mlsanityData to 7 Oct 2026

Certified Adversarial Robustness with Additive Noise

arXiv 1809.03113 ↗First posted 10 Sep 2018cs.LG cs.CR stat.MLcited by 178

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Abstract (arXiv)

The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning algorithm. Although a significant body of work on developing defensive models has been considered, most such models are heuristic and are often vulnerable to adaptive attacks. Defensive methods that provide theoretical robustness guarantees have been studied intensively, yet most fail to obtain non-trivial robustness when a large-scale model and data are present. To address these limitations, we introduce a framework that is scalable and provides certified bounds on the norm of the input manipulation for constructing adversarial examples. We establish a connection between robustness against adversarial perturbation and additive random noise, and propose a training strategy that can significantly improve the certified bounds. Our evaluation on MNIST, CIFAR-10 and ImageNet suggests that the proposed method is scalable to complicated models and large data sets, while providing competitive robustness to state-of-the-art provable defense methods.

Key facts. Cited by 178 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Sep 2018.

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Citing papers per year: 2021: 46; 2022: 45; 2023: 37; 2024: 22; 2025: 14; 2026: 14.

178 papers.

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  1. 2023Certifying LLM Safety against Adversarial Promptingcited by 248
  2. 2023Open Sesame! Universal Black Box Jailbreaking of Large Language Modelscited by 128
  3. 2021Skew Orthogonal Convolutionscited by 67
  4. 2021Training Certifiably Robust Neural Networks with Efficient Local Lipschitz Boundscited by 64
  5. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
  6. 2022Certified Training: Small Boxes are All You Needcited by 51
  7. 2021PointGuard: Provably Robust 3D Point Cloud Classificationcited by 49
  8. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
  9. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  10. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  11. 2021Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100cited by 47
  12. 2021Fast Certified Robust Training with Short Warmupcited by 45
38 more
  1. 2021Certified Patch Robustness via Smoothed Vision Transformerscited by 44
  2. 2021On the Certified Robustness for Ensemble Models and Beyondcited by 40
  3. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  4. 2021Policy Smoothing for Provably Robust Reinforcement Learningcited by 39
  5. 2022Almost-Orthogonal Layers for Efficient General-Purpose Lipschitz Networkscited by 39
  6. 2021Benchmarking the Robustness of Spatial-Temporal Models Against Corruptionscited by 35
  7. 2021Drawing Robust Scratch Tickets: Subnetworks with Inborn Robustness Are Found within Randomly Initialized Networkscited by 29
  8. 2021A Review of Adversarial Attack and Defense for Classification Methodscited by 29
  9. 2021Knowledge Enhanced Machine Learning Pipeline against Diverse Adversarial Attackscited by 24
  10. 2021Intriguing Properties of Input-dependent Randomized Smoothingcited by 24
  11. 2021Boosting the Certified Robustness of L-infinity Distance Netscited by 24
  12. 2021Efficient Certified Defenses Against Patch Attacks on Image Classifierscited by 23
  13. 2021ANCER: Anisotropic Certification via Sample-wise Volume Maximizationcited by 23
  14. 2022Double Sampling Randomized Smoothingcited by 22
  15. 2022A Comprehensive Study of the Robustness for LiDAR-based 3D Object Detectors against Adversarial Attackscited by 22
  16. 2022On the Limitations of Stochastic Pre-processing Defensescited by 21
  17. 2023On the Robustness of Latent Diffusion Modelscited by 21
  18. 2021Adversarial Robustness via Fisher-Rao Regularizationcited by 19
  19. 2021Center Smoothing: Certified Robustness for Networks with Structured Outputscited by 18
  20. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  21. 2023Improving the Accuracy-Robustness Trade-Off of Classifiers via Adaptive Smoothingcited by 18
  22. 2024Provably Unlearnable Data Examplescited by 18
  23. 2021On the Effectiveness of Small Input Noise for Defending Against Query-based Black-Box Attackscited by 17
  24. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 16
  25. 2022Robust Probabilistic Time Series Forecastingcited by 15
  26. 2022RetrievalGuard: Provably Robust 1-Nearest Neighbor Image Retrievalcited by 15
  27. 2022Do Perceptually Aligned Gradients Imply Adversarial Robustness?cited by 15
  28. 2022Double Bubble, Toil and Trouble: Enhancing Certified Robustness through Transitivitycited by 15
  29. 2024Adversarial Training on Purification (AToP): Advancing Both Robustness and Generalizationcited by 15
  30. 2021Learning Security Classifiers with Verified Global Robustness Propertiescited by 14
  31. 2024NLP Verification: Towards a General Methodology for Certifying Robustnesscited by 14
  32. 2022Robust and Accurate -- Compositional Architectures for Randomized Smoothingcited by 12
  33. 2023Improving Interpretation Faithfulness for Vision Transformerscited by 12
  34. 2022Holistic Adversarial Robustness of Deep Learning Modelscited by 11
  35. 2022Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothingcited by 11
  36. 2023Certified Zeroth-order Black-Box Defense with Robust UNet Denoisercited by 11
  37. 2023TAPS: Connecting Certified and Adversarial Trainingcited by 11
  38. 2023Projected Randomized Smoothing for Certified Adversarial Robustnesscited by 11

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