A method includes: providing a deep neural networks (DNN) model comprising a plurality of layers, each layer of the plurality of layers includes a plurality of nodes; sampling a change of a weight for each of a plurality of weights based on a distribution function, each weight of the plurality of weights corresponds to each node of the plurality of nodes; updating the weight with the change of the weight multiplied by a sign of the weight; and training the DNN model by iterating the steps of sampling the change and updating the weight. The plurality of weights has a high rate of sparsity after the training.