A Boundedness of a Batch Gradient Method with Smoothing L_(1?2)Regularization for Pi-sigma Neural Networks

This paper considers a batch gradient method with L_ (12) regularization for Pi sigma neural networks. In origin, by introducing an L_ (12) regularization term involves absolute value and is not differentiable into the error function. A key point of this paper, specifically, the smoothing L_ (12) regularization is a term proportional to the norm of the weights. The role of the smoothing L_ (12) regularization term is to control the magnitude of the weights and to improve the generalization performance of the networks. The weights are proved to be bounded during the training process, thus the conditions that are required for convergence analysis of batch gradient method in literature are simplified.