mlsanityData to 7 Oct 2026

Sharp Statistical Guarantees for Adversarially Robust Gaussian Classification

arXiv 2006.16384 ↗First posted 29 Jun 2020stat.ML cs.LGcited by 27

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Abstract (arXiv)

Adversarial robustness has become a fundamental requirement in modern machine learning applications. Yet, there has been surprisingly little statistical understanding so far. In this paper, we provide the first result of the optimal minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by citeschmidt2018adversarially. The results are stated in terms of the Adversarial Signal-to-Noise Ratio (AdvSNR), which generalizes a similar notion for standard linear classification to the adversarial setting. For the Gaussian mixtures with AdvSNR value of r, we establish an excess risk lower bound of order Theta(e^-(frac18+o(1)) r2 fracdn) and design a computationally efficient estimator that achieves this optimal rate. Our results built upon minimal set of assumptions while cover a wide spectrum of adversarial perturbations including ℓp balls for any p ≥ 1.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Jun 2020.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 8; 2024: 3; 2025: 2; 2026: 1.

27 papers.

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  1. 2023Cross-Entropy Loss Functions: Theoretical Analysis and Applicationscited by 206
  2. 2021When and How Mixup Improves Calibrationcited by 59
  3. 2022Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Powercited by 23
  4. 2023Regularization properties of adversarially-trained linear regressioncited by 17
  5. 2021Benign Overfitting in Adversarially Robust Linear Classificationcited by 11
  6. 2021Understanding Generalization in Adversarial Training via the Bias-Variance Decompositioncited by 10
  7. 2021Fairness Properties of Face Recognition and Obfuscation Systemscited by 9
  8. 2022A Law of Robustness beyond Isoperimetrycited by 9
  9. 2022Understanding the Impact of Adversarial Robustness on Accuracy Disparitycited by 9
  10. 2023It Is All About Data: A Survey on the Effects of Data on Adversarial Robustnesscited by 9
  11. 2022Adversarially Robust PAC Learnability of Real-Valued Functionscited by 8
  12. 2022GeoECG: Data Augmentation via Wasserstein Geodesic Perturbation for Robust Electrocardiogram Predictioncited by 8
15 more
  1. 2021Robust Classification Under ℓ0 Attack for the Gaussian Mixture Modelcited by 5
  2. 2023On the Clean Generalization and Robust Overfitting in Adversarial Training from Two Theoretical Views: Representation Complexity and Training Dynamicscited by 5
  3. 2021Exploring Adversarial Robustness of Deep Metric Learningcited by 4
  4. 2022Unlabeled Data Help: Minimax Analysis and Adversarial Robustnesscited by 4
  5. 2023Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesicscited by 3
  6. 2022SynBench: Task-Agnostic Benchmarking of Pretrained Representations using Synthetic Datacited by 2
  7. 2023Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Modelscited by 2
  8. 2024Towards the Effect of Examples on In-Context Learning: A Theoretical Case Studycited by 2
  9. 2023Adversarial Training with Generated Data in High-Dimensional Regression: An Asymptotic Studycited by 1
  10. 2024Can overfitted deep neural networks in adversarial training generalize? -- An approximation viewpointcited by 1
  11. 2025On the Existence of Consistent Adversarial Attacks in High-Dimensional Linear Classificationcited by 1
  12. 2023Designing an attack-defense game: how to increase robustness of financial transaction models via a competitioncited by 0
  13. 2024Better Representations via Adversarial Training in Pre-Training: A Theoretical Perspectivecited by 0
  14. 2025How to Enhance Downstream Adversarial Robustness (almost) without Touching the Pre-Trained Foundation Model?cited by 0
  15. 2026Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classificationcited by 0