mlsanityData to 7 Oct 2026

Provable Robustness of ReLU networks via Maximization of Linear Regions

arXiv 1810.07481 ↗First posted 17 Oct 2018cs.LG stat.MLcited by 51

Not on the map. Why?

Abstract (arXiv)

It has been shown that neural network classifiers are not robust. This raises concerns about their usage in safety-critical systems. We propose in this paper a regularization scheme for ReLU networks which provably improves the robustness of the classifier by maximizing the linear regions of the classifier as well as the distance to the decision boundary. Our techniques allow even to find the minimal adversarial perturbation for a fraction of test points for large networks. In the experiments we show that our approach improves upon adversarial training both in terms of lower and upper bounds on the robustness and is comparable or better than the state-of-the-art in terms of test error and robustness.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Oct 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 8; 2023: 9; 2024: 5; 2025: 3; 2026: 4.

51 papers.

Sort:

  1. 2021Globally-Robust Neural Networkscited by 106
  2. 2021On the Adversarial Robustness of Vision Transformerscited by 104
  3. 2021Skew Orthogonal Convolutionscited by 67
  4. 2021Relating Adversarially Robust Generalization to Flat Minimacited by 57
  5. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
  6. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  7. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  8. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  9. 2021Consistent Counterfactuals for Deep Modelscited by 37
  10. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  11. 2023Exploring and Exploiting Decision Boundary Dynamics for Adversarial Robustnesscited by 35
  12. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
38 more
  1. 2021Robust Models Are More Interpretable Because Attributions Look Normalcited by 21
  2. 2021Adversarial Robustness via Fisher-Rao Regularizationcited by 19
  3. 2021Towards Evaluating the Robustness of Deep Diagnostic Models by Adversarial Attackcited by 15
  4. 2021On the Expected Complexity of Maxout Networkscited by 15
  5. 2021How and When Adversarial Robustness Transfers in Knowledge Distillation?cited by 15
  6. 2021Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcited by 13
  7. 2023Unlocking Deterministic Robustness Certification on ImageNetcited by 13
  8. 2023Adversarial Attacks on Traffic Sign Recognition: A Surveycited by 13
  9. 2024FairProof : Confidential and Certifiable Fairness for Neural Networkscited by 13
  10. 2021Connections between Numerical Algorithms for PDEs and Neural Networkscited by 10
  11. 2023Deep Contract Design via Discontinuous Networkscited by 10
  12. 2022Improved techniques for deterministic l2 robustnesscited by 9
  13. 2022Towards Robust Dataset Learningcited by 9
  14. 2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
  15. 2024Multi-Sender Persuasion: A Computational Perspectivecited by 9
  16. 2024On the Local Complexity of Linear Regions in Deep ReLU Networkscited by 9
  17. 2021Recent Advances in Large Margin Learningcited by 7
  18. 2021Understanding and Accelerating Neural Architecture Search with Training-Free and Theory-Grounded Metricscited by 7
  19. 2021Relaxing Local Robustnesscited by 6
  20. 2022Reliable Robustness Evaluation via Automatically Constructed Attack Ensemblescited by 6
  21. 2022Robust Binary Models by Pruning Randomly-initialized Networkscited by 5
  22. 2023Deep ReLU Networks Have Surprisingly Simple Polytopescited by 5
  23. 2024Holistic Adversarially Robust Pruningcited by 5
  24. 2021The Fundamental Limits of Interval Arithmetic for Neural Networkscited by 4
  25. 2023Limitations of Piecewise Linearity for Efficient Robustness Certificationcited by 4
  26. 2023Certified Adversarial Robustness Within Multiple Perturbation Boundscited by 4
  27. 2021DISCO Verification: Division of Input Space into COnvex polytopes for neural network verificationcited by 1
  28. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  29. 2022Gradient Obfuscation Checklist Test Gives a False Sense of Securitycited by 1
  30. 2023Neural Polytopescited by 1
  31. 2024Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attackscited by 1
  32. 2025Adversarial Examples in Environment Perception for Automated Driving (Review)cited by 1
  33. 2026Learning Better Certified Models from Empirically-Robust Teacherscited by 1
  34. 2021Improving the Behaviour of Vision Transformers with Token-consistent Stochastic Layerscited by 0
  35. 2025Elytra: A Flexible Framework for Securing Large Vision Systemscited by 0
  36. 2025TrajSyn: Privacy-Preserving Dataset Distillation from Federated Model Trajectories for Server-Side Adversarial Trainingcited by 0
  37. 2026Theoretical Lower Bounds on the Robustness of Deep ReLU Networkscited by 0
  38. 2026Complexity of Linear Regions in Self-supervised Deep ReLU Networkscited by 0

50 most cited of 51 All 51 (JSON)