Generating Network Trajectories Using Gradient Descent in State Space

A local and simple learning algorithm is introduced that gradually minimizes an error function for neural states of a general network. Unlike standard backpropagation algorithms, it is based on linearizing the neurodynamics, which are interpreted as constraints for the different network variables. From the resulting equations, the weight update is deduced which has a minimal norm and produces state changes directed precisely towards target values. As an application, it is shown how to generate desired neural state space curves on recurrent Hopfield-type networks.