Pruning is one of the effective techniques for improving the generalization error of neural networks. Existing pruning techniques are derived mainly from the viewpoint of energy minimization, which is commonly used in gradient-based learning methods. In recurrent networks, extended Kalman filter (EKF)–based training has been shown to be superior to gradient-based learning methods in terms of speed. This article explains a pruning procedure for recurrent neural networks using EKF training. The sensitivity of a posterior probability is used as a measure of the importance of a weight instead of error sensitivity since posterior probability density is readily obtained from this training method. The pruning procedure is tested using three problems: (1) the prediction of a simple linear time series, (2) the identification of a nonlinear system, and (3) the prediction of an exchange-rate time series. Simulation results demonstrate that the proposed pruning method is able to reduce the number of parameters and improve the generalization ability of a recurrent network.
Nonfragile H∞ State Estimation for Recurrent Neural Networks With Time-Varying Delays: On Proportional-Integral Observer Design