On the existence of consistent adversarial attacks in high-dimensional linear classification
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909649180033024 |
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| author | Vilucchio, Matteo Zdeborová, Lenka Loureiro, Bruno |
| author_facet | Vilucchio, Matteo Zdeborová, Lenka Loureiro, Bruno |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of consistent adversarial attacks in high-dimensional linear classification Vilucchio, Matteo Zdeborová, Lenka Loureiro, Bruno Machine Learning Disordered Systems and Neural Networks Cryptography and Security 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. |
| title | On the existence of consistent adversarial attacks in high-dimensional linear classification |
| topic | Machine Learning Disordered Systems and Neural Networks Cryptography and Security |
| url | https://arxiv.org/abs/2506.12454 |