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.
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© 2006 Springer-Verlag Berlin Heidelberg
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Lopez, R., Oñate, E. (2006). A Variational Formulation for the Multilayer Perceptron. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840817_17
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DOI: https://doi.org/10.1007/11840817_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38625-4
Online ISBN: 978-3-540-38627-8
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