Neural networks, linear functions and neglected non-linearity

B. Curry () and P. Morgan

Computational Management Science, 2003, vol. 1, issue 1, 15-29

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. Copyright Springer-Verlag Berlin/Heidelberg 2003

Keywords: universal approximation; non-linear regression; network weights; hidden layers; skip-layer connections (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/s10287-003-0003-4

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