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Dynamics of structural learning with an adaptive forgetting rate

Structural learning with forgetting is a prominent method of multilayer feedforward neural network complexity regularization. The level of regularization is controlled by a parameter known as the forgetting rate. The goal of this paper is to establish a dynamical system framework for the study of structural learning both to offer new insights into this methodology and to potentially provide a means of either developing new or analytically justifying existing forgetting rate adaptation strategies. The resulting nonlinear model of structural learning is analyzed by developing a general linearized equation for the case of a quadratic error function. This analysis demonstrates the effectiveness of an adaptive forgetting rate. A simple example is provided to illustrate our approach.