HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery

TL;DR

HiDISC addresses DG-GCD by learning domain- and category-invariant embeddings in a curvature-aware hyperbolic space. The approach combines lightweight GPT-guided diffusion-based domain augmentation, Tangent CutMix for open-set sample generation, and a unified loss consisting of a Penalized Busemann term, a Hybrid Hyperbolic Contrastive term, and an Adaptive Outlier term, with a learnable curvature parameter. The empirical results on PACS, Office-Home, and DomainNet show state-of-the-art performance with markedly lower training FLOPs than episodic baselines, validating hyperbolic geometry as a principled foundation for open-world generalization. Theoretical analyses and ablations further justify the design, demonstrating tighter hyperbolic generalization bounds and robust performance under various domain and prototype configurations.

Abstract

Generalized Category Discovery (GCD) aims to classify test-time samples into either seen categories** -- available during training -- or novel ones, without relying on label supervision. Most existing GCD methods assume simultaneous access to labeled and unlabeled data during training and arising from the same domain, limiting applicability in open-world scenarios involving distribution shifts. Domain Generalization with GCD (DG-GCD) lifts this constraint by requiring models to generalize to unseen domains containing novel categories, without accessing targetdomain data during training. The only prior DG-GCD method, DG2CD-Net, relies on episodic training with multiple synthetic domains and task vector aggregation, incurring high computational cost and error accumulation. We propose HIDISC, a hyperbolic representation learning framework that achieves domain and category-level generalization without episodic simulation. To expose the model to minimal but diverse domain variations, we augment the source domain using GPT-guided diffusion, avoiding overfitting while maintaining efficiency. To structure the representation space, we introduce Tangent CutMix, a curvature-aware interpolation that synthesizes pseudo-novel samples in tangent space, preserving manifold consistency. A unified loss -- combining penalized Busemann alignment, hybrid hyperbolic contrastive regularization, and adaptive outlier repulsion -- **facilitates compact, semantically structured embeddings. A learnable curvature parameter further adapts the geometry to dataset complexity. HIDISC achieves state-of-the-art results on PACS , Office-Home , and DomainNet, consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines.

Figures (11)

• Figure 1: Spherical vs. hyperbolic (Poincaré) embeddings on PACS. Same-class samples from different domains (green/red) cluster more tightly in hyperbolic space, demonstrating improved class separation. Refer to Sup. Mat. for quantitative analysis.
• Figure 2: Illustration of the HiDISC pipeline for DG-GCD in hyperbolic space. The model is trained using labeled source data $\mathcal{D}_S$ (green borders) and 1–2 GPT-guided synthetic domains $\mathcal{D}_{\text{Syn}}^1$, $\mathcal{D}_{\text{Syn}}^2$ (orange borders) to simulate domain shift. Features from the shared encoder are projected to the Poincaré ball via $\exp_0^c$. To mimic novel categories, Tangent CutMix performs interpolation in the tangent space and maps the result $z_{\text{mix}}$ back to hyperbolic space. The embedding space is structured via: (i) penalized Busemann loss $\mathcal{L}_{\text{Buse}}$ for aligning seen classes to boundary-fixed prototypes; (ii) hybrid contrastive loss $\mathcal{L}_u$ for clustering and separability; and (iii) adaptive outlier loss $\mathcal{L}_{\text{out}}$ to repel pseudo-novel points. Together, these shape a curvature-aware space for generalization and discovery.
• Figure 2: Estimated number of clusters. Correct estimates are in green, small errors in orange, and large deviations in red.
• Figure 3: (Left) Effect of $\alpha_d$ in hybrid contrastive loss. A balanced combination of angular and geodesic components achieves the highest accuracy. (Right) Impact of synthetic domains on old and new category performance. While old-class accuracy increases due to augmented seen data, new-class performance slowly degrades with more synthetic domains, as they cause seen-class bias.
• Figure 4: Poincaré‐disk UMAP mcinnes2018umap embeddings of the target domain ("Photo") clusters, as produced by Hyp-GCD Liu2025HypCD, Hyp-SelfEx Liu2025HypCD, Hyp-DG2CD-Net, and HiDISC (Ours) for the PACS dataset, with "Sketch" as the source. HiDISC produces a visually clean and compact embedding space, supported by silhouette scoresrousseeuw1987silhouettes ($\in [-1.1]$, $\uparrow$), indicating improved cluster compactness and separation: (Hyp-GCD: -0.52, Hyp-SelfEx: -0.42, Hyp-DG$^2$CD-Net: -0.29, HiDisc: -0.14)