# Exploring the Adversarial Frontier: Quantifying Robustness via Adversarial Hypervolume

arXiv: https://arxiv.org/abs/2403.05100 · HTML: https://mlsanity.com/paper/2403.05100/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 72 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 30 of 48)

- [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)
- [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)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Fast is better than free: Revisiting adversarial training](https://mlsanity.com/paper/2001.03994/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Countering Adversarial Images using Input Transformations](https://mlsanity.com/paper/1711.00117/) (2017)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [Feature Squeezing: Detecting Adversarial Examples in Deep Neural Networks](https://mlsanity.com/paper/1704.01155/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [Uncovering the Limits of Adversarial Training against Norm-Bounded Adversarial Examples](https://mlsanity.com/paper/2010.03593/) (2020)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Trustworthy AI: From Principles to Practices](https://mlsanity.com/paper/2110.01167/) (2021)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [Efficient Decision-based Black-box Adversarial Attacks on Face Recognition](https://mlsanity.com/paper/1904.04433/) (2019)
- [Adversarial Sensor Attack on LiDAR-based Perception in Autonomous Driving](https://mlsanity.com/paper/1907.06826/) (2019)
- [(Certified!!) Adversarial Robustness for Free!](https://mlsanity.com/paper/2206.10550/) (2022)
- [Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?](https://mlsanity.com/paper/2104.09425/) (2021)

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

- [MOS-Attack: A Scalable Multi-objective Adversarial Attack Framework](https://mlsanity.com/paper/2501.07251/) (2025)
- [Quantifying the Risk of Transferred Black Box Attacks](https://mlsanity.com/paper/2511.05102/) (2025)
- [How Worst-Case Are Adversarial Attacks? Linking Adversarial and Perturbation Robustness](https://mlsanity.com/paper/2601.14519/) (2026)

## Abstract (arXiv)

The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial accuracy, which measures a model's performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this gap, we propose a new metric termed adversarial hypervolume, assessing the robustness of deep learning models comprehensively over a range of perturbation intensities from a multi-objective optimization standpoint. This metric allows for an in-depth comparison of defense mechanisms and recognizes the trivial improvements in robustness afforded by less potent defensive strategies. Additionally, we adopt a novel training algorithm that enhances adversarial robustness uniformly across various perturbation intensities, in contrast to methods narrowly focused on optimizing adversarial accuracy. Our extensive empirical studies validate the effectiveness of the adversarial hypervolume metric, demonstrating its ability to reveal subtle differences in robustness that adversarial accuracy overlooks. This research contributes a new measure of robustness and establishes a standard for assessing and benchmarking the resilience of current and future defensive models against adversarial threats.