# Data-Dependent Stability Analysis of Adversarial Training

arXiv: https://arxiv.org/abs/2401.03156 · HTML: https://mlsanity.com/paper/2401.03156/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 6 Jan 2024.

## Builds on (most cited first, 30 of 32)

- [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)
- [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)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Overfitting in adversarially robust deep learning](https://mlsanity.com/paper/2002.11569/) (2020)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [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)
- [Unlearnable Examples: Making Personal Data Unexploitable](https://mlsanity.com/paper/2101.04898/) (2021)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Adversarial Examples Make Strong Poisons](https://mlsanity.com/paper/2106.10807/) (2021)
- [Data-Dependent Stability of Stochastic Gradient Descent](https://mlsanity.com/paper/1703.01678/) (2017)
- [Learning to Confuse: Generating Training Time Adversarial Data with Auto-Encoder](https://mlsanity.com/paper/1905.09027/) (2019)
- [Availability Attacks Create Shortcuts](https://mlsanity.com/paper/2111.00898/) (2021)
- [On the Loss Landscape of Adversarial Training: Identifying Challenges and How to Overcome Them](https://mlsanity.com/paper/2006.08403/) (2020)
- [Better Safe Than Sorry: Preventing Delusive Adversaries with Adversarial Training](https://mlsanity.com/paper/2102.04716/) (2021)
- [Probabilistic Margins for Instance Reweighting in Adversarial Training](https://mlsanity.com/paper/2106.07904/) (2021)
- [Train simultaneously, generalize better: Stability of gradient-based minimax learners](https://mlsanity.com/paper/2010.12561/) (2020)
- [Robust Unlearnable Examples: Protecting Data Against Adversarial Learning](https://mlsanity.com/paper/2203.14533/) (2022)
- [Stability Analysis and Generalization Bounds of Adversarial Training](https://mlsanity.com/paper/2210.00960/) (2022)
- [Robust Weight Perturbation for Adversarial Training](https://mlsanity.com/paper/2205.14826/) (2022)
- [Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power](https://mlsanity.com/paper/2205.13863/) (2022)
- [Fooling Adversarial Training with Inducing Noise](https://mlsanity.com/paper/2111.10130/) (2021)

## Built on by (most cited first, 4 of 4)

- [Generalization Bound and New Algorithm for Clean-Label Backdoor Attack](https://mlsanity.com/paper/2406.00588/) (2024)
- [Generalizability of Memorization Neural Networks](https://mlsanity.com/paper/2411.00372/) (2024)
- [Generalizability of Neural Networks Minimizing Empirical Risk Based on Expressive Ability](https://mlsanity.com/paper/2503.04111/) (2025)
- [Adversarial generalization of unfolding (model-based) networks](https://mlsanity.com/paper/2509.15370/) (2025)

## Abstract (arXiv)

Stability analysis is an essential aspect of studying the generalization ability of deep learning, as it involves deriving generalization bounds for stochastic gradient descent-based training algorithms. Adversarial training is the most widely used defense against adversarial example attacks. However, previous generalization bounds for adversarial training have not included information regarding the data distribution. In this paper, we fill this gap by providing generalization bounds for stochastic gradient descent-based adversarial training that incorporate data distribution information. We utilize the concepts of on-average stability and high-order approximate Lipschitz conditions to examine how changes in data distribution and adversarial budget can affect robust generalization gaps. Our derived generalization bounds for both convex and non-convex losses are at least as good as the uniform stability-based counterparts which do not include data distribution information. Furthermore, our findings demonstrate how distribution shifts from data poisoning attacks can impact robust generalization.