Hyperbolic Category Discovery

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 Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery. 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.

Overall pipeline of our HypCD framework for parametric and non-parametric GCD baselines. (a) Hyperbolic representation learning. (b) Hyperbolic classifier. (c) Non-parametric label assignment. (d) Parametric label assignment.

We compare our method with recent GCD methods using both DINO and DINOv2 pretrained backbone. The evaluation encompasses performance on the SSB benchmark and generic datasets (CIFAR-10, CIFAR-100 and ImageNet-100). The hyperbolic methods applying our HypCD framework are indicated by the 'Hyp-' prefix. We can see that our method consistently achieve significant improvements on the three baselines (GCD, SimGCD and SelEx) and achieve a new SOTA performance.

T-SNE comparison between SimGCD and our Hyp-SimGCD using 40 randomly sampled instances from 10 randomly selected categories of the Stanford-Cars dataset. This comparison implies that Hyp-SimGCD enhances both intra-class compactness and inter-class separation through our hyperbolic representation and classifier learning method. Importantly, even within the original Euclidean space of the backbone network, Hyp-SimGCD exhibits robust clustering performance, which arises from the properties of hyperbolic space in encoding hierarchical structures.

Visualization of attention maps for the baseline (GCD) and our method (Hyp-GCD). Our approach effectively directs attention towards foreground objects, regardless of whether they belong to the 'Old' or 'New' classes.