Hierarchical Group Sparse Regularization for Deep Convolutional Neural Networks

In a deep neural network (DNN), the number of the parameters is usually huge to get high learning performances. For that reason, it costs a lot of memory and substantial computational resources, and also causes overfitting. It is known that some parameters are redundant and can be removed from the network without decreasing performance. Many sparse regularization criteria have been proposed to solve this problem. In a convolutional neural network (CNN), group sparse regularizations are often used to remove unnecessary subsets of the weights, such as filters or channels. When we apply a group sparse regularization for the weights connected to a neuron as a group, each convolution filter is not treated as a target group in the regularization. In this paper, we introduce the concept of hierarchical grouping to solve this problem, and we propose several hierarchical group sparse regularization criteria for CNNs. Our proposed the hierarchical group sparse regularization can treat the weight for the input-neuron or the output-neuron as a group and convolutional filter as a group in the same group to prune the unnecessary subsets of weights. As a result, we can prune the weights more adequately depending on the structure of the network and the number of channels keeping high performance. In the experiment, we investigate the effectiveness of the proposed sparse regularizations through intensive comparison experiments on public datasets with several network architectures. Code is available on GitHub: "https://github.com/K-Mitsuno/hierarchical-group-sparse-regularization"