# Asymptotic Behavior of Adversarial Training in Binary Classification

arXiv: https://arxiv.org/abs/2010.13275 · HTML: https://mlsanity.com/paper/2010.13275/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2020.

## Built on by (most cited first, 15 of 15)

- [Stability Analysis and Generalization Bounds of Adversarial Training](https://mlsanity.com/paper/2210.00960/) (2022)
- [Overparameterized Linear Regression under Adversarial Attacks](https://mlsanity.com/paper/2204.06274/) (2022)
- [Adversarial Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/2211.14966/) (2022)
- [Regularization properties of adversarially-trained linear regression](https://mlsanity.com/paper/2310.10807/) (2023)
- [Beyond the Universal Law of Robustness: Sharper Laws for Random Features and Neural Tangent Kernels](https://mlsanity.com/paper/2302.01629/) (2023)
- [Fundamental Tradeoffs in Distributionally Adversarial Training](https://mlsanity.com/paper/2101.06309/) (2021)
- [Benign Overfitting in Adversarially Robust Linear Classification](https://mlsanity.com/paper/2112.15250/) (2021)
- [Understanding Generalization in Adversarial Training via the Bias-Variance Decomposition](https://mlsanity.com/paper/2103.09947/) (2021)
- [Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspective](https://mlsanity.com/paper/2109.09859/) (2021)
- [Efficient Optimization Algorithms for Linear Adversarial Training](https://mlsanity.com/paper/2410.12677/) (2024)
- [Unlabeled Data Help: Minimax Analysis and Adversarial Robustness](https://mlsanity.com/paper/2202.06996/) (2022)
- [Kernel Learning with Adversarial Features: Numerical Efficiency and Adaptive Regularization](https://mlsanity.com/paper/2510.20883/) (2025)
- [Surprises in adversarially-trained linear regression](https://mlsanity.com/paper/2205.12695/) (2022)
- [Balanced Data, Imbalanced Spectra: Unveiling Class Disparities with Spectral Imbalance](https://mlsanity.com/paper/2402.11742/) (2024)
- [Homogenization of ℓ2-Adversarial Training in High-Dimensions: Exact Dynamics under Stochastic Gradient Descent](https://mlsanity.com/paper/2607.00207/) (2026)

## Abstract (arXiv)

It has been consistently reported that many machine learning models are susceptible to adversarial attacks i.e., small additive adversarial perturbations applied to data points can cause misclassification. Adversarial training using empirical risk minimization is considered to be the state-of-the-art method for defense against adversarial attacks. Despite being successful in practice, several problems in understanding generalization performance of adversarial training remain open. In this paper, we derive precise theoretical predictions for the performance of adversarial training in binary classification. We consider the high-dimensional regime where the dimension of data grows with the size of the training data-set at a constant ratio. Our results provide exact asymptotics for standard and adversarial test errors of the estimators obtained by adversarial training with ℓq-norm bounded perturbations (q ≥ 1) for both discriminative binary models and generative Gaussian-mixture models with correlated features. Furthermore, we use these sharp predictions to uncover several intriguing observations on the role of various parameters including the over-parameterization ratio, the data model, and the attack budget on the adversarial and standard errors.