Uncertainty Estimation via Hyperspherical Confidence Mapping

2026-05-07

AI Summary

This work addresses the critical challenge of efficiently and reliably quantifying uncertainty in neural networks for high-stakes applications such as autonomous driving, healthcare, and manufacturing. The authors propose the Hyperspherical Confidence Mapping (HCM) framework, which uniquely models uncertainty as the degree to which output vectors deviate from a unit hyperspherical geometric constraint. By decomposing network outputs into magnitude and direction components, HCM enables deterministic uncertainty estimation without sampling or distributional assumptions. The approach is universally applicable to both regression and classification tasks, offering strong interpretability and minimal computational overhead. Extensive experiments demonstrate that HCM consistently outperforms ensemble methods and evidential deep learning across multiple benchmarks and real-world industrial tasks, achieving superior calibration between confidence and error while maintaining comparable or better predictive accuracy and significantly higher inference efficiency.

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.

Problem

• uncertainty estimation
• neural networks
• sampling-free
• distribution-free
• geometric constraint

Innovation

• Uncertainty Estimation
• Hyperspherical Confidence Mapping
• Sampling-free
• Distribution-free
• Geometric Constraint