Uncertainty Estimation via Hyperspherical Confidence Mapping

TL;DR

Hyperspherical Confidence Mapping (HCM) offers a sampling-free, distribution-free method for neural network uncertainty estimation by leveraging geometric constraints on output representations, applicable to various tasks.

Contribution

HCM introduces a novel geometric framework for uncertainty estimation that is simple, efficient, and surpasses existing methods in accuracy and inference cost.

Findings

HCM matches or exceeds ensemble and evidential methods in benchmarks.

HCM provides deterministic, interpretable uncertainty estimates.

HCM has lower inference cost than sampling-based approaches.

Abstract

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional assumptions, we propose Hyperspherical Confidence Mapping (HCM), a simple yet principled framework for sampling-free and distribution-free uncertainty estimation. HCM decomposes outputs into a magnitude and a normalized direction vector constrained to lie on the unit hypersphere, enabling a novel interpretation of uncertainty as the degree of violation of this geometric constraint. This yields deterministic and interpretable estimates applicable to both regression and classification. Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment. Our results highlight the power of geometric structure in uncertainty estimation and position HCM as a versatile alternative to conventional techniques.