# Hyperbolic Structured Classification for Robust Single Positive Multi-label Learning

arXiv: https://arxiv.org/abs/2510.15296 · HTML: https://mlsanity.com/paper/2510.15296/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Multi-Label Learning from Single Positive Labels](https://mlsanity.com/paper/2106.09708/) (2021)
- [Large-Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/1806.00437/) (2018)
- [Large Loss Matters in Weakly Supervised Multi-Label Classification](https://mlsanity.com/paper/2206.03740/) (2022)
- [Hyperbolic Interaction Model For Hierarchical Multi-Label Classification](https://mlsanity.com/paper/1905.10802/) (2019)
- [Simple and Robust Loss Design for Multi-Label Learning with Missing Labels](https://mlsanity.com/paper/2112.07368/) (2021)
- [Acknowledging the Unknown for Multi-label Learning with Single Positive Labels](https://mlsanity.com/paper/2203.16219/) (2022)
- [Exploring Structured Semantic Prior for Multi Label Recognition with Incomplete Labels](https://mlsanity.com/paper/2303.13223/) (2023)
- [One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement](https://mlsanity.com/paper/2206.00517/) (2022)
- [Bridging the Gap between Model Explanations in Partially Annotated Multi-label Classification](https://mlsanity.com/paper/2304.01804/) (2023)
- [Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classification](https://mlsanity.com/paper/2306.14822/) (2023)
- [Vision-Language Pseudo-Labels for Single-Positive Multi-Label Learning](https://mlsanity.com/paper/2310.15985/) (2023)
- [Joint Learning of Hyperbolic Label Embeddings for Hierarchical Multi-label Classification](https://mlsanity.com/paper/2101.04997/) (2021)
- [Boosting Single Positive Multi-label Classification with Generalized Robust Loss](https://mlsanity.com/paper/2405.03501/) (2024)
- [Context Does Matter: End-to-end Panoptic Narrative Grounding with Deformable Attention Refined Matching Network](https://mlsanity.com/paper/2310.16616/) (2023)
- [SpliceMix: A Cross-scale and Semantic Blending Augmentation Strategy for Multi-label Image Classification](https://mlsanity.com/paper/2311.15200/) (2023)
- [Semantic-guided Representation Learning for Multi-Label Recognition](https://mlsanity.com/paper/2504.03801/) (2025)

## Abstract (arXiv)

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.