Strong Convergence of Gradient Methods for BP Networks Training

Gradient method is a simple and popular learning algorithm for feedforward neural network (FNN) training. Some strong convergence results for both batch and online gradient methods are established based on existing weak convergence results. In particular, it is shown that for gradient-penalty algorithms, strong convergence results are immediate consequences of weak convergence results. For other batch and online gradient methods, the weak convergence plus the boundedness of the weights leads to the strong convergence. A class of gradient methods for general optimization problems is also considered, and some strong convergence results are obtained under mild conditions