Training Recurrent Networks Using the Extended Kalman Filter

The extended Kalman lter (EKF) can be used as an on-line algorithm to determine the weights in a recurrent network given target outputs as it runs. This paper notes some relationships between the EKF as applied to recurrent net learning and some simpler techniques that are more widely used. In particular, making certain simpliications to the EKF gives rise to an algorithm essentially identical to the real-time recurrent learning (RTRL) algorithm. Since the EKF involves adjusting unit activity in the network, it also provides a principled generalization of the teacher forcing technique. Prelinary simulation experiments on simple nite-state Boolean tasks indicate that the EKF can provide substantial speed-up in number of time steps required for training on such problems when compared with simpler on-line gradient algorithms. The computational requirements of the EKF are steep, but turn out to scale with network size at the same rate as RTRL. These observations are intended to provide insights that may lead to recurrent net training techniques that allow better control over the tradeoo between computational cost and convergence time.