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IMA Journal of Management Mathematics 1999 10(3):225-244; doi:10.1093/imaman/10.3.225
© 1999 by Institute of Mathematics and its Applications
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Neural networks and finite-order approximations

BEYNON MALCOLM, CURRY BRUCE{dagger} and PETER MORGAN

Cardiff Business School, University of Wales Cardiff Colum Drive, Cardiff CF1 3EU, UK

Email: Curry{at}Cardiff.ac.uk

This paper investigates the approximation properties of standard feedforward neural networks (NNs) through the application of multivanate Thylor-series expansions. The capacity to approximate arbitrary functional forms is central to the NN philosophy, but is usually proved by allowing the number of hidden nodes to increase to infinity. The Thylor-series approach does not depend on such limiting cases, lie paper shows how the series approximation depends on individual network weights. The role of the bias term is taken as an example. We are also able to compare the sigmoid and hyperbolic-tangent activation functions, with particular emphasis on their impact on the bias term. The paper concludes by discussing the potential importance of our results for NN modelling: of particular importance is the training process.

Keywords: Neural network; feedforward logistic networks; Thylor series; activation function; bias term


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