# One Sample is Enough to Make Conformal Prediction Robust

arXiv: https://arxiv.org/abs/2506.16553 · HTML: https://mlsanity.com/paper/2506.16553/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 28 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)
- [(Certified!!) Adversarial Robustness for Free!](https://mlsanity.com/paper/2206.10550/) (2022)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Tight Certificates of Adversarial Robustness for Randomly Smoothed Classifiers](https://mlsanity.com/paper/1906.04948/) (2019)
- [Efficient Robustness Certificates for Discrete Data: Sparsity-Aware Randomized Smoothing for Graphs, Images and More](https://mlsanity.com/paper/2008.12952/) (2020)
- [Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework](https://mlsanity.com/paper/2002.09169/) (2020)
- [Certifying Confidence via Randomized Smoothing](https://mlsanity.com/paper/2009.08061/) (2020)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [Provably Robust Conformal Prediction with Improved Efficiency](https://mlsanity.com/paper/2404.19651/) (2024)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [Robust Yet Efficient Conformal Prediction Sets](https://mlsanity.com/paper/2407.09165/) (2024)
- [Verifiably Robust Conformal Prediction](https://mlsanity.com/paper/2405.18942/) (2024)
- [Robust Conformal Prediction with a Single Binary Certificate](https://mlsanity.com/paper/2503.05239/) (2025)
- [Efficient Robust Conformal Prediction via Lipschitz-Bounded Networks](https://mlsanity.com/paper/2506.05434/) (2025)

## Built on by (most cited first, 4 of 4)

- [Analyzing Uncertainty of LLM-as-a-Judge: Interval Evaluations with Conformal Prediction](https://mlsanity.com/paper/2509.18658/) (2025)
- [Multi-Condition Conformal Selection](https://mlsanity.com/paper/2510.08075/) (2025)
- [Fast and Flexible Robustness Certificates for Semantic Segmentation](https://mlsanity.com/paper/2512.06010/) (2025)
- [CAGE: Certified Authorization under Typed-Return Uncertainty for Tool-Using Agents](https://mlsanity.com/paper/2607.29190/) (2026)

## Abstract (arXiv)

For any black-box model, conformal prediction (CP) returns prediction sets guaranteed to include the true label with high adjustable probability. Robust CP (RCP) extends the guarantee to the worst case noise up to a pre-defined magnitude. For RCP, a well-established approach is to use randomized smoothing since it is applicable to any black-box model and provides smaller sets compared to deterministic methods. However, smoothing-based robustness requires many model forward passes per each input which is computationally expensive. We show that conformal prediction attains some robustness even with a single forward pass on a randomly perturbed input. Using any binary certificate we propose a single sample robust CP (RCP1). Our approach returns robust sets with smaller average set size compared to SOTA methods which use many (e.g. 100) passes per input. Our key insight is to certify the conformal procedure itself rather than individual conformity scores. Our approach is agnostic to the task (classification and regression). We further extend our approach to smoothing-based robust conformal risk control.