analiza aiqbench
This paper establishes rigorous theoretical bounds on the tradeoff between robustness and geometric accuracy for adversarial classifiers, demonstrating that high-complexity hypothesis classes can achieve optimal performance without sacrificing accuracy beyond $O(\sqrt{\varepsilon})$ or $O(\varepsilon)$. By applying to both infinite and finite data settings under arbitrary norms, these findings advance the mathematical foundations of adversarial training and clarify the limits of robustness in non-parametric binary classification.
On the tradeoff between robustness and geometric accuracy in adversarial training
arXiv:2610.22955v1 Announce Type: new Abstract: For non-parametric binary classification in the presence of an adversary, we prove an optimal quantitative estimate for adversarial classifiers controlling geometric accuracy, as measured by the Hausdorff distance to the Bayes classifier, in terms or their robustness, as encoded by the adversarial budget $\varepsilon$. This rigorously shows that robust classifiers sacrifice at most $O(\sqrt{\varepsilon})$ or $O(\varepsilon)$ in accuracy, depending on the regularity of the underlying Bayes classifier. In contrast to prior work on the incompatibility of robustness and accuracy over low-complexity hypothesis classes, our work shows that high-complexity hypothesis classes allow for robust classifiers with precisely quantified accuracy. Our results apply for adversaries determined by any norm on Euclidean space and in both the infinite and finite data settings.
Abstract:For non-parametric binary classification in the presence of an adversary, we prove an optimal quantitative estimate for adversarial classifiers controlling geometric accuracy, as measured by the Hausdorff distance to the Bayes classifier, in terms or their robustness, as encoded by the adversarial budget $\varepsilon$. This rigorously shows that robust classifiers sacrifice at most $O(\sqrt{\varepsilon})$ or $O(\varepsilon)$ in accuracy, depending on the regularity of the underlying Bayes classifier. In contrast to prior work on the incompatibility of robustness and accuracy over low-complexity hypothesis classes, our work shows that high-complexity hypothesis classes allow for robust classifiers with precisely quantified accuracy. Our results apply for adversaries determined by any norm on Euclidean space and in both the infinite and finite data settings.
Machine Learning (cs.LG); Analysis of PDEs (math.AP)
arXiv:2610.22955 [cs.LG]
(or arXiv:2610.22955v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.22955 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 217 cuvinte
Subiecte conexe
Projection sampling preserves capabilities but diminishes gains from alignment fine-tuning
LessWrong · 16 oct. 2026
Improving the Robustness/Accuracy Tradeoff Against Adversarial Attacks Using Information Bottleneck Distillation Through Dual Teachers
arXiv · 31 iul. 2026
Confirming Claims of Superposition and Adversarial Examples in Toy Models
LessWrong · 1 aug. 2026
Robust Privacy: Inference-Stage Privacy through Certified Robustness
arXiv · 12 iun. 2026