mlsanityData to 7 Oct 2026

Bayesian Inference with Certifiable Adversarial Robustness

arXiv 2102.05289 ↗First posted 10 Feb 2021cs.LG cs.CRcited by 26

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Abstract (arXiv)

We consider adversarial training of deep neural networks through the lens of Bayesian learning, and present a principled framework for adversarial training of Bayesian Neural Networks (BNNs) with certifiable guarantees. We rely on techniques from constraint relaxation of non-convex optimisation problems and modify the standard cross-entropy error model to enforce posterior robustness to worst-case perturbations in ε-balls around input points. We illustrate how the resulting framework can be combined with methods commonly employed for approximate inference of BNNs. In an empirical investigation, we demonstrate that the presented approach enables training of certifiably robust models on MNIST, FashionMNIST and CIFAR-10 and can also be beneficial for uncertainty calibration. Our method is the first to directly train certifiable BNNs, thus facilitating their deployment in safety-critical applications.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 29 of its 44 references that are in the map. First posted on arXiv 10 Feb 2021.

Builds on

29 of 44 references.

References · 29

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2013Intriguing properties of neural networkscited by 5,114
  4. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  5. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  6. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
  7. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  8. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  9. 2019A Simple Baseline for Bayesian Uncertainty in Deep Learningcited by 555
  10. 2015Weight Uncertainty in Neural Networkscited by 554
  11. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  12. 2017Wild Patterns: Ten Years After the Rise of Adversarial Machine Learningcited by 411
17 more
  1. 2018On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Modelscited by 322
  2. 2017Formal Verification of Piece-Wise Linear Feed-Forward Neural Networkscited by 241
  3. 2019Practical Deep Learning with Bayesian Principlescited by 158
  4. 2018Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adamcited by 131
  5. 2017Noisy Natural Gradient as Variational Inferencecited by 94
  6. 2017Uncertainty-Aware Reinforcement Learning for Collision Avoidancecited by 86
  7. 2013Multi-digit Number Recognition from Street View Imagery using Deep Convolutional Neural Networkscited by 84
  8. 2018The Description Length of Deep Learning Modelscited by 71
  9. 2018Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Networkcited by 68
  10. 2018CNN-Cert: An Efficient Framework for Certifying Robustness of Convolutional Neural Networkscited by 50
  11. 2020Robustness of Bayesian Neural Networks to Gradient-Based Attackscited by 48
  12. 2020Probabilistic Safety for Bayesian Neural Networkscited by 41
  13. 2019Statistical Guarantees for the Robustness of Bayesian Neural Networkscited by 35
  14. 2020Handling the Positive-Definite Constraint in the Bayesian Learning Rulecited by 31
  15. 2018Robustness Guarantees for Bayesian Inference with Gaussian Processescited by 23
  16. 2018The Limitations of Model Uncertainty in Adversarial Settingscited by 14
  17. 2018Bayesian Adversarial Spheres: Bayesian Inference and Adversarial Examples in a Noiseless Settingcited by 8

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Citing papers per year: 2021: 5; 2022: 9; 2023: 7; 2024: 3; 2025: 1; 2026: 1.

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  1. 2021Dangers of Bayesian Model Averaging under Covariate Shiftcited by 31
  2. 2022Individual Fairness Guarantees for Neural Networkscited by 23
  3. 2022Robust Explanation Constraints for Neural Networkscited by 23
  4. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  5. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  6. 2022On the Robustness of Bayesian Neural Networks to Adversarial Attackscited by 12
  7. 2021DeepAdversaries: Examining the Robustness of Deep Learning Models for Galaxy Morphology Classificationcited by 10
  8. 2022Robust Bayesian Learning for Reliable Wireless AI: Framework and Applicationscited by 9
  9. 2023Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networkscited by 9
  10. 2021Certification of Iterative Predictions in Bayesian Neural Networkscited by 8
  11. 2023BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programmingcited by 8
  12. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
14 more
  1. 2021Adversarial Robustness Guarantees for Gaussian Processescited by 5
  2. 2022Sequential Bayesian Neural Subnetwork Ensemblescited by 5
  3. 2022Bayesian Learning with Information Gain Provably Bounds Risk for a Robust Adversarial Defensecited by 4
  4. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 4
  5. 2023Individual Fairness in Bayesian Neural Networkscited by 3
  6. 2024PID Control-Based Self-Healing to Improve the Robustness of Large Language Modelscited by 3
  7. 2026Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformerscited by 3
  8. 2023Use Perturbations when Learning from Explanationscited by 2
  9. 2023Certification of Distributional Individual Fairnesscited by 2
  10. 2024Attacking Bayes: On the Adversarial Robustness of Bayesian Neural Networkscited by 2
  11. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  12. 2024R'enyi Neural Processescited by 1
  13. 2022Robustness of Control Design via Bayesian Learningcited by 0
  14. 2025Support is All You Need for Certified VAE Trainingcited by 0