A new algorithm for implementing a recursive neural network
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 , 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  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 .
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