# Towards Large Certified Radius in Randomized Smoothing using Quasiconcave Optimization

arXiv: https://arxiv.org/abs/2302.00209 · HTML: https://mlsanity.com/paper/2302.00209/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 28 of 28)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for real-time object detectors](https://mlsanity.com/paper/2207.02696/) (2022)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Audio Adversarial Examples: Targeted Attacks on Speech-to-Text](https://mlsanity.com/paper/1801.01944/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [MACER: Attack-free and Scalable Robust Training via Maximizing Certified Radius](https://mlsanity.com/paper/2001.02378/) (2020)
- [Shield: Fast, Practical Defense and Vaccination for Deep Learning using JPEG Compression](https://mlsanity.com/paper/1802.06816/) (2018)
- [Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness](https://mlsanity.com/paper/2002.03239/) (2020)
- [Improved deterministic l2 robustness on CIFAR-10 and CIFAR-100](https://mlsanity.com/paper/2108.04062/) (2021)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Improved, Deterministic Smoothing for L_1 Certified Robustness](https://mlsanity.com/paper/2103.10834/) (2021)
- [LOT: Layer-wise Orthogonal Training on Improving ℓ2 Certified Robustness](https://mlsanity.com/paper/2210.11620/) (2022)
- [Intriguing Properties of Input-dependent Randomized Smoothing](https://mlsanity.com/paper/2110.05365/) (2021)
- [Input-Specific Robustness Certification for Randomized Smoothing](https://mlsanity.com/paper/2112.12084/) (2021)
- [Tight Second-Order Certificates for Randomized Smoothing](https://mlsanity.com/paper/2010.10549/) (2020)
- [Insta-RS: Instance-wise Randomized Smoothing for Improved Robustness and Accuracy](https://mlsanity.com/paper/2103.04436/) (2021)

## Built on by (most cited first, 1 of 1)

- [CertDW: Towards Certified Dataset Ownership Verification via Conformal Calibration](https://mlsanity.com/paper/2506.13160/) (2025)

## Abstract (arXiv)

Randomized smoothing is currently the state-of-the-art method that provides certified robustness for deep neural networks. However, due to its excessively conservative nature, this method of incomplete verification often cannot achieve an adequate certified radius on real-world datasets. One way to obtain a larger certified radius is to use an input-specific algorithm instead of using a fixed Gaussian filter for all data points. Several methods based on this idea have been proposed, but they either suffer from high computational costs or gain marginal improvement in certified radius. In this work, we show that by exploiting the quasiconvex problem structure, we can find the optimal certified radii for most data points with slight computational overhead. This observation leads to an efficient and effective input-specific randomized smoothing algorithm. We conduct extensive experiments and empirical analysis on CIFAR-10 and ImageNet. The results show that the proposed method significantly enhances the certified radii with low computational overhead.