# Bridging the Theoretical Gap in Randomized Smoothing

arXiv: https://arxiv.org/abs/2504.02412 · HTML: https://mlsanity.com/paper/2504.02412/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 62 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networks](https://mlsanity.com/paper/1802.04034/) (2018)
- [(Certified!!) Adversarial Robustness for Free!](https://mlsanity.com/paper/2206.10550/) (2022)
- [Orthogonalizing Convolutional Layers with the Cayley Transform](https://mlsanity.com/paper/2104.07167/) (2021)
- [A Dynamical System Perspective for Lipschitz Neural Networks](https://mlsanity.com/paper/2110.12690/) (2021)
- [A Unified Algebraic Perspective on Lipschitz Neural Networks](https://mlsanity.com/paper/2303.03169/) (2023)
- [Higher-Order Certification for Randomized Smoothing](https://mlsanity.com/paper/2010.06651/) (2020)
- [Data-Dependent Randomized Smoothing](https://mlsanity.com/paper/2012.04351/) (2020)
- [Certifiably Robust Interpretation in Deep Learning](https://mlsanity.com/paper/1905.12105/) (2019)
- [Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration](https://mlsanity.com/paper/2305.16173/) (2023)
- [Unlocking Deterministic Robustness Certification on ImageNet](https://mlsanity.com/paper/2301.12549/) (2023)
- [Hierarchical Randomized Smoothing](https://mlsanity.com/paper/2310.16221/) (2023)
- [The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing](https://mlsanity.com/paper/2309.16883/) (2023)
- [Treatment of Statistical Estimation Problems in Randomized Smoothing for Adversarial Robustness](https://mlsanity.com/paper/2406.17830/) (2024)
- [Randomized Smoothing under Attack: How Good is it in Pratice?](https://mlsanity.com/paper/2204.14187/) (2022)

## Built on by (most cited first, 2 of 2)

- [The Double-Edged Nature of the Rashomon Set for Trustworthy Machine Learning](https://mlsanity.com/paper/2511.21799/) (2025)
- [Certified Robustness under Heterogeneous Perturbations via Hybrid Randomized Smoothing](https://mlsanity.com/paper/2605.12876/) (2026)

## 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.