An approximation by neural networks with a fixed weight
type: Item
instance of: scholarly article
title: An approximation by neural networks with a fixed weight
zbMATH Open document ID: 1065.41047
author: Nahmwoo Hahm
author: Bum Il Hong
publication date: 2005-03-08T00:00:00Z
review text: A function \(\sigma: {\mathbb R} \to {\mathbb R}\) is called sigmoidal if \(\lim_ {x\to -\infty} \sigma(x)=0\), \(\lim_ {x\to +\infty} \sigma(x)=1\). Theorem 1. Let \(\sigma\) be a bounded sigmoidal function on \({\mathbb R}\) and let \(\epsilon >0\) be given. If \(f\) is a continuous function on \({\mathbb R}\) such that \(\lim_{| x| \to \infty} f(x)=0\), then there exist constants \(b_i, c_i \in {\mathbb R}\) and positive integers \(N,K\) such that \[ \left | f(x)-\sum_{i=1}^N c_i \sigma (Kx+b_i)\right | <\epsilon, \qquad x \in {\mathbb R}. \] Another similar theorem is also proved and some numerical examples are given.
Mathematics Subject Classification ID: 41A46
zbMATH DE Number: 2142435
zbMATH Keywords: neural network
zbMATH Keywords: sigmoidal function
zbMATH Keywords: convolution
reviewed by: Yuly Makovoz
MaRDI profile type: Publication
full work available at URL: j.camwa.2003.06.008
OpenAlex ID: W1970705963
cites work: Extension of localised approximation by neural networks
cites work: Universal approximation bounds for superpositions of a sigmoidal function
cites work: Q4011460
cites work: Approximation by Ridge functions and neural networks with one hidden layer
cites work: Approximation by superpositions of a sigmoidal function
DOI: 10.1016/J.CAMWA.2003.06.008
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142435