Universal approximation in p-mean by neural networks

被引：16

作者：

Burton, RM

Dehling, HG ^{[1
]}

机构：

[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 USA

[2] Univ Groningen, Dept Math, NL-9700 AV Groningen, Netherlands

来源：

NEURAL NETWORKS | 1998年 / 11卷 / 04期

关键词：

approximation theory; L-p-approximation; neural networks; single hidden layer network; universal transfer functions;

D O I：

10.1016/S0893-6080(98)00009-4

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given by [GRAPHICS] where a(j), theta(j), w(ji) is an element of R. In this paper we study the approximation of arbitrary functions f: R-d --> R by a neural net in an L-p(mu) norm for some finite measure mu on R-d. We prove that under natural moment conditions, a neural net with non-polynomial function can approximate any given function. (C) 1998 Elsevier Science Ltd. All rights reserved.

引用

页码：661 / 667

页数：7

共 7 条

[1]

[Anonymous], P IEEE 2 INT C NEUR

[2]

Cybenko G., 1989, Mathematics of Control, Signals, and Systems, V2, P303, DOI 10.1007/BF02551274

[3] ON THE APPROXIMATE REALIZATION OF CONTINUOUS-MAPPINGS BY NEURAL NETWORKS [J].