The practical use of artificial networks: an investigation using Taylor series expansions of the network equations

Summary form only given, as follows. Current theorems suggest that a single hidden layered artificial neural network is sufficient to approximate any continuous function which describes the mapping between two spaces. These theorems do not provide a guide to the practical implementation of networks that are used with real problems. By considering the Taylor series expansion of the equations that describe nodal behavior an alternative description of the performance and limitations of networks can be produced. It was shown that bias is essential for a large class of problems which require even-symmetric mapping. The number of hidden units and the size of the training set required for a given problem is dependent upon the order of the equivalent approximating polynomial. The standard sigmoid output function can be replaced by finite series functions and improved performance can be achieved