# The Epistemic Uncertainty Hole: an issue of Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2407.01985 · HTML: https://mlsanity.com/paper/2407.01985/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 2 Jul 2024.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [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)
- [ResMLP: Feedforward networks for image classification with data-efficient training](https://mlsanity.com/paper/2105.03404/) (2021)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Estimating Risk and Uncertainty in Deep Reinforcement Learning](https://mlsanity.com/paper/1905.09638/) (2019)
- [A Comparison of Uncertainty Estimation Approaches in Deep Learning Components for Autonomous Vehicle Applications](https://mlsanity.com/paper/2006.15172/) (2020)

## Built on by (most cited first, 11 of 11)

- [(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models](https://mlsanity.com/paper/2409.02628/) (2024)
- [Position: Epistemic uncertainty estimation methods are fundamentally incomplete](https://mlsanity.com/paper/2505.23506/) (2025)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [From predictions to confidence intervals: an empirical study of conformal prediction methods for in-context learning](https://mlsanity.com/paper/2504.15722/) (2025)
- [Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?](https://mlsanity.com/paper/2605.22593/) (2026)
- [Trust Me, I Know the Way: Predictive Uncertainty in the Presence of Shortcut Learning](https://mlsanity.com/paper/2502.09137/) (2025)
- [Scaling Laws for Uncertainty in Deep Learning](https://mlsanity.com/paper/2506.09648/) (2025)
- [Rethinking Uncertainty Quantification and Entanglement in Image Segmentation](https://mlsanity.com/paper/2603.18792/) (2026)
- [Can we trust our models? Epistemic calibration in second-order classification](https://mlsanity.com/paper/2606.10777/) (2026)
- [ST-LoRA: Single Trajectory LoRA Ensemble for Uncertainty Aware Agricultural Segmentation](https://mlsanity.com/paper/2608.01530/) (2026)
- [Structural Limits of the Information-Theoretic Uncertainty Decomposition](https://mlsanity.com/paper/2609.39591/) (2026)

## Abstract (arXiv)

Bayesian Deep Learning (BDL) gives access not only to aleatoric uncertainty, as standard neural networks already do, but also to epistemic uncertainty, a measure of confidence a model has in its own predictions. In this article, we show through experiments that the evolution of epistemic uncertainty metrics regarding the model size and the size of the training set, goes against theoretical expectations. More precisely, we observe that the epistemic uncertainty collapses literally in the presence of large models and sometimes also of little training data, while we expect the exact opposite behaviour. This phenomenon, which we call "epistemic uncertainty hole", is all the more problematic as it undermines the entire applicative potential of BDL, which is based precisely on the use of epistemic uncertainty. As an example, we evaluate the practical consequences of this uncertainty hole on one of the main applications of BDL, namely the detection of out-of-distribution samples