# Being a Bit Frequentist Improves Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2106.10065 · HTML: https://mlsanity.com/paper/2106.10065/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 59 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 30 of 38)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples](https://mlsanity.com/paper/1711.09325/) (2017)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Multi30K: Multilingual English-German Image Descriptions](https://mlsanity.com/paper/1605.00459/) (2016)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)

## Built on by (most cited first, 15 of 15)

- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [A Simple Approach to Improve Single-Model Deep Uncertainty via Distance-Awareness](https://mlsanity.com/paper/2205.00403/) (2022)
- [Posterior Refinement Improves Sample Efficiency in Bayesian Neural Networks](https://mlsanity.com/paper/2205.10041/) (2022)
- [Uncertainty-Aware Graph Neural Networks: A Multi-Hop Evidence Fusion Approach](https://mlsanity.com/paper/2506.13083/) (2025)
- [Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization](https://mlsanity.com/paper/2304.08309/) (2023)
- [On the Disconnect Between Theory and Practice of Neural Networks: Limits of the NTK Perspective](https://mlsanity.com/paper/2310.00137/) (2023)
- [Robustness to corruption in pre-trained Bayesian neural networks](https://mlsanity.com/paper/2206.12361/) (2022)
- [Bayes without Underfitting: Fully Correlated Deep Learning Posteriors via Alternating Projections](https://mlsanity.com/paper/2410.16901/) (2024)
- [VIKING: Deep variational inference with stochastic projections](https://mlsanity.com/paper/2510.23684/) (2025)
- [Flat Posterior Does Matter For Bayesian Model Averaging](https://mlsanity.com/paper/2406.15664/) (2024)
- [Be Bayesian by Attachments to Catch More Uncertainty](https://mlsanity.com/paper/2310.13027/) (2023)
- [Preventing Arbitrarily High Confidence on Far-Away Data in Point-Estimated Discriminative Neural Networks](https://mlsanity.com/paper/2311.03683/) (2023)

## Abstract (arXiv)

Despite their compelling theoretical properties, Bayesian neural networks (BNNs) tend to perform worse than frequentist methods in classification-based uncertainty quantification (UQ) tasks such as out-of-distribution (OOD) detection. In this paper, based on empirical findings in prior works, we hypothesize that this issue is because even recent Bayesian methods have never considered OOD data in their training processes, even though this "OOD training" technique is an integral part of state-of-the-art frequentist UQ methods. To validate this, we treat OOD data as a first-class citizen in BNN training by exploring four different ways of incorporating OOD data into Bayesian inference. We show in extensive experiments that OOD-trained BNNs are competitive to recent frequentist baselines. This work thus provides strong baselines for future work in Bayesian UQ.