Mathematics and Neural Networks -A Glance at some Basic Connections

This paper presents a brief and easily accessible introduction to the theory of neural networks under special emphasis on the role of pure and applied mathematics in this interesting field of research. In order to allow a quick and direct approach even for nonspecialists, the paper only considers th...

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Bibliographic Details
Published inActa applicandae mathematicae Vol. 55; no. 3; p. 303
Main Author Lenze, Burkhard
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.02.1999
Subjects
Applied mathematics
Mathematical analysis
Network topologies
Neural networks
Neurons
Studies
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Summary:This paper presents a brief and easily accessible introduction to the theory of neural networks under special emphasis on the role of pure and applied mathematics in this interesting field of research. In order to allow a quick and direct approach even for nonspecialists, the paper only considers three-layer feedforward networks with sigmoidal transfer functions and do not cover general multi-layer, recursive or radial-basis-function networks. Moreover, the paper focuses its attention on density and complexity results while construction problems based on operator techniques are not discussed in detail. Especially, in connection with complexity results, this paper shows that neural networks in general have the power to approximate certain function spaces with a minimal number of free parameters. In other words, under this specific point of view neural networks represent one of the best possible approximation devices available.
ISSN:0167-8019
1572-9036
DOI:10.1023/A:1006161218940