Batch gradient method with smoothing L1/2L1/2 regularization for training of feedforward neural networks

The aim of this paper is to develop a novel method to prune feedforward neural networks by introducing an L1/2L1/2 regularization term into the error function. This procedure forces weights to become smaller during the training and can eventually removed after the training. The usual L1/2L1/2 regularization term involves absolute values and is not differentiable at the origin, which typically causes oscillation of the gradient of the error function during the training. A key point of this paper is to modify the usual L1/2L1/2 regularization term by smoothing it at the origin. This approach offers the following three advantages: First, it removes the oscillation of the gradient value. Secondly, it gives better pruning, namely the final weights to be removed are smaller than those produced through the usual L1/2L1/2 regularization. Thirdly, it makes it possible to prove the convergence of the training. Supporting numerical examples are also provided.