Out-Of-Distribution (OOD) detection is critical to deploy deep learning models in safety-critical applications. However, the inherent hierarchical concept structure of visual data, which is instrumental to OOD detection, is often poorly captured by conventional methods based on Euclidean geometry. This work proposes a metric framework that leverages the strengths of Hyperbolic geometry for OOD detection. Inspired by previous works that refine the decision boundary for OOD data with synthetic outliers, we extend this method to Hyperbolic space. Interestingly, we find that synthetic outliers do not benefit OOD detection in Hyperbolic space as they do in Euclidean space. Furthermore we explore the relationship between OOD detection performance and Hyperbolic embedding dimension, addressing practical concerns in resource-constrained environments. Extensive experiments show that our framework improves the FPR95 for OOD detection from 22\% to 15\% and from 49% to 28% on CIFAR-10 and CIFAR-100 respectively compared to Euclidean methods.

翻译：分布外（OOD）检测对于在安全关键应用中部署深度学习模型至关重要。然而，视觉数据固有的层次化概念结构——这对OOD检测具有重要作用，往往被基于欧几里得几何的传统方法所忽视。本文提出了一种利用双曲几何优势进行OOD检测的度量框架。受先前通过合成异常值优化OOD数据决策边界工作的启发，我们将此方法扩展至双曲空间。有趣的是，我们发现合成异常值在双曲空间中并不像在欧几里得空间中那样有益于OOD检测。此外，我们探究了OOD检测性能与双曲嵌入维度之间的关系，解决了资源受限环境下的实际考量问题。大量实验表明，与欧几里得方法相比，我们的框架将CIFAR-10和CIFAR-100数据集上的OOD检测FPR95分别从22%降低至15%，以及从49%降低至28%。