Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors

TL;DR

This paper introduces a rank-1 parameterization for Bayesian neural networks that enhances scalability and efficiency, combining benefits of BNNs and deep ensembles, and achieves state-of-the-art results on multiple benchmarks.

Contribution

The authors propose a novel rank-1 parameterization for BNNs and a memory-efficient mixture posterior approach, improving scalability and performance over existing methods.

Findings

Rank-1 BNNs outperform traditional BNNs in accuracy and calibration.

Mixture posteriors with minimal memory increase capture multiple modes effectively.

Achieves state-of-the-art results on ImageNet, CIFAR, and MIMIC-III datasets.

Abstract

Bayesian neural networks (BNNs) demonstrate promising success in improving the robustness and uncertainty quantification of modern deep learning. However, they generally struggle with underfitting at scale and parameter efficiency. On the other hand, deep ensembles have emerged as alternatives for uncertainty quantification that, while outperforming BNNs on certain problems, also suffer from efficiency issues. It remains unclear how to combine the strengths of these two approaches and remediate their common issues. To tackle this challenge, we propose a rank-1 parameterization of BNNs, where each weight matrix involves only a distribution on a rank-1 subspace. We also revisit the use of mixture approximate posteriors to capture multiple modes, where unlike typical mixtures, this approach admits a significantly smaller memory increase (e.g., only a 0.4% increase for a ResNet-50 mixture of size 10). We perform a systematic empirical study on the choices of prior, variational posterior, and methods to improve training. For ResNet-50 on ImageNet, Wide ResNet 28-10 on CIFAR-10/100, and an RNN on MIMIC-III, rank-1 BNNs achieve state-of-the-art performance across log-likelihood, accuracy, and calibration on the test sets and out-of-distribution variants.