mlsanityData to 14 Oct 2026

The Adversarial Consistency of Surrogate Risks for Binary Classification

arXiv 2305.09956 ↗First posted 17 May 2023cs.LG math.ST stat.THcited by 6

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Abstract (arXiv)

We study the consistency of surrogate risks for robust binary classification. It is common to learn robust classifiers by adversarial training, which seeks to minimize the expected 0-1 loss when each example can be maliciously corrupted within a small ball. We give a simple and complete characterization of the set of surrogate loss functions that are consistent, i.e., that can replace the 0-1 loss without affecting the minimizing sequences of the original adversarial risk, for any data distribution. We also prove a quantitative version of adversarial consistency for the ρ-margin loss. Our results reveal that the class of adversarially consistent surrogates is substantially smaller than in the standard setting, where many common surrogates are known to be consistent.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 16 of its 29 references that are in the map. First posted on arXiv 17 May 2023.

Builds on

16 of 29 references.

References · 16

  1. 2013Intriguing properties of neural networkscited by 5,155
  2. 2017Evasion Attacks against Machine Learning at Test Timecited by 689
  3. 2021Calibration and Consistency of Adversarial Surrogate Lossescited by 47
  4. 2020Calibrated Surrogate Losses for Adversarially Robust Classificationcited by 36
  5. 2022The Many Faces of Adversarial Riskcited by 28
  6. 2021A Finer Calibration Analysis for Adversarial Robustnesscited by 26
  7. 2021On the Existence of the Adversarial Bayes Classifier (Extended Version)cited by 25
  8. 2018Generalizability vs. Robustness: Adversarial Examples for Medical Imagingcited by 23
  9. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  10. 2021The Geometry of Adversarial Training in Binary Classificationcited by 20
  11. 2020Adversarial Classification: Necessary conditions and geometric flowscited by 19
  12. 2020When are Non-Parametric Methods Robust?cited by 15
4 more
  1. 2022Existence and Minimax Theorems for Adversarial Surrogate Risks in Binary Classificationcited by 15
  2. 2022Towards Consistency in Adversarial Classificationcited by 12
  3. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  4. 2021Consistent Non-Parametric Methods for Maximizing Robustnesscited by 7

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 2; 2026: 1.

6 papers.

  1. 2023Adversarial Training Should Be Cast as a Non-Zero-Sum Gamecited by 13
  2. 2024A Notion of Uniqueness for the Adversarial Bayes Classifiercited by 3
  3. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  4. 2025Adversarial Surrogate Risk Bounds for Binary Classificationcited by 1
  5. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1
  6. 2026Statistical Inference for Adversarial Training: Central Limit Theorems via Optimal Transportcited by 0