Hyperbolic Structured Classification for Robust Single Positive Multi-label Learning

Abstract--Single Positive Multi-Label Learning (SPMLL) addresses the challenging scenario where each training sample is annotated with only one positive label despite potentially belonging to multiple categories, making it difficult to capture complex label relationships and hierarchical structures. T o address these limitations, we propose the first hyperbolic classification framework for SPMLL that represents each label as a hyperbolic ball rather than a point or vector, enabling rich inter-label relationship modeling through geometric ball interactions. Our ball-based approach naturally captures multiple relationship types simultaneously: inclusion for hierarchical structures, overlap for co-occurrence patterns, and separation for semantic independence. Further, we introduce two key component innovations: a temperature-adaptive hyperbolic ball classifier and a physics-inspired double-well regularization that guides balls toward meaningful configurations. T o validate our approach, extensive experiments on four benchmark datasets (MS-COCO, PASCAL VOC, NUS-WIDE, CUB-200-2011) demonstrate competitive performance with superior interpretability compared to existing methods. Furthermore, statistical analysis reveals strong correlation between learned embeddings and real-world co-occurrence patterns, establishing hyperbolic geometry as a more robust paradigm for structured classification under incomplete supervision. Multi-label recognition (MLR) is a fundamental problem in domains such as computer vision, natural language processing, multimedia retrieval, and medical diagnosis.