Asymptotic Behavior of Adversarial Training in Binary Linear Classification
Bibliographic record
Abstract
Adversarial training using empirical risk minimization (ERM) is the state-of-the-art method for defense against adversarial attacks, that is, against small additive adversarial perturbations applied to test data leading to misclassification. Despite being successful in practice, understanding the generalization properties of adversarial training in classification remains widely open. In this article, we take the first step in this direction by precisely characterizing the robustness of adversarial training in binary linear classification. Specifically, we consider the high-dimensional regime where the model dimension grows with the size of the training set at a constant ratio. Our results provide exact asymptotics for both standard and adversarial test errors under general -norm bounded perturbations ( ) in both discriminative binary models and generative Gaussian-mixture models with correlated features. We use our sharp error formulae to explain how the adversarial and standard errors depend upon the over-parameterization ratio, the data model, and the attack budget. Finally, by comparing with the robust Bayes estimator, our sharp asymptotics allow us to study the fundamental limits of adversarial training.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.074 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".