mlsanityData to 7 Oct 2026

Probabilistic Safety for Bayesian Neural Networks

arXiv 2004.10281 ↗First posted 21 Apr 2020cs.LG stat.MLcited by 41

Not on the map. Why?

Abstract (arXiv)

We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, T subseteq ℝm, we study the probability w.r.t. the BNN posterior that all the points in T are mapped to the same region S in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Apr 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 5; 2023: 13; 2024: 8; 2025: 4; 2026: 4.

41 papers.

Sort:

By area:

  1. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  2. 2023Making Substitute Models More Bayesian Can Enhance Transferability of Adversarial Examplescited by 32
  3. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  4. 2022Individual Fairness Guarantees for Neural Networkscited by 23
  5. 2022Robust Explanation Constraints for Neural Networkscited by 23
  6. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  7. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  8. 2024Certified Robustness to Data Poisoning in Gradient-Based Trainingcited by 17
  9. 2023Provable Preimage Under-Approximation for Neural Networks (Full Version)cited by 13
  10. 2021Towards Practical Robustness Analysis for DNNs based on PAC-Model Learningcited by 12
  11. 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 12
  12. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
29 more
  1. 2023Distributionally Robust Statistical Verification with Imprecise Neural Networkscited by 12
  2. 2021Certification of Iterative Predictions in Bayesian Neural Networkscited by 8
  3. 2023BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programmingcited by 8
  4. 2023TrajPAC: Towards Robustness Verification of Pedestrian Trajectory Prediction Modelscited by 8
  5. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  6. 2023When to Trust AI: Advances and Challenges for Certification of Neural Networkscited by 6
  7. 2024Certification for Differentially Private Prediction in Gradient-Based Trainingcited by 6
  8. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  9. 2024Tight Verification of Probabilistic Robustness in Bayesian Neural Networkscited by 5
  10. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 4
  11. 2024Solving Probabilistic Verification Problems of Neural Networks using Branch and Boundcited by 4
  12. 2021The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networkscited by 3
  13. 2023Individual Fairness in Bayesian Neural Networkscited by 3
  14. 2023Improving Transferability of Adversarial Examples via Bayesian Attackscited by 3
  15. 2024Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selectioncited by 3
  16. 2026Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformerscited by 3
  17. 2023Incremental Satisfiability Modulo Theory for Verification of Deep Neural Networkscited by 2
  18. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  19. 2025Verification of Bit-Flip Attacks against Quantized Neural Networkscited by 2
  20. 2025Provably Safe Model Updatescited by 2
  21. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  22. 2025Certified Guidance for Planning with Deep Generative Modelscited by 1
  23. 2023General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothingcited by 0
  24. 2024Patch Synthesis for Property Repair of Deep Neural Networkscited by 0
  25. 2024Risk-Averse Certification of Bayesian Neural Networkscited by 0
  26. 2025Support is All You Need for Certified VAE Trainingcited by 0
  27. 2026SafeAdapt: Provably Safe Policy Updates in Deep Reinforcement Learningcited by 0
  28. 2026Certified Uncertainty Propagation in One-Shot Federated Bayesian Models via Posterior Event Transportcited by 0
  29. 2026Certification-Based Differentially Private Learningcited by 0