mlsanityData to 7 Oct 2026

Stratified Adversarial Robustness with Rejection

arXiv 2305.01139 ↗First posted 2 May 2023cs.LG cs.CR cs.CVcited by 4

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Abstract (arXiv)

Recently, there is an emerging interest in adversarially training a classifier with a rejection option (also known as a selective classifier) for boosting adversarial robustness. While rejection can incur a cost in many applications, existing studies typically associate zero cost with rejecting perturbed inputs, which can result in the rejection of numerous slightly-perturbed inputs that could be correctly classified. In this work, we study adversarially-robust classification with rejection in the stratified rejection setting, where the rejection cost is modeled by rejection loss functions monotonically non-increasing in the perturbation magnitude. We theoretically analyze the stratified rejection setting and propose a novel defense method -- Adversarial Training with Consistent Prediction-based Rejection (CPR) -- for building a robust selective classifier. Experiments on image datasets demonstrate that the proposed method significantly outperforms existing methods under strong adaptive attacks. For instance, on CIFAR-10, CPR reduces the total robust loss (for different rejection losses) by at least 7.3% under both seen and unseen attacks.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 25 of its 38 references that are in the map. First posted on arXiv 2 May 2023.

Builds on

25 of 38 references.

References · 25

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
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  4. 2019Theoretically Principled Trade-off between Robustness and Accuracycited by 1,510
  5. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,442
  6. 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
  7. 2017Evasion Attacks against Machine Learning at Test Timecited by 686
  8. 2020RobustBench: a standardized adversarial robustness benchmarkcited by 659
  9. 2020On Adaptive Attacks to Adversarial Example Defensescited by 547
  10. 2017Wild Patterns: Ten Years After the Rise of Adversarial Machine Learningcited by 411
  11. 2019SelectiveNet: A Deep Neural Network with an Integrated Reject Optioncited by 333
  12. 2020Consistent Estimators for Learning to Defer to an Expertcited by 262
13 more
  1. 2020Bag of Tricks for Adversarial Trainingcited by 199
  2. 2020Perceptual Adversarial Robustness: Defense Against Unseen Threat Modelscited by 137
  3. 2020Classification with Rejection Based on Cost-sensitive Classificationcited by 55
  4. 2021Detecting Adversarial Examples Is (Nearly) As Hard As Classifying Themcited by 46
  5. 2020Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examplescited by 44
  6. 2019GAT: Generative Adversarial Training for Adversarial Example Detection and Robust Classificationcited by 20
  7. 2017Blocking Transferability of Adversarial Examples in Black-Box Learning Systemscited by 19
  8. 2022Robustly-reliable learners under poisoning attackscited by 19
  9. 2021Two Coupled Rejection Metrics Can Tell Adversarial Examples Apartcited by 14
  10. 2020An Analysis of Robustness of Non-Lipschitz Networkscited by 12
  11. 2019Playing it Safe: Adversarial Robustness with an Abstain Optioncited by 9
  12. 2020ATRO: Adversarial Training with a Rejection Optioncited by 8
  13. 2023ASPEST: Bridging the Gap Between Active Learning and Selective Predictioncited by 3

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Cited by year (2026 to 7 Oct)

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

4 papers.

  1. 2025AutoAdvExBench: Benchmarking autonomous exploitation of adversarial example defensescited by 14
  2. 2024Adversarial Consistency and the Uniqueness of the Adversarial Bayes Classifiercited by 2
  3. 2024Towards Calibrated Losses for Adversarial Robust Reject Option Classificationcited by 0
  4. 2026Laws of Learning Dynamics and the Core of Learnerscited by 0