Hyperbolic Category Discovery

TL;DR

HypCD is introduced, a simple Hyperbolic framework for learning hierarchy-aware representations and classifiers for generalized Category Discovery that 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.

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.

Figures (6)

• Figure 1: (a) Spherical-based vs. Hyperbolic-based methods, where hyperbolic space better accommodates variations in scale and improves connections between samples. (b) Average ACC comparison of our method and previous SOTA across 'All', 'Old', and 'New' categories on the SSB vaze2022semantic benchmark using DINO caron2021emerging.
• Figure 2: Hierarchical relations in GCD. (a) Inter-category relationships within the Stanford-Cars dataset krause20133d. (b) Intra-category relationships within CUB wah2011caltech dataset.
• Figure 3: 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.
• Figure 4: Comparison of baseline and hyperbolic counterparts on the SSB. Left: 'All' ACC (higher is better). Right: Discrepancy between 'Old' and 'New' ACC (smaller is better).
• Figure 5: T-SNE van2008visualizing comparison between SimGCD wen2023parametric and our Hyp-SimGCD using 40 randomly sampled instances from 10 randomly selected categories of the Stanford-Cars dataset krause20133d.