# Uniform Convergence of Adversarially Robust Classifiers

arXiv: https://arxiv.org/abs/2406.14682 · HTML: https://mlsanity.com/paper/2406.14682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 28 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 22 of 22)

- [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)
- [Imperceptible, Robust, and Targeted Adversarial Examples for Automatic Speech Recognition](https://mlsanity.com/paper/1903.10346/) (2019)
- [Calibration and Consistency of Adversarial Surrogate Losses](https://mlsanity.com/paper/2104.09658/) (2021)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Adversarial Risk via Optimal Transport and Optimal Couplings](https://mlsanity.com/paper/1912.02794/) (2019)
- [Calibrated Surrogate Losses for Adversarially Robust Classification](https://mlsanity.com/paper/2005.13748/) (2020)
- [The Many Faces of Adversarial Risk](https://mlsanity.com/paper/2201.08956/) (2022)
- [On the Existence of the Adversarial Bayes Classifier (Extended Version)](https://mlsanity.com/paper/2112.01694/) (2021)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)
- [The Geometry of Adversarial Training in Binary Classification](https://mlsanity.com/paper/2111.13613/) (2021)
- [Adversarial Classification: Necessary conditions and geometric flows](https://mlsanity.com/paper/2011.10797/) (2020)
- [Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classification](https://mlsanity.com/paper/2206.09098/) (2022)
- [Towards Consistency in Adversarial Classification](https://mlsanity.com/paper/2205.10022/) (2022)
- [Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning](https://mlsanity.com/paper/2211.15223/) (2022)
- [On the existence of solutions to adversarial training in multiclass classification](https://mlsanity.com/paper/2305.00075/) (2023)
- [On Proper Learnability between Average- and Worst-case Robustness](https://mlsanity.com/paper/2211.05656/) (2022)
- [On the Role of Randomization in Adversarially Robust Classification](https://mlsanity.com/paper/2302.07221/) (2023)
- [A mean curvature flow arising in adversarial training](https://mlsanity.com/paper/2404.14402/) (2024)
- [It begins with a boundary: A geometric view on probabilistically robust learning](https://mlsanity.com/paper/2305.18779/) (2023)

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

- [Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions](https://mlsanity.com/paper/2510.01969/) (2025)

## Abstract (arXiv)

In recent years there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with an associated trade-off between accuracy and robustness. This work considers a general framework for adversarially-perturbed classification problems, in a large data or population-level limit. In such a regime, we demonstrate that as adversarial strength goes to zero that optimal classifiers converge to the Bayes classifier in the Hausdorff distance. This significantly strengthens previous results, which generally focus on L1-type convergence. The main argument relies upon direct geometric comparisons and is inspired by techniques from geometric measure theory.