AdaGeo: Adaptive Local Geometry Modeling for Long-Tail Out-of-Distribution Detection

Long-tailed class imbalance presents a fundamental challenge for out-of-distribution (OOD) detection. Limited supervision yields sparse, unreliable representations for tail classes, and large intra-class variation prevents class-level representations from fully capturing the geometric structure of head classes. We observe that these head-class features often form multiple compact local structures rather than concentrating around a single global prototype. This motivates us to reconsider long-tailed OOD detection from the perspective of geometry modeling. Specifically, we propose AdaGeo, an adaptive local geometry framework that represents each class with multiple geometric components and jointly exploits their location, compactness, and empirical support. Based on this representation, we introduce a density-aware geometry learning objective that assigns stronger supervision to samples that deviate from their matched centers relative to the local geometric scale. Further, to keep this learned geometry aligned with the available evidence, we propose an adaptive mechanism that removes redundant local components according to their effective support and compactness. At the inference phase, we combine the global energy-based confidence with local geometric evidence, including intra-class cohesion and inter-class separation, to obtain a geometry-aware OOD score. Experiments on CIFAR-10-LT, CIFAR-100-LT, and ImageNet-LT demonstrate that AdaGeo improves in-distribution (ID) classification accuracy over the evaluated baselines and achieves competitive OOD detection performance, with the best average OOD results on CIFAR-100-LT and ImageNet-LT.