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Indexed by:期刊论文

Date of Publication:2007-10-01

Journal:INTERNATIONAL JOURNAL OF NEURAL SYSTEMS

Included Journals:SCIE、EI、PubMed、Scopus

Volume:17

Issue:5

Page Number:419-424

ISSN No.:0129-0657

Key Words:neural networks; approximation capability; sum-of-product neural networks; sigma-pi-sigma neural networks; density

Abstract:This paper studies the L-p 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 the SOPNN with its activation function in L-loc(p)(R) is dense in L-p(K) for any compact set K subset of R-N, if and only if the activation function is not a polynomial almost everywhere. It is also shown that if the activation function of the SPSNN is in L-loc(infinity)(R), then the functions generated by the SPSNN are dense in L-p(K) if and only if the activation function is not a constant (a.e.).