The essential order of approximation for Suzuki's neural networks

Authors:
Feng-Jun Li;Zong-Ben Xu;Yue-Ting Zhou
Affiliations:
Faculty of Science, Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China and School of Mathematics and Computer Science, Ningxia Univer ...;Faculty of Science, Institute for Information and System Science, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China;Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, People's Republic of China
Venue:
Neurocomputing
Year:
2008

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Abstract

For three kinds of neural networks constructed by Suzuki [Constructive function approximation by three layer artificial neural networks, Neural Networks 11 (1998) 1049-1058], by establishing both upper and lower bound estimations on approximation order, the essential approximation order of these networks is estimated and the theorem of saturation (the largest capacity of approximation) is proved. These results can precisely characterize the approximation ability of these networks and clarify the relationship among the rate of approximation, the number of hidden-layer units and the properties of approximated functions. Our paper extends and perfects the error estimations of Suzuki [Constructive function approximation by three layer artificial neural networks, Neural Networks 11 (1998) 1049-1058]. On the basis of the numerical example, we can conclude that the accuracy of our estimations outperform to the Suzuki's results.