Uniform Approximation Capabilities of Sum-of-Product and Sigma-Pi-Sigma Neural Networks

Authors:
Jinling Long;Wei Wu;Dong Nan
Affiliations:
Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China;Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China;Dept. Appl. Math., Dalian University of Technology, Dalian 116023, P.R. China
Venue:
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Advances in Neural Networks
Year:
2007

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Abstract

Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNNwith its activation function in C(ï戮驴) is dense in $C(\mathbb{K})$ for any compact $\mathbb{K}\in \mathbb{R}^N$, if and only if the activation function is not a polynomial. It is also shown that if the activation function of an SPSNNis in C(ï戮驴), then the functions generated by the SPSNNare dense in $C(\mathbb{K})$ if and only if the activation function is not a constant.