# DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety

arXiv: https://arxiv.org/abs/2407.00616 · HTML: https://mlsanity.com/paper/2407.00616/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 42 references that are in the map.
- First posted on arXiv 30 Jun 2024.

## Builds on (most cited first, 26 of 26)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020)
- [Deep Ensembles from a Bayesian Perspective](https://mlsanity.com/paper/2105.13283/) (2021)
- [Bayesian Learning-Based Adaptive Control for Safety Critical Systems](https://mlsanity.com/paper/1910.02325/) (2019)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [Refining Control Barrier Functions through Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2204.12507/) (2022)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Robust Control Barrier Functions with Sector-Bounded Uncertainties](https://mlsanity.com/paper/2109.02537/) (2021)
- [Safe Control Synthesis with Uncertain Dynamics and Constraints](https://mlsanity.com/paper/2202.09557/) (2022)
- [ToolNet: Using Commonsense Generalization for Predicting Tool Use for Robot Plan Synthesis](https://mlsanity.com/paper/2006.05478/) (2020)
- [Control Barrier Functions for Systems with Multiple Control Inputs](https://mlsanity.com/paper/2203.07978/) (2022)

## Built on by (most cited first, 3 of 3)

- [Confidence Calibration in Vision-Language-Action Models](https://mlsanity.com/paper/2507.17383/) (2025)
- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)

## Abstract (arXiv)

Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.