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Improving Generalization Capabilities of Dynamic Neural Networks

galicki{at}imsid.uni-jena.de, Institute of Medical Statistics, Computer Sciences and Documentation, Friedrich Schiller University, Jena, Germany, and Department of Management, University of Zielona Góra, Zielona Góra, Podgórna 50, Poland

Lutz Leistritz

i6lelu{at}imsid.uni-jena.de, Institute of Medical Statistics, Computer Sciences and Documentation, Friedrich Schiller University Jena, Germany

Ernst Bernhard Zwick

ernst.zwick{at}kfunigraz.ac.at, Department of Pediatric Orthopedics, Karl-Franzens-University, Graz, Austria

Herbert Witte

iew{at}imsid.uni-jena.de, Institute of Medical Statistics, Computer Sciences and Documentation, Friedrich Schiller University, Jena, Germany

This work addresses the problem of improving the generalization capabilities of continuous recurrent neural networks. The learning task is transformed into an optimal control framework in which the weights and the initial network state are treated as unknown controls. A new learning algorithm based on a variational formulation of Pontrayagin's maximum principle is proposed. Under reasonable assumptions, its convergence is discussed. Numerical examples are given that demonstrate an essential improvement of generalization capabilities after the learning process of a dynamic network.