mlsanityData to 14 Oct 2026

Robustness of Bayesian Neural Networks to Gradient-Based Attacks

arXiv 2002.04359 ↗First posted 11 Feb 2020cs.LG stat.MLcited by 48

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Abstract (arXiv)

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.

Key facts. Cited by 48 papers in the map (data through 14 Oct 2026). First posted on arXiv 11 Feb 2020.

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Citing papers per year: 2021: 13; 2022: 9; 2023: 17; 2024: 6; 2025: 2; 2026: 1.

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  1. 2021Advances in adversarial attacks and defenses in computer vision: A surveycited by 127
  2. 2023Making Substitute Models More Bayesian Can Enhance Transferability of Adversarial Examplescited by 32
  3. 2021Dangers of Bayesian Model Averaging under Covariate Shiftcited by 31
  4. 2021Bayesian Inference with Certifiable Adversarial Robustnesscited by 26
  5. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  6. 2022Audio-based AI classifiers show no evidence of improved COVID-19 screening over simple symptoms checkerscited by 12
  7. 2022Robust Bayesian Learning for Reliable Wireless AI: Framework and Applicationscited by 9
  8. 2022A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunitiescited by 9
  9. 2023Bayesian Neural Networks Avoid Encoding Complex and Perturbation-Sensitive Conceptscited by 9
  10. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  11. 2021Certification of Iterative Predictions in Bayesian Neural Networkscited by 8
  12. 2023BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programmingcited by 8
36 more
  1. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  2. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  3. 2021Adversarial for Good? How the Adversarial ML Community's Values Impede Socially Beneficial Uses of Attackscited by 5
  4. 2023A Bayesian approach to quantifying uncertainties and improving generalizability in traffic prediction modelscited by 5
  5. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 5
  6. 2024Tight Verification of Probabilistic Robustness in Bayesian Neural Networkscited by 5
  7. 2021Robustness of Bayesian Neural Networks to White-Box Adversarial Attackscited by 4
  8. 2022Bayesian Learning with Information Gain Provably Bounds Risk for a Robust Adversarial Defensecited by 4
  9. 2021The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networkscited by 3
  10. 2022Learning Uncertainty with Artificial Neural Networks for Improved Predictive Process Monitoringcited by 3
  11. 2023On the Robustness of Randomized Ensembles to Adversarial Perturbationscited by 3
  12. 2023Individual Fairness in Bayesian Neural Networkscited by 3
  13. 2023Improving Transferability of Adversarial Examples via Bayesian Attackscited by 3
  14. 2025Poisoning Bayesian Inference via Data Deletion and Replicationcited by 3
  15. 2026Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformerscited by 3
  16. 2021Adversarial Examples Detection with Bayesian Neural Networkcited by 2
  17. 2023Certification of Distributional Individual Fairnesscited by 2
  18. 2024Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networkscited by 2
  19. 2024On the Robustness of Adversarial Training Against Uncertainty Attackscited by 2
  20. 2021Random Projections for Improved Adversarial Robustnesscited by 1
  21. 2021Resilience of Bayesian Layer-Wise Explanations under Adversarial Attackscited by 1
  22. 2021Localized Uncertainty Attackscited by 1
  23. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  24. 2022Success of Uncertainty-Aware Deep Models Depends on Data Manifold Geometrycited by 1
  25. 2022Probabilistic Inverse Modeling: An Application in Hydrologycited by 1
  26. 2023Post-train Black-box Defense via Bayesian Boundary Correctioncited by 1
  27. 2023Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustnesscited by 1
  28. 2024On the Convergence of Locally Adaptive and Scalable Diffusion-Based Sampling Methods for Deep Bayesian Neural Network Posteriorscited by 1
  29. 2021Machine learning in the social and health sciencescited by 0
  30. 2023Attacks on Online Learners: a Teacher-Student Analysiscited by 0
  31. 2023Blending adversarial training and representation-conditional purification via aggregation improves adversarial robustnesscited by 0
  32. 2023Uncertainty Quantification in Inverse Models in Hydrologycited by 0
  33. 2023Bayesian Neural Networks: A Min-Max Game Frameworkcited by 0
  34. 2024Transferable 3D Adversarial Shape Completion using Diffusion Modelscited by 0
  35. 2024Variational Bayesian Bow tie Neural Networks with Shrinkagecited by 0
  36. 2025Feature Statistics with Uncertainty Help Adversarial Robustnesscited by 0