# Adversarial Training with Generated Data in High-Dimensional Regression: An Asymptotic Study

arXiv: https://arxiv.org/abs/2306.12582 · HTML: https://mlsanity.com/paper/2306.12582/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 44 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Using Pre-Training Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1901.09960/) (2019)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Attacks Which Do Not Kill Training Make Adversarial Learning Stronger](https://mlsanity.com/paper/2002.11242/) (2020)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [Better Diffusion Models Further Improve Adversarial Training](https://mlsanity.com/paper/2302.04638/) (2023)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [Adversarial Training Can Hurt Generalization](https://mlsanity.com/paper/1906.06032/) (2019)
- [On the Convergence and Robustness of Adversarial Training](https://mlsanity.com/paper/2112.08304/) (2021)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [Curriculum Adversarial Training](https://mlsanity.com/paper/1805.04807/) (2018)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Understanding Double Descent Requires a Fine-Grained Bias-Variance Decomposition](https://mlsanity.com/paper/2011.03321/) (2020)
- [Robustness to Adversarial Perturbations in Learning from Incomplete Data](https://mlsanity.com/paper/1905.13021/) (2019)
- [The Curious Case of Adversarially Robust Models: More Data Can Help, Double Descend, or Hurt Generalization](https://mlsanity.com/paper/2002.11080/) (2020)
- [Kernel regression in high dimensions: Refined analysis beyond double descent](https://mlsanity.com/paper/2010.02681/) (2020)
- [Over-parameterized Adversarial Training: An Analysis Overcoming the Curse of Dimensionality](https://mlsanity.com/paper/2002.06668/) (2020)
- [Stability Analysis and Generalization Bounds of Adversarial Training](https://mlsanity.com/paper/2210.00960/) (2022)
- [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)
- [Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized models](https://mlsanity.com/paper/2010.13933/) (2020)
- [Statistical Guarantees for Regularized Neural Networks](https://mlsanity.com/paper/2006.00294/) (2020)
- [Improving Adversarial Robustness via Unlabeled Out-of-Domain Data](https://mlsanity.com/paper/2006.08476/) (2020)
- [Adversarially Robust Estimate and Risk Analysis in Linear Regression](https://mlsanity.com/paper/2012.10278/) (2020)
- [Adversarial Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/2211.14966/) (2022)

## Built on by (most cited first, 1 of 1)

- [Ensuring Calibration Robustness in Split Conformal Prediction Under Adversarial Attacks](https://mlsanity.com/paper/2511.18562/) (2025)

## Abstract (arXiv)

In recent years, studies such as citecarmon2019unlabeled,gowal2021improving,xing2022artificial have demonstrated that incorporating additional real or generated data with pseudo-labels can enhance adversarial training through a two-stage training approach. In this paper, we perform a theoretical analysis of the asymptotic behavior of this method in high-dimensional linear regression. While a double-descent phenomenon can be observed in ridgeless training, with an appropriate L2 regularization, the two-stage adversarial training achieves a better performance. Finally, we derive a shortcut cross-validation formula specifically tailored for the two-stage training method.