mlsanityData to 7 Oct 2026

Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing

arXiv 2406.02309 ↗First posted 4 Jun 2024cs.LGcited by 1

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Abstract (arXiv)

Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against ℓp adversaries, the interaction between the smoothing distribution and the robustness certification still remains vague. In this work, we comprehensively study the effect of two families of distributions, named Exponential Standard Gaussian (ESG) and Exponential General Gaussian (EGG) distributions, on Randomized Smoothing and Double Sampling Randomized Smoothing (DSRS). We derive an analytic formula for ESG's certified radius, which converges to the origin formula of RS as the dimension d increases. Additionally, we prove that EGG can provide tighter constant factors than DSRS in providing Omega(√d) lower bounds of ℓ2 certified radius, and thus further addresses the curse of dimensionality in RS. Our experiments on real-world datasets confirm our theoretical analysis of the ESG distributions, that they provide almost the same certification under different exponents η for both RS and DSRS. In addition, EGG brings a significant improvement to the DSRS certification, but the mechanism can be different when the classifier properties are different. Compared to the primitive DSRS, the increase in certified accuracy provided by EGG is prominent, up to 6.4% on ImageNet.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 36 of its 48 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

36 of 48 references.

References · 36

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24 more
  1. 2018Semidefinite relaxations for certifying robustness to adversarial examplescited by 178
  2. 2020Randomized Smoothing of All Shapes and Sizescited by 146
  3. 2018Scaling provable adversarial defensescited by 141
  4. 2020(De)Randomized Smoothing for Certifiable Defense against Patch Attackscited by 97
  5. 2020Consistency Regularization for Certified Robustness of Smoothed Classifierscited by 73
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  7. 2020Curse of Dimensionality on Randomized Smoothing for Certifiable Robustnesscited by 56
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  9. 2021SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustnesscited by 49
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  11. 2020Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Frameworkcited by 45
  12. 2021Improved, Deterministic Smoothing for L_1 Certified Robustnesscited by 39
  13. 2022Certified Neural Network Watermarks with Randomized Smoothingcited by 39
  14. 2020Random Smoothing Might be Unable to Certify ℓ_∞ Robustness for High-Dimensional Imagescited by 35
  15. 2021Scalable Certified Segmentation via Randomized Smoothingcited by 35
  16. 2020Certified Robustness of Community Detection against Adversarial Structural Perturbation via Randomized Smoothingcited by 29
  17. 2021Intriguing Properties of Input-dependent Randomized Smoothingcited by 24
  18. 2022GSmooth: Certified Robustness against Semantic Transformations via Generalized Randomized Smoothingcited by 23
  19. 2022Double Sampling Randomized Smoothingcited by 22
  20. 2022Denoising Masked AutoEncoders Help Robust Classificationcited by 21
  21. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  22. 2021DeformRS: Certifying Input Deformations with Randomized Smoothingcited by 17
  23. 2022Certified Defences Against Adversarial Patch Attacks on Semantic Segmentationcited by 15
  24. 2022Double Bubble, Toil and Trouble: Enhancing Certified Robustness through Transitivitycited by 15

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