# On the Role of Randomization in Adversarially Robust Classification

arXiv: https://arxiv.org/abs/2302.07221 · HTML: https://mlsanity.com/paper/2302.07221/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 53 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 30 of 39)

- [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)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [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)
- [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)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Robustness via curvature regularization, and vice versa](https://mlsanity.com/paper/1811.09716/) (2018)
- [Stochastic Activation Pruning for Robust Adversarial Defense](https://mlsanity.com/paper/1803.01442/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Parametric Noise Injection: Trainable Randomness to Improve Deep Neural Network Robustness against Adversarial Attack](https://mlsanity.com/paper/1811.09310/) (2018)
- [DVERGE: Diversifying Vulnerabilities for Enhanced Robust Generation of Ensembles](https://mlsanity.com/paper/2009.14720/) (2020)
- [Improving Adversarial Robustness of Ensembles with Diversity Training](https://mlsanity.com/paper/1901.09981/) (2019)
- [TRS: Transferability Reduced Ensemble via Encouraging Gradient Diversity and Model Smoothness](https://mlsanity.com/paper/2104.00671/) (2021)
- [Randomization matters. How to defend against strong adversarial attacks](https://mlsanity.com/paper/2002.11565/) (2020)
- [Theoretical evidence for adversarial robustness through randomization](https://mlsanity.com/paper/1902.01148/) (2019)
- [Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution](https://mlsanity.com/paper/1810.12272/) (2018)
- [The Many Faces of Adversarial Risk](https://mlsanity.com/paper/2201.08956/) (2022)
- [On the Existence of the Adversarial Bayes Classifier (Extended Version)](https://mlsanity.com/paper/2112.01694/) (2021)
- [On the Hardness of Robust Classification](https://mlsanity.com/paper/1909.05822/) (2019)
- [Ensembles of Locally Independent Prediction Models](https://mlsanity.com/paper/1911.01291/) (2019)
- [Mixed Nash Equilibria in the Adversarial Examples Game](https://mlsanity.com/paper/2102.06905/) (2021)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)

## Built on by (most cited first, 4 of 4)

- [A Notion of Uniqueness for the Adversarial Bayes Classifier](https://mlsanity.com/paper/2404.16956/) (2024)
- [Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifier](https://mlsanity.com/paper/2404.17358/) (2024)
- [Uniform Convergence of Adversarially Robust Classifiers](https://mlsanity.com/paper/2406.14682/) (2024)
- [Unveiling the Role of Randomization in Multiclass Adversarial Classification: Insights from Graph Theory](https://mlsanity.com/paper/2503.14299/) (2025)

## Abstract (arXiv)

Deep neural networks are known to be vulnerable to small adversarial perturbations in test data. To defend against adversarial attacks, probabilistic classifiers have been proposed as an alternative to deterministic ones. However, literature has conflicting findings on the effectiveness of probabilistic classifiers in comparison to deterministic ones. In this paper, we clarify the role of randomization in building adversarially robust classifiers. Given a base hypothesis set of deterministic classifiers, we show the conditions under which a randomized ensemble outperforms the hypothesis set in adversarial risk, extending previous results. Additionally, we show that for any probabilistic binary classifier (including randomized ensembles), there exists a deterministic classifier that outperforms it. Finally, we give an explicit description of the deterministic hypothesis set that contains such a deterministic classifier for many types of commonly used probabilistic classifiers, i.e. randomized ensembles and parametric/input noise injection.