mlsanityData to 7 Oct 2026

Theoretical evidence for adversarial robustness through randomization

arXiv 1902.01148 ↗First posted 4 Feb 2019cs.LG cs.CR stat.MLcited by 33

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Abstract (arXiv)

This paper investigates the theory of robustness against adversarial attacks. It focuses on the family of randomization techniques that consist in injecting noise in the network at inference time. These techniques have proven effective in many contexts, but lack theoretical arguments. We close this gap by presenting a theoretical analysis of these approaches, hence explaining why they perform well in practice. More precisely, we make two new contributions. The first one relates the randomization rate to robustness to adversarial attacks. This result applies for the general family of exponential distributions, and thus extends and unifies the previous approaches. The second contribution consists in devising a new upper bound on the adversarial generalization gap of randomized neural networks. We support our theoretical claims with a set of experiments.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Feb 2019.

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Citing papers per year: 2021: 12; 2022: 8; 2023: 7; 2024: 4; 2025: 2.

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  1. 2023How Does Information Bottleneck Help Deep Learning?cited by 92
  2. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
  3. 2021PointGuard: Provably Robust 3D Point Cloud Classificationcited by 49
  4. 2021Provably Efficient Black-Box Action Poisoning Attacks Against Reinforcement Learningcited by 29
  5. 2021Noisy Feature Mixupcited by 27
  6. 2023R-LPIPS: An Adversarially Robust Perceptual Similarity Metriccited by 27
  7. 2021Mixed Nash Equilibria in the Adversarial Examples Gamecited by 22
  8. 2021On the Effectiveness of Small Input Noise for Defending Against Query-based Black-Box Attackscited by 17
  9. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 16
  10. 2023LipSim: A Provably Robust Perceptual Similarity Metriccited by 15
  11. 2024A Simple and Yet Fairly Effective Defense for Graph Neural Networkscited by 12
  12. 2021On the robustness of randomized classifiers to adversarial examplescited by 9
21 more
  1. 2021Adversarial Robustness by Design through Analog Computing and Synthetic Gradientscited by 7
  2. 2023PerturbScore: Connecting Discrete and Continuous Perturbations in NLPcited by 5
  3. 2021Learning distinct features helps, provablycited by 4
  4. 2022Pre-trained Encoders in Self-Supervised Learning Improve Secure and Privacy-preserving Supervised Learningcited by 4
  5. 2023On the Role of Randomization in Adversarially Robust Classificationcited by 4
  6. 2024Exploring Adversarial Robustness of Deep State Space Modelscited by 4
  7. 2022Causal Information Bottleneck Boosts Adversarial Robustness of Deep Neural Networkcited by 3
  8. 2021ROPUST: Improving Robustness through Fine-tuning with Photonic Processors and Synthetic Gradientscited by 2
  9. 2022Rethinking Feature Uncertainty in Stochastic Neural Networks for Adversarial Robustnesscited by 2
  10. 2022Towards Evading the Limits of Randomized Smoothing: A Theoretical Analysiscited by 2
  11. 2022Metric-Fair Classifier Derandomizationcited by 2
  12. 2023Towards Better Certified Segmentation via Diffusion Modelscited by 2
  13. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  14. 2022How Sampling Impacts the Robustness of Stochastic Neural Networkscited by 1
  15. 2022Unifying Gradients to Improve Real-world Robustness for Deep Networkscited by 1
  16. 2021Robustifying ℓ_∞ Adversarial Training to the Union of Perturbation Modelscited by 0
  17. 2021Improving the Behaviour of Vision Transformers with Token-consistent Stochastic Layerscited by 0
  18. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  19. 2024Enhance DNN Adversarial Robustness and Efficiency via Injecting Noise to Non-Essential Neuronscited by 0
  20. 2025Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theorycited by 0
  21. 2025The Double-Edged Nature of the Rashomon Set for Trustworthy Machine Learningcited by 0