用几何约束实现无需采样的高精度不确定性估计
Uncertainty Estimation via Hyperspherical Confidence Mapping
- 将输出分解为幅度与单位方向向量，利用球面约束量化不确定性
- 在多个基准和工业任务中表现优于集成与证据方法，推理成本更低
- 适合对可靠性要求高的自动驾驶、医疗等场景
在自动驾驶、医疗和制造等高风险领域，量化神经网络预测的不确定性至关重要。现有方法通常依赖昂贵的采样或严格的分布假设，我们提出无采样、无分布假设的超球面置信度映射（HCM）框架。HCM将输出分解为幅度和单位方向向量，约束其位于单位超球面上，将不确定性定义为对该几何约束的违反程度。该方法生成确定且可解释的估计，适用于回归与分类任务。在多样化的基准和真实工业任务上的实验表明，HCM在性能上匹配或超越集成与证据方法，推理开销显著更低，置信度与误差一致性更强。结果凸显几何结构在不确定性估计中的潜力，使HCM成为传统技术的有力替代。
原文摘要 · Abstract (English)
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.
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