# Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds

arXiv: https://arxiv.org/abs/2602.16015 · HTML: https://mlsanity.com/paper/2602.16015/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [A Smooth Representation of Belief over SO(3) for Deep Rotation Learning with Uncertainty](https://mlsanity.com/paper/2006.01031/) (2020)
- [Split Conformal Prediction in the Function Space with Neural Operators](https://mlsanity.com/paper/2509.04623/) (2025)

## Built on by (most cited first, 2 of 2)

- [Where Does Reasoning Break? Step-Level Hallucination Detection via Hidden-State Transport Geometry](https://mlsanity.com/paper/2605.13772/) (2026)
- [Adaptive Geodesic Conformal Prediction for Egocentric Camera Pose Estimation](https://mlsanity.com/paper/2605.00233/) (2026)

## Abstract (arXiv)

Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces. When the response lies on a Riemannian manifold, Euclidean residuals and coordinate-based regions can ignore the geometry that defines meaningful error. We propose adaptive geodesic conformal prediction, a simple framework that builds nonconformity scores from geodesic distances and normalizes them with a cross-validated estimate of local prediction difficulty. On the sphere, this produces geodesic caps whose area is independent of position, while their radii still adapt to heteroscedastic noise. In both a synthetic sphere experiment and an IGRF-14 geomagnetic field forecasting task, the adaptive method preserves valid marginal coverage, reduces variation in conditional coverage, and improves worst-case coverage relative to non-adaptive and coordinate-based baselines.