Higher degree error backpropagation in cross-coupled Hopfield nets

The author discusses higher-degree error backpropagation in cross-coupled Hopfield nets employing exponential energy functions for cross-coupling. He constructs a Lyapunov function to derive a total network architecture and a learning algorithm for training nonlinear multilayered internetworks. In the derived architecture, each internetwork for cross-coupling has a forward subnet and a backward subnet. The backward subnet consists of multiple planes, each of which has the same connection weights as those in the forward subnet. From linear to higher degree errors respectively backpropagate in the different planes. The final outputs from the multiple planes are utilized effectively for network relaxation. At the same time, the interactions between the errors in each plane and the signals in the forward subnet contribute to the connectionistic learning. The result obtained indicates that higher-degree error backpropagation is effective for fast learning