Bridging the Theoretical Gap in Randomized Smoothing
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Abstract (arXiv)
Randomized smoothing has become a leading approach for certifying adversarial robustness in machine learning models. However, a persistent gap remains between theoretical certified robustness and empirical robustness accuracy. This paper introduces a new framework that bridges this gap by leveraging Lipschitz continuity for certification and proposing a novel, less conservative method for computing confidence intervals in randomized smoothing. Our approach tightens the bounds of certified robustness, offering a more accurate reflection of model robustness in practice. Through rigorous experimentation we show that our method improves the robust accuracy, compressing the gap between empirical findings and previous theoretical results. We argue that investigating local Lipschitz constants and designing ad-hoc confidence intervals can further enhance the performance of randomized smoothing. These results pave the way for a deeper understanding of the relationship between Lipschitz continuity and certified robustness.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 23 of its 62 references that are in the map. First posted on arXiv 3 Apr 2025.
Builds on
23 of 62 references.
References · 23
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- 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
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- 2022(Certified!!) Adversarial Robustness for Free!cited by 130
- 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
11 more
- 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
- 2023A Unified Algebraic Perspective on Lipschitz Neural Networkscited by 58
- 2020Data-Dependent Randomized Smoothingcited by 37
- 2020Higher-Order Certification for Randomized Smoothingcited by 36
- 2019Certifiably Robust Interpretation in Deep Learningcited by 35
- 2023Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iterationcited by 19
- 2023Unlocking Deterministic Robustness Certification on ImageNetcited by 13
- 2023Hierarchical Randomized Smoothingcited by 9
- 2024Treatment of Statistical Estimation Problems in Randomized Smoothing for Adversarial Robustnesscited by 8
- 2022Randomized Smoothing under Attack: How Good is it in Pratice?cited by 7
- 2023The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothingcited by 6
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.