Shadowing property in analysis of neural networks dynamics

Authors:
Andrzej Bielecki;Jerzy Ombach
Affiliations:
Institute of Computer Science, Jagiellonian University, ul Nawojki 11, Kraków 30072, Poland;Institute of Mathematics, Jagiellonian University, Kraków, Poland
Venue:
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Year:
2004

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Abstract

We show that the shadowing and the inverse shadowing, the notions considered in the theory of dynamical systems, may be successfully applied in the analysis of a multilayer neural networks learning process. Our main result is, that generically any such a process is robust. Implementation implications are discussed as well.