Existence and learning of oscillations in recurrent neural networks

Author

Townley, S. ; Ilchmann, A. ; Weiß, M.G. ; Mcclements, W. ; Ruiz, A.C. ; Owens, D.H. ; Pratzel-Wolters, D.

Author_Institution

Sch. of Math. Sci., Exeter Univ., UK

Volume

11

Issue

1

fYear

2000

fDate

1/1/2000 12:00:00 AM

Firstpage

205

Lastpage

214

Abstract

We study a particular class of n-node recurrent neural networks (RNNs). In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. We then investigate whether RNNs of this class can adapt their internal parameters so as to “learn” and then replicate autonomously (in feedback) certain external periodic signals. Our learning algorithm is similar to the identification algorithms in adaptive control theory. The main feature of the algorithm is that global exponential convergence of parameters is guaranteed. We also obtain partial convergence results in the n-node case

Keywords

circuit oscillations; learning (artificial intelligence); nonlinear dynamical systems; recurrent neural nets; exponential convergence; identification; learning algorithm; monotone dynamical systems; nonlinear dynamics; recurrent neural networks; Adaptive control; Biological system modeling; Brain modeling; Chaos; Control system synthesis; Convergence; Intelligent networks; Limit-cycles; Neural networks; Recurrent neural networks;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.822523

Filename

822523