Curvature Dynamic Black-box Attack: revisiting adversarial robustness via dynamic curvature estimation

Peiran Sun
Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, PMLR 282:513-528, 2026.

Abstract

Adversarial attack reveals the vulnerability of deep learning models. It is assumed that high curvature may give rise to rough decision boundary and thus result in less robust models. However, the most commonly used \textit{curvature} is the curvature of loss function, scores or other parameters from within the model as opposed to decision boundary curvature, since the former can be relatively easily formed using second order derivative. In this paper, we propose a new query-efficient method, dynamic curvature estimation (DCE), to estimate the decision boundary curvature in a black-box setting. Our approach is based on CGBA, a black-box adversarial attack. By performing DCE on a wide range of classifiers, we discovered, statistically, a connection between decision boundary curvature and adversarial robustness. We also propose a new attack method, curvature dynamic black-box attack (CDBA) with improved performance using the estimated curvature.

Cite this Paper

BibTeX
@InProceedings{pmlr-v282-sun26a, title = {Curvature Dynamic Black-box Attack: revisiting adversarial robustness via dynamic curvature estimation}, author = {Sun, Peiran}, booktitle = {Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations}, pages = {513--528}, year = {2026}, editor = {Acosta, Francisco and Azeglio, Simone and Tolooshams, Bahareh and van de Geijn, Chase and Shewmake, Christian and Sanborn, Sophia and Miolane, Nina}, volume = {282}, series = {Proceedings of Machine Learning Research}, month = {14 Dec 2024--07 Dec 2025}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v282/main/assets/sun26a/sun26a.pdf}, url = {https://proceedings.mlr.press/v282/sun26a.html}, abstract = {Adversarial attack reveals the vulnerability of deep learning models. It is assumed that high curvature may give rise to rough decision boundary and thus result in less robust models. However, the most commonly used \textit{curvature} is the curvature of loss function, scores or other parameters from within the model as opposed to decision boundary curvature, since the former can be relatively easily formed using second order derivative. In this paper, we propose a new query-efficient method, dynamic curvature estimation (DCE), to estimate the decision boundary curvature in a black-box setting. Our approach is based on CGBA, a black-box adversarial attack. By performing DCE on a wide range of classifiers, we discovered, statistically, a connection between decision boundary curvature and adversarial robustness. We also propose a new attack method, curvature dynamic black-box attack (CDBA) with improved performance using the estimated curvature.} }
Endnote
%0 Conference Paper %T Curvature Dynamic Black-box Attack: revisiting adversarial robustness via dynamic curvature estimation %A Peiran Sun %B Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2026 %E Francisco Acosta %E Simone Azeglio %E Bahareh Tolooshams %E Chase van de Geijn %E Christian Shewmake %E Sophia Sanborn %E Nina Miolane %F pmlr-v282-sun26a %I PMLR %P 513--528 %U https://proceedings.mlr.press/v282/sun26a.html %V 282 %X Adversarial attack reveals the vulnerability of deep learning models. It is assumed that high curvature may give rise to rough decision boundary and thus result in less robust models. However, the most commonly used \textit{curvature} is the curvature of loss function, scores or other parameters from within the model as opposed to decision boundary curvature, since the former can be relatively easily formed using second order derivative. In this paper, we propose a new query-efficient method, dynamic curvature estimation (DCE), to estimate the decision boundary curvature in a black-box setting. Our approach is based on CGBA, a black-box adversarial attack. By performing DCE on a wide range of classifiers, we discovered, statistically, a connection between decision boundary curvature and adversarial robustness. We also propose a new attack method, curvature dynamic black-box attack (CDBA) with improved performance using the estimated curvature.
APA
Sun, P.. (2026). Curvature Dynamic Black-box Attack: revisiting adversarial robustness via dynamic curvature estimation. Proceedings of the 4th (2025) and 3rd (2024) NeurIPS Workshops on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 282:513-528 Available from https://proceedings.mlr.press/v282/sun26a.html.

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