caa a22 4500 477097278 CHVBK 20180405111531.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF01188988 doi (NATIONALLICENCE)springer-10.1007/BF01188988 Universal approximation capability of EBF neural networks with arbitrary activation functions [Elektronische Daten] [Tianping Chen, Hong Chen] The purpose of this paper is to investigate the approximation capability of elliptic basis function (EBF) neural networks. The main results are: (1) A necessary and sufficient condition for a functionS′ (R 1) to be qualified as an activation function in the hidden layer of an EBF neural network is given. (2) Every nonzero functionG ε L 2(R n ) is qualified to be an activation function in the elliptic neural network to approximate any function in L2(Rn). (3) As applications, we give new proofs of the theorems concerning the approximation capability of affine basis function (ABF) neural networks and generalized radial basis function (GRBF) neural networks (including radial basis function neural networks) with arbitrary activation functions. In particular, we solve the problem of the approximation capability of sigma-pi neural networks. Birkhäuser, 1996 Chen Tianping Department of Mathematics, Fudan University, Shanghai, People's Republic of China aut Chen Hong Sun Microsystems Inc., 2550 Garcia Avenue, MS USUN02-203, 94043-1100, Mountain View, California aut Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/5(1996-09-01), 671-683 0278-081X 15:5<671 1996 15 34 https://doi.org/10.1007/BF01188988 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01188988 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Tianping Department of Mathematics, Fudan University, Shanghai, People's Republic of China aut NATIONALLICENCE 700 1- Chen Hong Sun Microsystems Inc., 2550 Garcia Avenue, MS USUN02-203, 94043-1100, Mountain View, California aut NATIONALLICENCE 773 0- Circuits, Systems and Signal Processing Birkhäuser-Verlag 15/5(1996-09-01), 671-683 0278-081X 15:5<671 1996 15 34 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer