# Certified Robustness via Randomized Smoothing over Multiplicative Parameters of Input Transformations

arXiv: https://arxiv.org/abs/2106.14432 · HTML: https://mlsanity.com/paper/2106.14432/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 28 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [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)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Adversarial Risk and the Dangers of Evaluating Against Weak Attacks](https://mlsanity.com/paper/1802.05666/) (2018)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Mitigating Evasion Attacks to Deep Neural Networks via Region-based Classification](https://mlsanity.com/paper/1709.05583/) (2017)
- [Curse of Dimensionality on Randomized Smoothing for Certifiable Robustness](https://mlsanity.com/paper/2002.03239/) (2020)
- [Certified Defense to Image Transformations via Randomized Smoothing](https://mlsanity.com/paper/2002.12463/) (2020)
- [TSS: Transformation-Specific Smoothing for Robustness Certification](https://mlsanity.com/paper/2002.12398/) (2020)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Extensions and limitations of randomized smoothing for robustness guarantees](https://mlsanity.com/paper/2006.04208/) (2020)

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

- [Backdoor Cleansing with Unlabeled Data](https://mlsanity.com/paper/2211.12044/) (2022)
- [Invariance-Aware Randomized Smoothing Certificates](https://mlsanity.com/paper/2211.14207/) (2022)
- [Certification of Speaker Recognition Models to Additive Perturbations](https://mlsanity.com/paper/2404.18791/) (2024)
- [KS-Lottery: Finding Certified Lottery Tickets for Multilingual Language Models](https://mlsanity.com/paper/2402.02801/) (2024)
- [General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothing](https://mlsanity.com/paper/2309.16710/) (2023)
- [Certified Adversarial Robustness via Partition-based Randomized Smoothing](https://mlsanity.com/paper/2409.13546/) (2024)

## Abstract (arXiv)

Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters. Using this method we construct certifiably robust classifiers with respect to a gamma correction perturbation and compare the result with classifiers obtained via other smoothing distributions (Gaussian, Laplace, uniform). The experiments show that asymmetrical Rayleigh distribution allows to obtain better certificates for some values of perturbation parameters. To the best of our knowledge it is the first work concerning certified robustness against the multiplicative gamma correction transformation and the first to study effects of asymmetrical distributions in randomized smoothing.