Higher-Order Certified Robustness for Regression

Claire Jie Zhang, Natalie Frank
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:155482-155531, 2026.

Abstract

Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model’s prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, $\alpha$-smoothing.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-zhang26ay, title = {Higher-Order Certified Robustness for Regression}, author = {Zhang, Claire Jie and Frank, Natalie}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {155482--155531}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/zhang26ay/zhang26ay.pdf}, url = {https://proceedings.mlr.press/v306/zhang26ay.html}, abstract = {Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model’s prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, $\alpha$-smoothing.} }
Endnote
%0 Conference Paper %T Higher-Order Certified Robustness for Regression %A Claire Jie Zhang %A Natalie Frank %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-zhang26ay %I PMLR %P 155482--155531 %U https://proceedings.mlr.press/v306/zhang26ay.html %V 306 %X Randomized smoothing has emerged as a scalable technique for certifying the adversarial robustness of classifiers. However, its application to regression remains under-explored and faces unique challenges. Existing regression certificates rely on probabilistic acceptance regions and fail to exploit the local geometry of the function. In this work, we present a novel framework for certified robust regression that addresses these limitations. We derive a prediction-centered certificate that guarantees the stability of the smoothed model’s prediction and ensures practical computability at test time. We investigate several alternatives for constructing these certificates by explicitly incorporating means, variances, and gradients. In particular we demonstrate on the MNIST rotation task that utilizing gradient information yields significantly tighter robustness certificates compared to the current state-of-the-art, $\alpha$-smoothing.
APA
Zhang, C.J. & Frank, N.. (2026). Higher-Order Certified Robustness for Regression. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:155482-155531 Available from https://proceedings.mlr.press/v306/zhang26ay.html.

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