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Existence and Learning of Oscillations in Recurrent Neural Networks

  • In this paper 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.Then, within the usual 'learning' context of NeuralNetworks, we investigate whether RNNs of this class can adapt their internal parameters soas to 'learn' and then replicate autonomously certain external periodic signals.Our learning algorithm is similar to identification algorithms in adaptivecontrol theory. The main feature of the adaptation algorithm is that global exponential convergenceof parameters is guaranteed. We also obtain partial convergence results in the \(n\)-node case.

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Author:Stuart Townley, Achim Ilchmann, Martin G. Weiß, Warren McClements, Antonio C. Ruiz, David H. Owens, Dieter Prätzel-Wolters
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (202)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Learning systems; Monotone dynamical systems; Nonlinear dynamics; Recurrent neural networks
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C15 Nonlinear oscillations, coupled oscillators
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C40 Adaptive control
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp; lp, etc.)
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D15 Stabilization of systems by feedback
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011