Treating weights as dynamical variables-a new approach to neurodynamics

The recall and learning dynamics of artificial neural networks are described by means of a partial differential equation (PDE) that may incorporate weights either as parameters or variables. For the case in which weights are interpreted as variables, a new type of neurodynamics is discovered when weights have to obey second-order differential equations called learning laws. Experiments on the association of time-varying patterns indicates the superiority of the learning law over the known types of learning rules. It is also shown that a single first-order Hamilton-Jacobi parametric PDE suffices to derive the various neurodynamical paradigms used currently