Transformed ℓ regularization for learning sparse deep neural networks.

Deep Neural Networks (DNNs) have achieved extraordinary success in numerous areas. However, DNNs often carry a large number of weight parameters, leading to the challenge of heavy memory and computation costs. Overfitting is another challenge for DNNs when the training data are insufficient. These challenges severely hinder the application of DNNs in resource-constrained platforms. In fact, many network weights are redundant and can be removed from the network without much loss of performance. In this paper, we introduce a new non-convex integrated transformed ℓ regularizer to promote sparsity for DNNs, which removes redundant connections and unnecessary neurons simultaneously. Specifically, we apply the transformed ℓ regularizer to the matrix space of network weights and utilize it to remove redundant connections. Besides, group sparsity is integrated to remove unnecessary neurons. An efficient stochastic proximal gradient algorithm is presented to solve the new model. To the best of our knowledge, this is the first work to develop a non-convex regularizer in sparse optimization based method to simultaneously promote connection-level and neuron-level sparsity for DNNs. Experiments on public datasets demonstrate the effectiveness of the proposed method.