Training Bayesian Neural Networks with Sparse Subspace Variational Inference

Junbo Li, Zichen Miao, Qiang Qiu, Ruqi Zhang

Keywords: Bayesian neural networks, sparse Bayesian learning, variational inference

TL;DR: We propose the first fully sparse Bayesian training framework that achieves state-of-the-art performance in the realm of sparse Bayesian neural networks.

Abstract: Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly introducing sparsity throughout the training or by post-training compression of dense BNNs. The dilemma of how to cut down massive training costs remains, particularly given the requirement to learn about the uncertainty. To solve this challenge, we introduce Sparse Subspace Variational Inference (SSVI), the first fully sparse BNN framework that maintains a consistently sparse Bayesian model throughout the training and inference phases. Starting from a randomly initialized low-dimensional sparse subspace, our approach alternately optimizes the sparse subspace basis selection and its associated parameters. While basis selection is characterized as a non-differentiable problem, we approximate the optimal solution with a removal-and-addition strategy, guided by novel criteria based on weight distribution statistics. Our extensive experiments show that SSVI sets new benchmarks in crafting sparse BNNs, achieving, for instance, a 10-20× compression in model size with under 3% performance drop, and up to 20× FLOPs reduction during training. Remarkably, SSVI also demonstrates enhanced robustness to hyperparameters, reducing the need for intricate tuning in VI and occasionally even surpassing VI-trained dense BNNs.

Submission Number: 26