mlsanityData to 7 Oct 2026

Provable robustness against all adversarial lp-perturbations for p≥ 1

arXiv 1905.11213 ↗First posted 27 May 2019cs.LG cs.CR stat.MLcited by 39

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Abstract (arXiv)

In recent years several adversarial attacks and defenses have been proposed. Often seemingly robust models turn out to be non-robust when more sophisticated attacks are used. One way out of this dilemma are provable robustness guarantees. While provably robust models for specific lp-perturbation models have been developed, we show that they do not come with any guarantee against other lq-perturbations. We propose a new regularization scheme, MMR-Universal, for ReLU networks which enforces robustness wrt l1- and l_∞-perturbations and show how that leads to the first provably robust models wrt any lp-norm for p≥ 1.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2021: 12; 2022: 9; 2023: 8; 2024: 6; 2025: 3; 2026: 1.

39 papers.

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  1. 2021Advances in adversarial attacks and defenses in computer vision: A surveycited by 127
  2. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
  3. 2022A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologiescited by 44
  4. 2021Consistency Regularization for Adversarial Robustnesscited by 42
  5. 2021A Comprehensive Evaluation Framework for Deep Model Robustnesscited by 41
  6. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  7. 2021Adversarial Robustness against Multiple and Single lp-Threat Models via Quick Fine-Tuning of Robust Classifierscited by 23
  8. 2021Adaptive Image Transformations for Transfer-based Adversarial Attackcited by 22
  9. 2025X-Transfer Attacks: Towards Super Transferable Adversarial Attacks on CLIPcited by 21
  10. 2022UniCR: Universally Approximated Certified Robustness via Randomized Smoothingcited by 10
  11. 2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
  12. 2023Multi-scale Diffusion Denoised Smoothingcited by 9
27 more
  1. 2024FullLoRA: Efficiently Boosting the Robustness of Pretrained Vision Transformerscited by 9
  2. 2022Formulating Robustness Against Unforeseen Attackscited by 8
  3. 2023MultiRobustBench: Benchmarking Robustness Against Multiple Attackscited by 7
  4. 2021Relaxing Local Robustnesscited by 6
  5. 2021Selection of Source Images Heavily Influences the Effectiveness of Adversarial Attackscited by 6
  6. 2022Learning Sample Reweighting for Accuracy and Adversarial Robustnesscited by 6
  7. 2023Optimization and Optimizers for Adversarial Robustnesscited by 6
  8. 2021The Fundamental Limits of Interval Arithmetic for Neural Networkscited by 4
  9. 2022Reverse Engineering ℓp attacks: A block-sparse optimization approach with recovery guaranteescited by 4
  10. 2023Certified Adversarial Robustness Within Multiple Perturbation Boundscited by 4
  11. 2021The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networkscited by 3
  12. 2022Provably Adversarially Robust Nearest Prototype Classifierscited by 2
  13. 2022Multiple Perturbation Attack: Attack Pixelwise Under Different ℓp-norms For Better Adversarial Performancecited by 2
  14. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  15. 2025Adapting to Evolving Adversaries with Regularized Continual Robust Trainingcited by 2
  16. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  17. 2023PRAT: PRofiling Adversarial aTtackscited by 1
  18. 2024Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attackscited by 1
  19. 2024Position: Towards Resilience Against Adversarial Examplescited by 1
  20. 2024Deep Adversarial Defense Against Multilevel-Lp Attackscited by 1
  21. 2025Defending Against Frequency-Based Attacks with Diffusion Modelscited by 1
  22. 2026Efficient Adversarial Training via Criticality-Aware Fine-Tuningcited by 1
  23. 2021Improving Local Effectiveness for Global robust trainingcited by 0
  24. 2023Bridging Models to Defend: A Population-Based Strategy for Robust Adversarial Defensecited by 0
  25. 2023Cooperation or Competition: Avoiding Player Domination for Multi-Target Robustness via Adaptive Budgetscited by 0
  26. 2023Parameter-Saving Adversarial Training: Reinforcing Multi-Perturbation Robustness via Hypernetworkscited by 0
  27. 2024Towards Robust Domain Generation Algorithm Classificationcited by 0