Continuous-time temporal back-propagation with adaptable time delays

Backpropagation is extended to continuous-time feedforward networks with internal, adaptable time delays. The new technique is suitable for parallel hardware implementation, with continuous multidimensional training signals. The resulting networks can be used for signal prediction, signal production, and spatiotemporal pattern recognition tasks. Unlike conventional backpropagation networks, they can easily adapt while performing true signal prediction. Simulation results are presented for networks trained to predict future values of the Mackey-Glass chaotic signal, using its present value as an input. For this application, networks with adaptable delays had less than half the prediction error of networks with fixed delays, and about one-quarter the error of conventional networks. After training, the network can be operated in a signal production configuration, where it autonomously generates a close approximation to the Mackey-Glass signal.