We propose an efficient method to learn both unstructured and structured sparse neural networks during training, utilizing a novel generalization of the sparse envelope function (SEF) used as a regularizer, termed {\itshape{weighted group sparse envelope function}} (WGSEF). The WGSEF acts as a neuron group selector, which is leveraged to induce structured sparsity. The method ensures a hardware-friendly structured sparsity of a deep neural network (DNN) to efficiently accelerate the DNN's evaluation. Notably, the method is adaptable, letting any hardware specify group definitions, such as filters, channels, filter shapes, layer depths, a single parameter (unstructured), etc. Owing to the WGSEF's properties, the proposed method allows to a pre-define sparsity level that would be achieved at the training convergence, while maintaining negligible network accuracy degradation or even improvement in the case of redundant parameters. We introduce an efficient technique to calculate the exact value of the WGSEF along with its proximal operator in a worst-case complexity of $O(n)$, where $n$ is the total number of group variables. In addition, we propose a proximal-gradient-based optimization method to train the model, that is, the non-convex minimization of the sum of the neural network loss and the WGSEF. Finally, we conduct an experiment and illustrate the efficiency of our proposed technique in terms of the completion ratio, accuracy, and inference latency.
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