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Neural networks, linear functions and neglected non-linearity

Curry, Bruce and Morgan, Peter Huw 2003. Neural networks, linear functions and neglected non-linearity. Computational Management Science 1 (1) , pp. 15-29. 10.1007/s10287-003-0003-4

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Abstract

The multiplicity of approximation theorems for Neural Networks do not relate to approximation of linear functions per se. The problem for the network is to construct a linear function by superpositions of non-linear activation functions such as the sigmoid function. This issue is important for applications of NNs in statistical tests for neglected nonlinearity, where it is common practice to include a linear function through skip-layer connections. Our theoretical analysis and evidence point in a similar direction, suggesting that the network can in fact provide linear approximations without additional ‘assistance’. Our paper suggests that skip-layer connections are unnecessary, and if employed could lead to misleading results.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Business (Including Economics)
Subjects: H Social Sciences > H Social Sciences (General)
H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords: Universal approximation; non-linear regression; network weights; hidden layers; skip-layer connections
Publisher: Springer
ISSN: 1619-697X
Last Modified: 04 Jun 2017 04:23
URI: http://orca.cf.ac.uk/id/eprint/37873

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