Asymptotic Description of Neural Networks with Correlated Synaptic Weights

Entropy

Olivier Faugeras¹  James MacLaurin² 

[1] INRIA Sophia Antipolis Mediterannee, 2004 Route Des Lucioles, Sophia Antipolis, 06410, France; E-Mail

关键词: large deviations;    good rate function;    stationary gaussian processes;    stationary measures;    spectral representations;    neural networks;    firing rate neurons;    correlated synaptic weights;   

DOI  :  10.3390/e17074701

来源: mdpi

【 摘 要 】

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe the asymptotic law of the network when the number of neurons goes to infinity. We introduce the process-level empirical measure of the trajectories of the solutions to the equations of the finite network of neurons and the averaged law (with respect to the synaptic weights) of the trajectories of the solutions to the equations of the network of neurons. The main result of this article is that the image law through the empirical measure satisfies a large deviation principle with a good rate function which is shown to have a unique global minimum. Our analysis of the rate function allows us also to characterize the limit measure as the image of a stationary Gaussian measure defined on a transformed set of trajectories.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland