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A new algorithm for implementing a recursive neural network

  • V. Giménez
  • P. Gómez-Vilda
  • E. Torrano
  • M. Pérez-Castellanos
Computational Models of Neurons and Neural Nets
Part of the Lecture Notes in Computer Science book series (LNCS, volume 930)

Abstract

This paper describes a method of designing a procedure based in a new vision of the well known Hopfield algorithm. Our approach is also a Hebb's law based algorithm for describing a Recursive Neural Network. In the training stage we used a Graph method for acquiring the data [1], the energy associated to any possible state of the net is represented as a energy point (a,b) in the plane ℝ2. We prove that all the states with similar energy level are on an hyperbolic surface, x,y=k, when the net changes its state its associated energy point is placed in a utter hyperbolic surface x.y=q, (q>k); in this way a convergence is proved. When a pattern is called for retrieving, a parameter may be used for controlling the radius of attraction and the number of fixed points in the system; this parameter is related with a coloring [2] or partition neighborhood of the Resulting Graph obtained after training. As a clear application we have developed an example where we may see the frequency distribution associated with a given state and the incidence of the parameter on the the number of fixed points [3].

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References

  1. [1]
    V. Giménez, P. Gómez-Vilda, M. Pérez-Castellanos and V. Rodellar, A New Approach for Finding the Weights in a Neural Network using Graphs, Proc. of the 36th Midwest Symposium on Circuits and Systems, Detroit, August 16–18, 1993, pp. 113–116.Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • V. Giménez
    • 1
  • P. Gómez-Vilda
    • 2
  • E. Torrano
    • 1
  • M. Pérez-Castellanos
    • 2
  1. 1.Departamento de Matemática Aplicada, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de Arquitectaray Tecnología de Sistemas Informáticos, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain

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