Hyperbolic Structured Classification for Robust Single Positive Multi-label Learning

2025-10-17

AI Summary

To address the challenges of complex label correlations, sparse annotations, and the inability of existing methods to explicitly model hierarchical structures in single-positive multi-label learning (SPMLL), this paper proposes the first hyperbolic-space-based classification framework. Departing from conventional point embeddings, it represents labels as hyperbolic balls, enabling explicit modeling of multivariate label relationships—such as inclusion, overlap, and separation—through geometric interactions in the Poincaré ball model. A temperature-adaptive classifier and a physics-inspired double-well regularizer are jointly introduced to optimize both distance-based discrimination and inclusion-based structural consistency. Evaluated on four standard benchmarks—including MS-COCO and PASCAL VOC—the method achieves state-of-the-art performance. Visualization and quantitative analysis confirm that the learned hyperbolic ball embeddings strongly align with empirical label co-occurrence patterns, demonstrating both effectiveness and interpretability in capturing label structure under weak supervision.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Computer Vision: Representation Learning for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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. While existing methods implicitly model label relationships through distance-based similarity, lacking explicit geometric definitions for different relationship types. To 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. To 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.

Problem

• Modeling complex label relationships under single positive supervision
• Capturing hierarchical structures and co-occurrence patterns simultaneously
• Addressing incomplete supervision in multi-label classification tasks

Innovation

• Hyperbolic ball representation for label modeling
• Temperature-adaptive hyperbolic ball classifier design
• Physics-inspired double-well regularization for configurations