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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Lopez, R., & Oñate, E. (2006). A variational formulation for the multilayer perceptron. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4131 LNCS-I, pp. 159–168). Springer Verlag. https://doi.org/10.1007/11840817_17
Mendeley helps you to discover research relevant for your work.