Neural networks, linear functions and neglected non-linearity

Curry, Bruce and Morgan, Peter Huw ORCID: https://orcid.org/0000-0002-8555-3493 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:	21 Oct 2022 09:49
URI:	https://orca.cardiff.ac.uk/id/eprint/37873

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