On the existence of consistent adversarial attacks in high-dimensional linear classification

• URL: http://arxiv.org/abs/2506.12454v1
• Date: Sat, 14 Jun 2025 11:25:35 GMT
• Title: On the existence of consistent adversarial attacks in high-dimensional linear classification
• Authors: Matteo Vilucchio, Lenka Zdeborová, Bruno Loureiro,
• Abstract summary: We introduce a new error metric that quantifying model vulnerability to consistent adversarial attacks.<n>Our main technical contribution is an exact and rigorous characterization of these metrics in both well-specified models and latent space models.
• Score: 19.8106461427356
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: What fundamentally distinguishes an adversarial attack from a misclassification due to limited model expressivity or finite data? In this work, we investigate this question in the setting of high-dimensional binary classification, where statistical effects due to limited data availability play a central role. We introduce a new error metric that precisely capture this distinction, quantifying model vulnerability to consistent adversarial attacks -- perturbations that preserve the ground-truth labels. Our main technical contribution is an exact and rigorous asymptotic characterization of these metrics in both well-specified models and latent space models, revealing different vulnerability patterns compared to standard robust error measures. The theoretical results demonstrate that as models become more overparameterized, their vulnerability to label-preserving perturbations grows, offering theoretical insight into the mechanisms underlying model sensitivity to adversarial attacks.

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