Synthesis of Feedforward Networks in Supremum Error Bound

by

Krzysztof Ciesielski, Jaroslaw P. Sacha, and Krzysztof J. Cios

IEEE Trans. on Neural Networks 11(6) (2000), 1213-1227.

The main result of this paper is a constructive proof of a formula for the upper bound of the approximation error in L\infty (supremum norm) of multi-dimensional functions by feedforward networks with one hidden layer of sigmoidal units and a linear output. This result is applied to formulate a new method of neural network synthesis. The result can also be used to estimate complexity of the maximum-error network and/or to initialize that network weights. An example of the network synthesis is given.