# On the Robustness of Randomized Ensembles to Adversarial Perturbations

arXiv: https://arxiv.org/abs/2302.01375 · HTML: https://mlsanity.com/paper/2302.01375/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 49 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [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)
- [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)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Stochastic Activation Pruning for Robust Adversarial Defense](https://mlsanity.com/paper/1803.01442/) (2018)
- [DPatch: An Adversarial Patch Attack on Object Detectors](https://mlsanity.com/paper/1806.02299/) (2018)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [Adversarial Camouflage: Hiding Physical-World Attacks with Natural Styles](https://mlsanity.com/paper/2003.08757/) (2020)
- [When NAS Meets Robustness: In Search of Robust Architectures against Adversarial Attacks](https://mlsanity.com/paper/1911.10695/) (2019)
- [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)
- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [ME-Net: Towards Effective Adversarial Robustness with Matrix Estimation](https://mlsanity.com/paper/1905.11971/) (2019)

## Built on by (most cited first, 3 of 3)

- [On the Role of Randomization in Adversarially Robust Classification](https://mlsanity.com/paper/2302.07221/) (2023)
- [Adversarial attacks for mixtures of classifiers](https://mlsanity.com/paper/2307.10788/) (2023)
- [Lattice Climber Attack: Adversarial attacks for randomized mixtures of classifiers](https://mlsanity.com/paper/2506.10888/) (2025)

## Abstract (arXiv)

Randomized ensemble classifiers (RECs), where one classifier is randomly selected during inference, have emerged as an attractive alternative to traditional ensembling methods for realizing adversarially robust classifiers with limited compute requirements. However, recent works have shown that existing methods for constructing RECs are more vulnerable than initially claimed, casting major doubts on their efficacy and prompting fundamental questions such as: "When are RECs useful?", "What are their limits?", and "How do we train them?". In this work, we first demystify RECs as we derive fundamental results regarding their theoretical limits, necessary and sufficient conditions for them to be useful, and more. Leveraging this new understanding, we propose a new boosting algorithm (BARRE) for training robust RECs, and empirically demonstrate its effectiveness at defending against strong ℓ_∞ norm-bounded adversaries across various network architectures and datasets. Our code can be found at https://github.com/hsndbk4/BARRE.