Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2007-10-01

Journal: INTERNATIONAL JOURNAL OF NEURAL SYSTEMS

Included Journals: Scopus、PubMed、EI、SCIE

Volume: 17

Issue: 5

Page Number: 419-424

ISSN: 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.).