# Higher-Order Certified Robustness for Regression

arXiv: https://arxiv.org/abs/2607.05536 · HTML: https://mlsanity.com/paper/2607.05536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 11 of 11)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [RepViT: Revisiting Mobile CNN From ViT Perspective](https://mlsanity.com/paper/2307.09283/) (2023)
- [MobileOne: An Improved One millisecond Mobile Backbone](https://mlsanity.com/paper/2206.04040/) (2022)
- [Benchmarking foundation models as feature extractors for weakly-supervised computational pathology](https://mlsanity.com/paper/2408.15823/) (2024)
- [Distilling foundation models for robust and efficient models in digital pathology](https://mlsanity.com/paper/2501.16239/) (2025)
- [Unsupervised Foundation Model-Agnostic Slide-Level Representation Learning](https://mlsanity.com/paper/2411.13623/) (2024)
- [A Deployment-Friendly Foundational Framework for Efficient Computational Pathology](https://mlsanity.com/paper/2602.14010/) (2026)

## Abstract (arXiv)

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.