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Neural networks, linear functions and neglected non-linearity

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  • B. Curry
  • P. Morgan

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

Suggested Citation

  • B. Curry & P. Morgan, 2003. "Neural networks, linear functions and neglected non-linearity," Computational Management Science, Springer, vol. 1(1), pages 15-29, December.
    • Handle: RePEc:spr:comgts:v:1:y:2003:i:1:p:15-29
    DOI: 10.1007/s10287-003-0003-4
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    Cited by:

    1. Darren Beriro & Robert Abrahart & Nick Mount & C. Nathanail, 2012. "Letter to the Editor on “Precipitation Forecasting Using Wavelet-Genetic Programming and Wavelet-Neuro-Fuzzy Conjunction Models” by Ozgur Kisi & Jalal Shiri [Water Resources Management 25 (2011) 3135–," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(12), pages 3653-3662, September.

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