# A new algorithm for implementing a recursive neural network

## 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 ℝ^{2}. 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].

## Preview

Unable to display preview. Download preview PDF.

## References

- [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 - [2]F. S. Roberts,
*Applied Combinatorics*, Prentice-Hall Inc., New Jersey, 1985.Google Scholar - [3]V. Giménez, P. Gómez-Vilda, M. Pérez-Castellanos and E. Torrano,
*A New Approach for improving the capacity limit on a Recursive Neural Network*, Proc. of the AMS'94. IASTED, Lugano, Suiza, June 20–22, 1994, pp. 90–93.Google Scholar - [4]V. Rodellar, P. Gómez, M. Herrnida and R. W. Newcomb,
*An Auditory Neural System for Speech Processing and Recognition*, Proceedings of the ICARCV92, Singapore, September 16–18, 1992, pp. INV-6.2.1-5.Google Scholar - [5]Yves Kamp and Martin Hasler,
*Recursive Neural Networks for Associative Memory*, Wiley-Interscience Series in Systems and Optimization, England, 1990, pp. 10–34.Google Scholar - [6]R. Shonkwiler,
*Separating the Vertice of N-Cubes by Hyperplanes and its Application to Artificial Neural Networks*, IEEE Trans. on Neural Networks, Vol. 4, No. 2, March 1993, pp. 343–347.Google Scholar