# Enhanced Estimation Techniques for Certified Radii in Randomized Smoothing

arXiv: https://arxiv.org/abs/2503.08801 · HTML: https://mlsanity.com/paper/2503.08801/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 28 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [Audio Adversarial Examples: Targeted Attacks on Speech-to-Text](https://mlsanity.com/paper/1801.01944/) (2018)
- [On Detecting Adversarial Perturbations](https://mlsanity.com/paper/1702.04267/) (2017)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Adversarial Attacks Against Medical Deep Learning Systems](https://mlsanity.com/paper/1804.05296/) (2018)
- [The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing](https://mlsanity.com/paper/2309.16883/) (2023)

## Built on by (most cited first, 6 of 6)

- [Feature-Optimized Vision for Adaptive 3D Scene Reconstruction](https://mlsanity.com/paper/2605.31534/) (2026)
- [SPECTRA: Synthetic IR Test Collections with Relevance Oracles and Controlled Distractor Diagnostics](https://mlsanity.com/paper/2605.31575/) (2026)
- [SEMBridge: Tagless-Final Program Semantics with Weakest-Precondition and Bounded-Checking Interpretations](https://mlsanity.com/paper/2606.00220/) (2026)
- [SECUREVENT: Hybrid AI/ML Security Monitoring for Distributed Event-Based Systems](https://mlsanity.com/paper/2606.01741/) (2026)
- [Acceptance-Test-Driven Evaluation Protocols for Business-Centric LLM Systems](https://mlsanity.com/paper/2606.02755/) (2026)
- [Anycast Performance in Context](https://mlsanity.com/paper/2606.04298/) (2026)

## Abstract (arXiv)

This paper presents novel methods for estimating certified radii in randomized smoothing, a technique crucial for certifying the robustness of neural networks against adversarial perturbations. Our proposed techniques significantly improve the accuracy of certified test-set accuracy by providing tighter bounds on the certified radii. We introduce advanced algorithms for both discrete and continuous domains, demonstrating their effectiveness on CIFAR-10 and ImageNet datasets. The new methods show considerable improvements over existing approaches, particularly in reducing discrepancies in certified radii estimates. We also explore the impact of various hyperparameters, including sample size, standard deviation, and temperature, on the performance of these methods. Our findings highlight the potential for more efficient certification processes and pave the way for future research on tighter confidence sequences and improved theoretical frameworks. The study concludes with a discussion of potential future directions, including enhanced estimation techniques for discrete domains and further theoretical advancements to bridge the gap between empirical and theoretical performance in randomized smoothing.