Capacity and parasitic fixed points control in a recursive neural network

Abstract

This paper describes a new method for controlling the capacity and for diminishing the number of parasitic fixed points in a Recursive Neural Network RNN. Based on preliminary researches [1] a Recursive Neural Network may be seen as a graph. The matrix of weights W presents certain properties for which it may be called a tetrahedral matrix [2]. The geometrical properties of these kind of matrices may be used for classifying the n-dimensional state-vector space in n classes[2]. In the recall stage, a parameter vector σ may be introduced, which is related with the capacity of the network [3]. It may be shown that the bigger is the value of the i-th component the vector σ the higher became the capacity of the i class of the state-vector space[2]. Once the capacity has been controlled with the parameter σ, we introduce a new parameter that use the statistical deviation of the prototypes to compare them with those that appears as fixed points, eliminating in this way a great number of parasitic fixed points.