Spike-and-slab shrinkage priors for structurally sparse Bayesian neural networks
This work addresses computational challenges in deep learning for applications requiring low latency and energy efficiency, but it is incremental as it adapts existing shrinkage techniques to Bayesian neural networks.
The paper tackles the problem of network complexity and computational inefficiency in deep learning by proposing structurally sparse Bayesian neural networks that prune excessive nodes using spike-and-slab priors, achieving competitive performance in prediction accuracy, model compression, and inference latency compared to baselines.
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 over-parameterized 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 paper, we explore two well-established shrinkage techniques, Lasso and Horseshoe, for model compression in Bayesian neural networks. To this end, we propose structurally sparse Bayesian neural networks which systematically prune excessive nodes with (i) Spike-and-Slab Group Lasso (SS-GL), and (ii) Spike-and-Slab 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, layer-wise node cardinalities, and bounds on the network weights. We empirically demonstrate the competitive performance of our models compared to the baseline models in prediction accuracy, model compression, and inference latency.