Pointwise approximation for neural networks

Authors:
Feilong Cao;Zongben Xu;Youmei Li
Affiliations:
Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou, Zhejiang, China;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shanxi, China;Department of Computer Science, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang, China
Venue:
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Year:
2005

Citing 6
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Abstract

It is shown in this paper by a constructive method that for any f∈C(m)[a,b], the function and its m order derivatives can be simultaneously approximated by a neural network with one hidden layer in the pointwise sense. This approach naturally yields the design of the hidden layer and the estimate of rate of convergence. The obtained results describe the relationship among the approximation degree of networks, the number of neurons in the hidden layer and the input sample, and reveal that the approximation speed of the constructed networks depends on the smoothness of approximated function.