mlsanityData to 7 Oct 2026

Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability

arXiv 1809.03008 ↗First posted 9 Sep 2018cs.LG cs.CR cs.NEcited by 67

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Abstract (arXiv)

We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more easily. To this end, we identify two properties of network models - weight sparsity and so-called ReLU stability - that turn out to significantly impact the complexity of the corresponding verification task. We demonstrate that improving weight sparsity alone already enables us to turn computationally intractable verification problems into tractable ones. Then, improving ReLU stability leads to an additional 4-13x speedup in verification times. An important feature of our methodology is its "universality," in the sense that it can be used with a broad range of training procedures and verification approaches.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Sep 2018.

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Citing papers per year: 2021: 21; 2022: 16; 2023: 14; 2024: 5; 2025: 8; 2026: 3.

67 papers.

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  1. 2021Advances in adversarial attacks and defenses in computer vision: A surveycited by 127
  2. 2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 64
  3. 2021Handcrafted Backdoors in Deep Neural Networkscited by 57
  4. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
  5. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  6. 2021Fast Certified Robust Training with Short Warmupcited by 45
  7. 2021Certified Patch Robustness via Smoothed Vision Transformerscited by 44
  8. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  9. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  10. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  11. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  12. 2023Expressive Losses for Verified Robustness via Convex Combinationscited by 23
38 more
  1. 2023A DPLL(T) Framework for Verifying Deep Neural Networkscited by 23
  2. 2021Taxonomy of Machine Learning Safety: A Survey and Primercited by 22
  3. 2021Adaptive Image Transformations for Transfer-based Adversarial Attackcited by 22
  4. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  5. 2021Scaling Up Exact Neural Network Compression by ReLU Stabilitycited by 19
  6. 2023Model-Based Control with Sparse Neural Dynamicscited by 16
  7. 2021Towards Evaluating the Robustness of Deep Diagnostic Models by Adversarial Attackcited by 15
  8. 2022Can pruning improve certified robustness of neural networks?cited by 14
  9. 2024Harnessing Neuron Stability to Improve DNN Verificationcited by 13
  10. 2022Pruning Adversarially Robust Neural Networks without Adversarial Examplescited by 12
  11. 2022Linearity Grafting: Relaxed Neuron Pruning Helps Certifiable Robustnesscited by 10
  12. 2024Optimization Over Trained Neural Networks: Taking a Relaxing Walkcited by 10
  13. 2022Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systemscited by 9
  14. 2022MultiGuard: Provably Robust Multi-label Classification against Adversarial Examplescited by 9
  15. 2022Towards Robust Dataset Learningcited by 9
  16. 2022Confidence-aware Training of Smoothed Classifiers for Certified Robustnesscited by 9
  17. 2025Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verificationcited by 9
  18. 2021NoiLIn: Improving Adversarial Training and Correcting Stereotype of Noisy Labelscited by 8
  19. 2023Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regionscited by 8
  20. 2021Relaxing Local Robustnesscited by 6
  21. 2021Fast Training of Provably Robust Neural Networks by SinglePropcited by 5
  22. 2022On the Convergence of Certified Robust Training with Interval Bound Propagationcited by 5
  23. 2021Impact of Attention on Adversarial Robustness of Image Classification Modelscited by 4
  24. 2021The Fundamental Limits of Interval Arithmetic for Neural Networkscited by 4
  25. 2022A Scalable, Interpretable, Verifiable & Differentiable Logic Gate Convolutional Neural Network Architecture From Truth Tablescited by 4
  26. 2022Improving Adversarial Robustness via Joint Classification and Multiple Explicit Detection Classescited by 4
  27. 2022Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxationscited by 4
  28. 2023Limitations of Piecewise Linearity for Efficient Robustness Certificationcited by 4
  29. 2023On the Robustness of Randomized Ensembles to Adversarial Perturbationscited by 3
  30. 2023Verifiable Learning for Robust Tree Ensemblescited by 3
  31. 2024Adversarial Robustification via Text-to-Image Diffusion Modelscited by 3
  32. 2022Provably Adversarially Robust Nearest Prototype Classifierscited by 2
  33. 2023Computational Asymmetries in Robust Classificationcited by 2
  34. 2023Vulnerability Analysis of Transformer-based Optical Character Recognition to Adversarial Attackscited by 2
  35. 2023E2E-AT: A Unified Framework for Tackling Uncertainty in Task-aware End-to-end Learningcited by 2
  36. 2025An analysis of optimization problems involving ReLU neural networkscited by 2
  37. 2021Adversarial Robustness: What fools you makes you strongercited by 1
  38. 2021Resilience from Diversity: Population-based approach to harden models against adversarial attackscited by 1

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