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论文类型：期刊论文

发表时间：2007-10-01

发表刊物：INTERNATIONAL JOURNAL OF NEURAL SYSTEMS

收录刊物：SCIE、EI、PubMed、Scopus

卷号：17

期号：5

页面范围：419-424

ISSN号：0129-0657

关键字：neural networks; approximation capability; sum-of-product neural networks; sigma-pi-sigma neural networks; density

摘要：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.).