Qualitative behavior of differential equations associated with artificial neural networks
type: Item
instance of: scholarly article
title: Qualitative behavior of differential equations associated with artificial neural networks
zbMATH Open document ID: 1071.34047
author: James Jamison
author: Fernanda Botelho
published in: Journal of Dynamics and Differential Equations
publication date: 2005-01-17T00:00:00Z
review text: Here, the following matrix differential equation is considered \[ \frac{dW}{dt}=T_{\varepsilon}CW-WW^TCW, \tag{1} \] where \(W(t)\) is a real \(n\times k\)-matrix, \(C\) is a symmetric matrix and \(T_{\varepsilon}\) is a tridiagonal matrix. Equation (1) is proposed by Oja, Kingsley and Adams as a learning model, more precisely, a model that describes the dynamics of an artificial neural network. The elements of the matrix \(W\) are related with the change of information between the neurons, while the parameter \(\varepsilon\) describes the probability of temporary synaptic formation. Using techniques from matrix calculus, the authors establish conditions under which (1) is a gradient, semi-gradient or a gradient-like system. They also study the asymptotic behavior of solutions of system (1).
reviewed by: Adriana Buică
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 2128705
zbMATH Keywords: learning models
zbMATH Keywords: matrix differential equations
zbMATH Keywords: gradient systems
zbMATH Keywords: asymptotic behaviour
MaRDI profile type: Publication
full work available at URL: b:jody.0000041285.36221.bf
OpenAlex ID: W1988992375
DOI: 10.1023/B:JODY.0000041285.36221.BF
description: scientific article; zbMATH DE number 2128705