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 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 pattem 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 aider 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].