# Adversarial Surrogate Risk Bounds for Binary Classification

arXiv: https://arxiv.org/abs/2506.09348 · HTML: https://mlsanity.com/paper/2506.09348/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 19 of 19)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks](https://mlsanity.com/paper/2103.14749/) (2021)
- [Lower Bounds on Adversarial Robustness from Optimal Transport](https://mlsanity.com/paper/1909.12272/) (2019)
- [Calibration and Consistency of Adversarial Surrogate Losses](https://mlsanity.com/paper/2104.09658/) (2021)
- [Adversarial Robustness Limits via Scaling-Law and Human-Alignment Studies](https://mlsanity.com/paper/2404.09349/) (2024)
- [Adversarial Risk via Optimal Transport and Optimal Couplings](https://mlsanity.com/paper/1912.02794/) (2019)
- [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)
- [Generalizability vs. Robustness: Adversarial Examples for Medical Imaging](https://mlsanity.com/paper/1804.00504/) (2018)
- [The Geometry of Adversarial Training in Binary Classification](https://mlsanity.com/paper/2111.13613/) (2021)
- [Surrogate Regret Bounds for Polyhedral Losses](https://mlsanity.com/paper/2110.14031/) (2021)
- [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)
- [Characterizing the Optimal 0-1 Loss for Multi-class Classification with a Test-time Attacker](https://mlsanity.com/paper/2302.10722/) (2023)
- [The Adversarial Consistency of Surrogate Risks for Binary Classification](https://mlsanity.com/paper/2305.09956/) (2023)
- [Binary Excess Risk for Smooth Convex Surrogates](https://mlsanity.com/paper/1402.1792/) (2014)
- [A Notion of Uniqueness for the Adversarial Bayes Classifier](https://mlsanity.com/paper/2404.16956/) (2024)
- [Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifier](https://mlsanity.com/paper/2404.17358/) (2024)

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

- [Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transport](https://mlsanity.com/paper/2609.22240/) (2026)

## Abstract (arXiv)

A central concern in classification is the vulnerability of machine learning models to adversarial attacks. Adversarial training is one of the most popular techniques for training robust classifiers, which involves minimizing an adversarial surrogate risk. Recent work has characterized the conditions under which any sequence minimizing the adversarial surrogate risk also minimizes the adversarial classification risk in the binary setting, a property known as adversarial consistency. However, these results do not address the rate at which the adversarial classification risk approaches its optimal value along such a sequence. This paper provides surrogate risk bounds that quantify that convergence rate.