One Sample is Enough to Make Conformal Prediction Robust

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. $\sim 100$) 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.