Flat Seeking Bayesian Neural Networks

TL;DR

This paper introduces a sharpness-aware Bayesian posterior for neural networks, leading to flatter models with improved generalization, demonstrated through experiments with state-of-the-art Bayesian Neural Networks.

Contribution

It develops a novel sharpness-aware Bayesian inference framework that encourages flatter, better-generalizing neural network models, addressing limitations of traditional posterior formulations.

Findings

Sharpness-aware posterior models exhibit better flatness.

Flat-seeking Bayesian Neural Networks outperform baselines in all metrics.

The approach enhances model generalization through improved flatness.

Abstract

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the posterior distribution can be used for providing ensemble predictions and quantifying prediction uncertainty. It is well-known that deep learning models with lower sharpness have better generalization ability. However, existing posterior inferences are not aware of sharpness/flatness in terms of formulation, possibly leading to high sharpness for the models sampled from them. In this paper, we develop theories, the Bayesian setting, and the variational inference approach for the sharpness-aware posterior. Specifically, the models sampled from our sharpness-aware posterior, and the optimal approximate posterior estimating this sharpness-aware posterior, have better flatness, hence possibly possessing higher generalization ability. We conduct experiments by leveraging the sharpness-aware posterior with state-of-the-art Bayesian Neural Networks, showing that the flat-seeking counterparts outperform their baselines in all metrics of interest.