theoretically investigated. Various causes of non-equilibrium dynamics are identified in terms of the properties and symmetry of the network connections and…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…