# Certification of Iterative Predictions in Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2105.10134 · HTML: https://mlsanity.com/paper/2105.10134/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 21 May 2021.

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

- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam](https://mlsanity.com/paper/1806.04854/) (2018)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network](https://mlsanity.com/paper/1810.01279/) (2018)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [Learning and Policy Search in Stochastic Dynamical Systems with Bayesian Neural Networks](https://mlsanity.com/paper/1605.07127/) (2016)
- [Robustness of Bayesian Neural Networks to Gradient-Based Attacks](https://mlsanity.com/paper/2002.04359/) (2020)
- [Probabilistic Safety for Bayesian Neural Networks](https://mlsanity.com/paper/2004.10281/) (2020)
- [Formal Verification of Neural Network Controlled Autonomous Systems](https://mlsanity.com/paper/1810.13072/) (2018)
- [Certified Reinforcement Learning with Logic Guidance](https://mlsanity.com/paper/1902.00778/) (2019)
- [Statistical Guarantees for the Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/1903.01980/) (2019)
- [Bayesian Inference with Certifiable Adversarial Robustness](https://mlsanity.com/paper/2102.05289/) (2021)
- [Robustness Guarantees for Bayesian Inference with Gaussian Processes](https://mlsanity.com/paper/1809.06452/) (2018)
- [Probabilistic Guarantees for Safe Deep Reinforcement Learning](https://mlsanity.com/paper/2005.07073/) (2020)
- [Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems](https://mlsanity.com/paper/1901.01576/) (2019)
- [Adversarial Robustness Guarantees for Classification with Gaussian Processes](https://mlsanity.com/paper/1905.11876/) (2019)
- [Safe Policy Search with Gaussian Process Models](https://mlsanity.com/paper/1712.05556/) (2017)
- [Safety Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2004.01821/) (2020)
- [How Wrong Am I? - Studying Adversarial Examples and their Impact on Uncertainty in Gaussian Process Machine Learning Models](https://mlsanity.com/paper/1711.06598/) (2017)
- [Data-Efficient Reinforcement Learning in Continuous-State POMDPs](https://mlsanity.com/paper/1602.02523/) (2016)

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

- [Adversarial Robustness Certification for Bayesian Neural Networks](https://mlsanity.com/paper/2306.13614/) (2023)
- [When to Trust AI: Advances and Challenges for Certification of Neural Networks](https://mlsanity.com/paper/2309.11196/) (2023)
- [Probabilistic Reach-Avoid for Bayesian Neural Networks](https://mlsanity.com/paper/2310.01951/) (2023)
- [Provably Safe Model Updates](https://mlsanity.com/paper/2512.01899/) (2025)
- [Risk-Averse Certification of Bayesian Neural Networks](https://mlsanity.com/paper/2411.19729/) (2024)
- [LTL Verification of Memoryful Neural Agents](https://mlsanity.com/paper/2503.02512/) (2025)
- [SafeAdapt: Provably Safe Policy Updates in Deep Reinforcement Learning](https://mlsanity.com/paper/2604.09452/) (2026)
- [Hybrid Robustness Verification for Spatio-Temporal Neural Networks](https://mlsanity.com/paper/2606.09746/) (2026)

## Abstract (arXiv)

We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than 10 dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.