Hopfield net generation, encoding and classification of temporal trajectories

Hopfield network transient dynamics have been exploited for resolving both path planning and temporal pattern classification. For these problems Lagrangian techniques and two well-known learning algorithms for recurrent networks have been used. For path planning, the Williams and Zisper´s learning algorithm has been implemented and a set of temporal trajectories which join two points, pass through others, avoid obstacles and jointly form the shortest path possible are discovered and encoded in the weights of the net. The temporal pattern classification is based on an extension of the Pearlmutter´s algorithm for the generation of temporal patterns which is obtained by means of variational methods. The algorithm is applied to a simple problem of recognizing five temporal trajectories with satisfactory robustness to distortions