CP$^2$: Leveraging Geometry for Conformal Prediction via Canonicalization

Abstract

We study the problem of *conformal prediction* (CP) under geometric data shifts, where data samples are susceptible to transformations such as rotations or flips. While CP endows prediction models with *post-hoc* uncertainty quantification and formal coverage guarantees, their practicality breaks under distribution shifts that deteriorate model performance. To address this issue, we propose integrating geometric information-such as geometric pose-into the conformal procedure to reinstate its guarantees and ensure robustness under geometric shifts. In particular, we explore recent advancements on pose *canonicalization* as a suitable information extractor for this purpose. Evaluating the combined approach across discrete and continuous shifts and against equivariant and augmentation-based baselines, we find that integrating geometric information with CP yields a principled way to address geometric shifts while maintaining broad applicability to black-box predictors.