A variational formulation for the multilayer perceptron

Published in ICANN 2006, S. Kollias et al (Eds.), ICANN 2006, Part I, LNCS 4131, pp. 19-168, Germany, 2006
DOI: 10.1007/11840817_17

Abstract

In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for the multilayer perceptron provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique we use a multilayer perceptron to solve some classical problems in the calculus of variations.