Spike-and-Slab Shrinkage Priors for Structurally Sparse Bayesian Neural Networks

Network complexity and computational efficiency have become increasingly significant aspects of deep learning. Sparse deep learning addresses these challenges by recovering a sparse representation of the underlying target function by reducing heavily overparameterized deep neural networks. Specifically, deep neural architectures compressed via structured sparsity (e.g., node sparsity) provide low-latency inference, higher data throughput, and reduced energy consumption. In this article, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks (BNNs). To this end, we propose structurally sparse BNNs, which systematically prune excessive nodes with the following: 1) spike-and-slab group Lasso (SS-GL) and 2) SS group Horseshoe (SS-GHS) priors, and develop computationally tractable variational inference, including continuous relaxation of Bernoulli variables. We establish the contraction rates of the variational posterior of our proposed models as a function of the network topology, layerwise node cardinalities, and bounds on the network weights. We empirically demonstrate the competitive performance of our models compared with the baseline models in prediction accuracy, model compression, and inference latency.