Periodic motions, mapping ordered sequences, and training of dynamic neural networks to generate continuous and discontinuous trajectories

Designing efficient methods for training dynamic neural networks for learning spatio-temporal patterns is of great interest at present. In particular, the "trajectory generation problem" that involves training the network to learn and replicate autonomously a specified time-varying periodic motion has attracted considerable attention. A systematic approach to solve this problem by decomposing the overall task into two sub-tasks, a spatio-temporal sequence assignment and a mapping of ordered sequences, is presented. This decomposition permits the dynamic neural network to be realized as a cascade of a simple recurrent net followed by a non-recurrent one that yields considerable reduction in training complexity. A detailed performance evaluation of the present scheme is given by considering several trajectory generation experiments that highlight the strong points of this approach, which include simplicity and accuracy in training, flexibility to include control parameters in order to modify online the shape of the trajectory learned and the speed of repetition along a cyclic trajectory, and the possibility of learning both continuous and discontinuous trajectory patterns.