mlsanityData to 7 Oct 2026

Certified Defenses against Adversarial Examples

arXiv 1801.09344 ↗First posted 29 Jan 2018cs.LGcited by 305

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Abstract (arXiv)

While neural networks have achieved high accuracy on standard image classification benchmarks, their accuracy drops to nearly zero in the presence of small adversarial perturbations to test inputs. Defenses based on regularization and adversarial training have been proposed, but often followed by new, stronger attacks that defeat these defenses. Can we somehow end this arms race? In this work, we study this problem for neural networks with one hidden layer. We first propose a method based on a semidefinite relaxation that outputs a certificate that for a given network and test input, no attack can force the error to exceed a certain value. Second, as this certificate is differentiable, we jointly optimize it with the network parameters, providing an adaptive regularizer that encourages robustness against all attacks. On MNIST, our approach produces a network and a certificate that no attack that perturbs each pixel by at most ε = 0.1 can cause more than 35% test error.

Key facts. Cited by 305 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jan 2018.

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Citing papers per year: 2021: 105; 2022: 63; 2023: 66; 2024: 40; 2025: 14; 2026: 17.

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  1. 2024Jailbreaking Leading Safety-Aligned LLMs with Simple Adaptive Attackscited by 450
  2. 2023SmoothLLM: Defending Large Language Models Against Jailbreaking Attackscited by 434
  3. 2021Unsolved Problems in ML Safetycited by 291
  4. 2021Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalizationcited by 248
  5. 2021Trustworthy AI: From Principles to Practicescited by 206
  6. 2021Admix: Enhancing the Transferability of Adversarial Attackscited by 155
  7. 2021Advances in adversarial attacks and defenses in computer vision: A surveycited by 127
  8. 2024Dissecting Adversarial Robustness of Multimodal LM Agentscited by 118
  9. 2021Globally-Robust Neural Networkscited by 106
  10. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  11. 2021Trustworthy AI: A Computational Perspectivecited by 93
  12. 2023Robust Classification via a Single Diffusion Modelcited by 79
38 more
  1. 2021PatchCleanser: Certifiably Robust Defense against Adversarial Patches for Any Image Classifiercited by 63
  2. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
  3. 2021Meta Gradient Adversarial Attackcited by 55
  4. 2022Planting Undetectable Backdoors in Machine Learning Modelscited by 55
  5. 2022Robust Counterfactual Explanations for Tree-Based Ensemblescited by 49
  6. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 49
  7. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  8. 2021Boosting Randomized Smoothing with Variance Reduced Classifierscited by 47
  9. 2021Detecting Adversarial Examples Is (Nearly) As Hard As Classifying Themcited by 46
  10. 2021Fast Certified Robust Training with Short Warmupcited by 45
  11. 2021Certified Patch Robustness via Smoothed Vision Transformerscited by 44
  12. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  13. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  14. 2021A Comprehensive Evaluation Framework for Deep Model Robustnesscited by 41
  15. 2021CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothingcited by 41
  16. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  17. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  18. 2021Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neuronscited by 40
  19. 2022How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspectivecited by 39
  20. 2021CausalAdv: Adversarial Robustness through the Lens of Causalitycited by 37
  21. 2021Improving the Transferability of Adversarial Examples with Resized-Diverse-Inputs, Diversity-Ensemble and Region Fittingcited by 37
  22. 2021Adversarial Training Helps Transfer Learning via Better Representationscited by 36
  23. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  24. 2021Evading Adversarial Example Detection Defenses with Orthogonal Projected Gradient Descentcited by 34
  25. 2023Diversifying the High-level Features for better Adversarial Transferabilitycited by 34
  26. 2021A Review of Formal Methods applied to Machine Learningcited by 33
  27. 2021A Little Robustness Goes a Long Way: Leveraging Robust Features for Targeted Transfer Attackscited by 33
  28. 2022Visual Prompting for Adversarial Robustnesscited by 33
  29. 2022DensePure: Understanding Diffusion Models towards Adversarial Robustnesscited by 33
  30. 2021Deep Learning-Based Autonomous Driving Systems: A Survey of Attacks and Defensescited by 29
  31. 2021Learning to Give Checkable Answers with Prover-Verifier Gamescited by 29
  32. 2021DetectorGuard: Provably Securing Object Detectors against Localized Patch Hiding Attackscited by 28
  33. 2023Provably Bounding Neural Network Preimagescited by 28
  34. 2023Adversarial Illusions in Multi-Modal Embeddingscited by 28
  35. 2021Enhancing Adversarial Robustness via Test-time Transformation Ensemblingcited by 27
  36. 2023WAT: Improve the Worst-class Robustness in Adversarial Trainingcited by 27
  37. 2023Towards quantum enhanced adversarial robustness in machine learningcited by 26
  38. 2021Fooling LiDAR Perception via Adversarial Trajectory Perturbationcited by 25

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