mlsanityData to 7 Oct 2026

Semidefinite relaxations for certifying robustness to adversarial examples

arXiv 1811.01057 ↗First posted 2 Nov 2018cs.LG cs.CR stat.MLcited by 178

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Abstract (arXiv)

Despite their impressive performance on diverse tasks, neural networks fail catastrophically in the presence of adversarial inputs---imperceptibly but adversarially perturbed versions of natural inputs. We have witnessed an arms race between defenders who attempt to train robust networks and attackers who try to construct adversarial examples. One promise of ending the arms race is developing certified defenses, ones which are provably robust against all attackers in some family. These certified defenses are based on convex relaxations which construct an upper bound on the worst case loss over all attackers in the family. Previous relaxations are loose on networks that are not trained against the respective relaxation. In this paper, we propose a new semidefinite relaxation for certifying robustness that applies to arbitrary ReLU networks. We show that our proposed relaxation is tighter than previous relaxations and produces meaningful robustness guarantees on three different "foreign networks" whose training objectives are agnostic to our proposed relaxation.

Key facts. Cited by 178 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Nov 2018.

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Citing papers per year: 2021: 49; 2022: 53; 2023: 34; 2024: 16; 2025: 15; 2026: 11.

178 papers.

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  1. 2023Certifying LLM Safety against Adversarial Promptingcited by 248
  2. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 224
  3. 2024Robust Prompt Optimization for Defending Language Models Against Jailbreaking Attackscited by 150
  4. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  5. 2021PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximationscited by 77
  6. 2021Skew Orthogonal Convolutionscited by 67
  7. 2022Adversarial Training for High-Stakes Reliabilitycited by 60
  8. 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 58
  9. 2021Meaningfully Debugging Model Mistakes using Conceptual Counterfactual Explanationscited by 53
  10. 2022Certified Training: Small Boxes are All You Needcited by 51
  11. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  12. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
38 more
  1. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  2. 2021Fast Certified Robust Training with Short Warmupcited by 45
  3. 2021Improved Branch and Bound for Neural Network Verification via Lagrangian Decompositioncited by 44
  4. 2021A Comprehensive Evaluation Framework for Deep Model Robustnesscited by 41
  5. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  6. 2021Partition-based formulations for mixed-integer optimization of trained ReLU neural networkscited by 39
  7. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  8. 2021Policy Smoothing for Provably Robust Reinforcement Learningcited by 39
  9. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  10. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  11. 2022OMLT: Optimization & Machine Learning Toolkitcited by 34
  12. 2022DensePure: Understanding Diffusion Models towards Adversarial Robustnesscited by 33
  13. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  14. 2021Adversarially Robust Learning with Unknown Perturbation Setscited by 24
  15. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  16. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  17. 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopescited by 24
  18. 2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23
  19. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
  20. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  21. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  22. 2023DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothingcited by 20
  23. 2023Convex Bounds on the Softmax Function with Applications to Robustness Verificationcited by 19
  24. 2023Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularizationcited by 19
  25. 2021Make Sure You're Unsure: A Framework for Verifying Probabilistic Specificationscited by 18
  26. 2021Center Smoothing: Certified Robustness for Networks with Structured Outputscited by 18
  27. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  28. 2022Scalable Verification of GNN-based Job Schedulerscited by 18
  29. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  30. 2023On the Robustness of Removal-Based Feature Attributionscited by 18
  31. 2021Adversarial Robustness with Non-uniform Perturbationscited by 17
  32. 2021DeformRS: Certifying Input Deformations with Randomized Smoothingcited by 17
  33. 2021ROMAX: Certifiably Robust Deep Multiagent Reinforcement Learning via Convex Relaxationcited by 17
  34. 2024Compact Proofs of Model Performance via Mechanistic Interpretabilitycited by 17
  35. 2021Robustness Certification for Point Cloud Modelscited by 16
  36. 2022Toward Certified Robustness Against Real-World Distribution Shiftscited by 16
  37. 2023Run-Off Election: Improved Provable Defense against Data Poisoning Attackscited by 16
  38. 2022Robust Probabilistic Time Series Forecastingcited by 15

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