Hyperbolic Category Discovery

2025-04-08

AI Summary

Generalized Category Discovery (GCD) aims to jointly identify all unlabeled images—including those from both known and unknown classes—in an open-world setting with inherent hierarchical structure. Conventional Euclidean or spherical representations struggle to capture such intrinsic hierarchies. This work pioneers the adaptation of GCD to hyperbolic space, proposing a unified framework that jointly learns hierarchy-aware representations and classifiers in the Poincaré ball. We introduce a novel joint metric combining hyperbolic distance and angular similarity to enhance knowledge transfer from known to unknown classes. Our approach integrates Poincaré embedding, Euclidean-to-hyperbolic mapping, and self-supervised backbone fine-tuning. Extensive experiments on multiple GCD benchmarks demonstrate significant improvements over state-of-the-art methods, validating the effectiveness and superiority of hyperbolic geometry for hierarchical category discovery in open-world scenarios.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Computer Vision: Representation Learning for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Generalized Category Discovery (GCD) is an intriguing open-world problem that has garnered increasing attention. Given a dataset that includes both labelled and unlabelled images, GCD aims to categorize all images in the unlabelled subset, regardless of whether they belong to known or unknown classes. In GCD, the common practice typically involves applying a spherical projection operator at the end of the self-supervised pretrained backbone, operating within Euclidean or spherical space. However, both of these spaces have been shown to be suboptimal for encoding samples that possesses hierarchical structures. In contrast, hyperbolic space exhibits exponential volume growth relative to radius, making it inherently strong at capturing the hierarchical structure of samples from both seen and unseen categories. Therefore, we propose to tackle the category discovery challenge in the hyperbolic space. We introduce HypCD, a simple underline{Hyp}erbolic framework for learning hierarchy-aware representations and classifiers for generalized underline{C}ategory underline{D}iscovery. HypCD first transforms the Euclidean embedding space of the backbone network into hyperbolic space, facilitating subsequent representation and classification learning by considering both hyperbolic distance and the angle between samples. This approach is particularly helpful for knowledge transfer from known to unknown categories in GCD. We thoroughly evaluate HypCD on public GCD benchmarks, by applying it to various baseline and state-of-the-art methods, consistently achieving significant improvements.

Problem

• GCD categorizes unlabeled images, including unknown classes
• Euclidean and spherical spaces poorly encode hierarchical structures
• Hyperbolic space better captures hierarchical sample structures

Innovation

• Hyperbolic space for hierarchical representation
• Combines hyperbolic distance and angle
• Transforms Euclidean to hyperbolic space