Geometric rates of approximation by neural networks

Authors:
Věra Kůrková;Marcello Sanguineti
Affiliations:
Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague 8, Czech Republic;Department of Communications, Computer, and System Sciences, University of Genova, Genova, Italy
Venue:
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Year:
2008

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Abstract

Model complexity of feedforward neural networks is studied in terms of rates of variable-basis approximation. Sets of functions, for which the errors in approximation by neural networks with n hidden units converge to zero geometrically fast with increasing number n, are described. However, the geometric speed of convergence depends on parameters, which are specific for each function to be approximated. The results are illustrated by examples of estimates of such parameters for functions in infinite-dimensional Hilbert spaces.