# Gradient-based Uncertainty Attribution for Explainable Bayesian Deep Learning

arXiv: https://arxiv.org/abs/2304.04824 · HTML: https://mlsanity.com/paper/2304.04824/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 10 Apr 2023.

## Builds on (most cited first, 30 of 31)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Snapshot Ensembles: Train 1, get M for free](https://mlsanity.com/paper/1704.00109/) (2017)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Understanding Deep Networks via Extremal Perturbations and Smooth Masks](https://mlsanity.com/paper/1910.08485/) (2019)
- [Real Time Image Saliency for Black Box Classifiers](https://mlsanity.com/paper/1705.07857/) (2017)
- [Full-Gradient Representation for Neural Network Visualization](https://mlsanity.com/paper/1905.00780/) (2019)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Hyperparameter Ensembles for Robustness and Uncertainty Quantification](https://mlsanity.com/paper/2006.13570/) (2020)
- [Guided Integrated Gradients: An Adaptive Path Method for Removing Noise](https://mlsanity.com/paper/2106.09788/) (2021)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [Attribution in Scale and Space](https://mlsanity.com/paper/2004.03383/) (2020)
- [Robust Explainability: A Tutorial on Gradient-Based Attribution Methods for Deep Neural Networks](https://mlsanity.com/paper/2107.11400/) (2021)
- [Deep Sub-Ensembles for Fast Uncertainty Estimation in Image Classification](https://mlsanity.com/paper/1910.08168/) (2019)
- [Diverse, Global and Amortised Counterfactual Explanations for Uncertainty Estimates](https://mlsanity.com/paper/2112.02646/) (2021)
- [Scalable Uncertainty for Computer Vision with Functional Variational Inference](https://mlsanity.com/paper/2003.03396/) (2020)
- [MFPP: Morphological Fragmental Perturbation Pyramid for Black-Box Model Explanations](https://mlsanity.com/paper/2006.02659/) (2020)
- [Attribution of Predictive Uncertainties in Classification Models](https://mlsanity.com/paper/2107.08756/) (2021)

## Built on by (most cited first, 8 of 8)

- [Identifying Drivers of Predictive Aleatoric Uncertainty](https://mlsanity.com/paper/2312.07252/) (2023)
- [Conceptualizing Uncertainty: A Concept-based Approach to Explaining Uncertainty](https://mlsanity.com/paper/2503.03443/) (2025)
- [PEdger++: Practical Edge Detection via Assembling Cross Information](https://mlsanity.com/paper/2508.11961/) (2025)
- [Uncertainty Quantification in Federated Granger Causality Learning](https://mlsanity.com/paper/2602.13004/) (2026)
- [No Single Metric Tells the Whole Story: A Multi-Dimensional Evaluation Framework for Uncertainty Attributions](https://mlsanity.com/paper/2603.24524/) (2026)
- [Visualizing Uncertainty: Spatial Maps of Missing and Conflicting Evidence in Deep Learning](https://mlsanity.com/paper/2606.15767/) (2026)
- [Attribution and Uncertainty Behavior of Learned Residual Gyro Correction for Gyro-Stellar Estimation](https://mlsanity.com/paper/2607.24608/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While current efforts focus on improving uncertainty quantification accuracy and efficiency, there is a need to identify uncertainty sources and take actions to mitigate their effects on predictions. Therefore, we propose to develop explainable and actionable Bayesian deep learning methods to not only perform accurate uncertainty quantification but also explain the uncertainties, identify their sources, and propose strategies to mitigate the uncertainty impacts. Specifically, we introduce a gradient-based uncertainty attribution method to identify the most problematic regions of the input that contribute to the prediction uncertainty. Compared to existing methods, the proposed UA-Backprop has competitive accuracy, relaxed assumptions, and high efficiency. Moreover, we propose an uncertainty mitigation strategy that leverages the attribution results as attention to further improve the model performance. Both qualitative and quantitative evaluations are conducted to demonstrate the effectiveness of our proposed methods.