Time Dependent Adaptive Neural Networks

Fernando J. Pineda Center for Microelectronics Technology Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 ABSTRACT A comparison of algorithms that minimize error functions to train the trajectories of recurrent networks, reveals how complexity is traded off for causality. These algorithms are also related to time-independent fonnalisms. It is suggested that causal and scalable algorithms are possible when the activation dynamics of adaptive neurons is fast compared to the behavior to be learned. Standard continuous-time recurrent backpropagation is used in an example. 1 INTRODUCTION Training the time dependent behavior of a neural network model involves the minimization of a function that measures the difference between an actual trajectory and a desired trajectory. The standard method of accomplishing this minimization is to calculate the gradient of an error function with respect to the weights of the system and then to use the gradient in a minimization algorithm (e.g.