Sparse Deep Learning Models with the $\ell_1$ Regularization
This work addresses the need for efficient sparse models in deep learning, though it is incremental as it builds on existing regularization methods.
The paper tackles the problem of controlling sparsity in neural networks by studying how regularization parameters affect sparsity levels, and it develops algorithms to select parameters that achieve predetermined sparsity with satisfactory accuracy, as demonstrated in numerical experiments.
Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive the $\ell_1$-norm sparsity-promoting deep learning models including single and multiple regularization parameters models, from a statistical viewpoint. We then characterize the sparsity level of a regularized neural network in terms of the choice of the regularization parameters. Based on the characterizations, we develop iterative algorithms for selecting regularization parameters so that the weight parameters of the resulting deep neural network enjoy prescribed sparsity levels. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithms in choosing desirable regularization parameters and obtaining corresponding neural networks having both of predetermined sparsity levels and satisfactory approximation accuracy.