A variational formulation for the multilayer perceptron

Authors:
Roberto Lopez;Eugenio Oñate
Affiliations:
International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Barcelona, Spain;International Center for Numerical Methods in Engineering (CIMNE), Technical University of Catalonia (UPC), Barcelona, Spain
Venue:
ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I
Year:
2006

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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.