Explicit Group Sparse Projection with Applications to Deep Learning and NMF
This work addresses the problem of efficient sparsity control in machine learning for researchers and practitioners, though it is incremental as it builds on existing projection methods.
The authors tackled the problem of achieving a desired average sparsity level for a group of vectors by designing a new explicit sparse projection method, which in deep neural network pruning on ResNet50 produced significantly higher accuracies at corresponding sparsity values compared to existing competitors.
We design a new sparse projection method for a set of vectors that guarantees a desired average sparsity level measured leveraging the popular Hoyer measure (an affine function of the ratio of the $\ell_1$ and $\ell_2$ norms). Existing approaches either project each vector individually or require the use of a regularization parameter which implicitly maps to the average $\ell_0$-measure of sparsity. Instead, in our approach we set the sparsity level for the whole set explicitly and simultaneously project a group of vectors with the sparsity level of each vector tuned automatically. We show that the computational complexity of our projection operator is linear in the size of the problem. Additionally, we propose a generalization of this projection by replacing the $\ell_1$ norm by its weighted version. We showcase the efficacy of our approach in both supervised and unsupervised learning tasks on image datasets including CIFAR10 and ImageNet. In deep neural network pruning, the sparse models produced by our method on ResNet50 have significantly higher accuracies at corresponding sparsity values compared to existing competitors. In nonnegative matrix factorization, our approach yields competitive reconstruction errors against state-of-the-art algorithms.