Global convergence of training methods for neural networks based on the state-estimation

Although the EKF (Extended Kalman Filter) has been widely used as a training method for neural networks (NN), it is known to have a poor robustness to disturbances. Recently an EHF(Extended H-infinity Filter)-based training method was proposed, which is improved in the robustness to the nature of noises. However, its convergence property is not yet known. In this paper, we show that EHF-based method can be regarded as a minimization method of the least square problem and that it has the deterministic global convergence property. Moreover, we propose a new simplified method for EKF or EHF-based methods for NN and verify the efficiency of the proposed method.