Stabilising priors for robust Bayesian deep learning

TL;DR

This paper introduces self-stabilising priors for Bayesian neural networks, enhancing training stability and robustness, especially for deep architectures and noisy data, by reformulating the ELBO and adjusting priors before each forward pass.

Contribution

It proposes a novel stabilising prior that influences signal propagation in BNNs, enabling the training of deeper networks with improved convergence and robustness.

Findings

Enhanced training stability for deep BNNs

Improved robustness in noisy settings

Facilitated training of deeper architectures

Abstract

Bayesian neural networks (BNNs) have developed into useful tools for probabilistic modelling due to recent advances in variational inference enabling large scale BNNs. However, BNNs remain brittle and hard to train, especially: (1) when using deep architectures consisting of many hidden layers and (2) in situations with large weight variances. We use signal propagation theory to quantify these challenges and propose self-stabilising priors. This is achieved by a reformulation of the ELBO to allow the prior to influence network signal propagation. Then, we develop a stabilising prior, where the distributional parameters of the prior are adjusted before each forward pass to ensure stability of the propagating signal. This stabilised signal propagation leads to improved convergence and robustness making it possible to train deeper networks and in more noisy settings.