Neural networks and finite-order approximations

Email: Curry{at}Cardiff.ac.uk This paper investigates the approximation properties of standardfeedforward neural networks (NNs) through the application ofmultivanate Thylor-series expansions. The capacity to approximatearbitrary functional forms is central to the NN philosophy,but is usually proved by allowing the number of hidden nodesto increase to infinity. The Thylor-series approach does notdepend on such limiting cases, lie paper shows how the seriesapproximation depends on individual network weights. The roleof the bias term is taken as an example. We are also able tocompare the sigmoid and hyperbolic-tangent activation functions,with particular emphasis on their impact on the bias term. Thepaper concludes by discussing the potential importance of ourresults for NN modelling: of particular importance is the trainingprocess.