# Understanding the Impact of Adversarial Robustness on Accuracy Disparity

arXiv: https://arxiv.org/abs/2211.15762 · HTML: https://mlsanity.com/paper/2211.15762/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 28 Nov 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [BREEDS: Benchmarks for Subpopulation Shift](https://mlsanity.com/paper/2008.04859/) (2020)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [To be Robust or to be Fair: Towards Fairness in Adversarial Training](https://mlsanity.com/paper/2010.06121/) (2020)
- [Is Robustness the Cost of Accuracy? -- A Comprehensive Study on the Robustness of 18 Deep Image Classification Models](https://mlsanity.com/paper/1808.01688/) (2018)
- [Adversarial Training Can Hurt Generalization](https://mlsanity.com/paper/1906.06032/) (2019)
- [Trustworthy AI: A Computational Perspective](https://mlsanity.com/paper/2107.06641/) (2021)
- [Fairness Through Robustness: Investigating Robustness Disparity in Deep Learning](https://mlsanity.com/paper/2006.12621/) (2020)
- [Lower Bounds on Adversarial Robustness from Optimal Transport](https://mlsanity.com/paper/1909.12272/) (2019)
- [Robustness May Be at Odds with Fairness: An Empirical Study on Class-wise Accuracy](https://mlsanity.com/paper/2010.13365/) (2020)
- [Provable tradeoffs in adversarially robust classification](https://mlsanity.com/paper/2006.05161/) (2020)
- [Analysis and Applications of Class-wise Robustness in Adversarial Training](https://mlsanity.com/paper/2105.14240/) (2021)
- [Sharp Statistical Guarantees for Adversarially Robust Gaussian Classification](https://mlsanity.com/paper/2006.16384/) (2020)
- [More Data Can Expand the Generalization Gap Between Adversarially Robust and Standard Models](https://mlsanity.com/paper/2002.04725/) (2020)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)

## Built on by (most cited first, 9 of 9)

- [DAFA: Distance-Aware Fair Adversarial Training](https://mlsanity.com/paper/2401.12532/) (2024)
- [Investigating the Impact of Quantization on Adversarial Robustness](https://mlsanity.com/paper/2404.05639/) (2024)
- [DD-RobustBench: An Adversarial Robustness Benchmark for Dataset Distillation](https://mlsanity.com/paper/2403.13322/) (2024)
- [SoK: Unintended Interactions among Machine Learning Defenses and Risks](https://mlsanity.com/paper/2312.04542/) (2023)
- [Adversarially Robust Feature Learning for Breast Cancer Diagnosis](https://mlsanity.com/paper/2402.08768/) (2024)
- [Distribution-restrained Softmax Loss for the Model Robustness](https://mlsanity.com/paper/2303.12363/) (2023)
- [Combining Machine Learning Defenses without Conflicts](https://mlsanity.com/paper/2411.09776/) (2024)
- [VTruST: Controllable value function based subset selection for Data-Centric Trustworthy AI](https://mlsanity.com/paper/2403.05174/) (2024)
- [TRIX- Trading Adversarial Fairness via Mixed Adversarial Training](https://mlsanity.com/paper/2507.07768/) (2025)

## Abstract (arXiv)

While it has long been empirically observed that adversarial robustness may be at odds with standard accuracy and may have further disparate impacts on different classes, it remains an open question to what extent such observations hold and how the class imbalance plays a role within. In this paper, we attempt to understand this question of accuracy disparity by taking a closer look at linear classifiers under a Gaussian mixture model. We decompose the impact of adversarial robustness into two parts: an inherent effect that will degrade the standard accuracy on all classes due to the robustness constraint, and the other caused by the class imbalance ratio, which will increase the accuracy disparity compared to standard training. Furthermore, we also show that such effects extend beyond the Gaussian mixture model, by generalizing our data model to the general family of stable distributions. More specifically, we demonstrate that while the constraint of adversarial robustness consistently degrades the standard accuracy in the balanced class setting, the class imbalance ratio plays a fundamentally different role in accuracy disparity compared to the Gaussian case, due to the heavy tail of the stable distribution. We additionally perform experiments on both synthetic and real-world datasets to corroborate our theoretical findings. Our empirical results also suggest that the implications may extend to nonlinear models over real-world datasets. Our code is publicly available on GitHub at https://github.com/Accuracy-Disparity/AT-on-AD.