Title: HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery
Venue: NeurIPS 2025
Accepted: yes
Keywords: Domain Generalization

Category Discovery

Hyperbolic Spaces
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 target-domain data during training.
The only prior DG-GCD method, DG$^2$CD-Net~\cite{dg2net}, relies on episodic training with multiple synthetic domains and task vector aggregation, incurring high computational cost and error accumulation. We propose \textsc{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 \emph{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.
\textsc{HiDISC} achieves state-of-the-art results on PACS~\cite{pacs}, Office-Home~\cite{officehome}, and DomainNet~\cite{domainnet}, consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines.

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

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, DG 2 CD-Net [1], 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 GPTguided 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-ofthe-art results on PACS [2], Office-Home [3], and DomainNet [4], consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines. 1

1 Introduction

Deep neural networks have achieved impressive success in visual recognition [5, 6], yet typically assume a shared domain and label space between training and test data. This assumption breaks down in real-world applications such as autonomous driving [7] and medical diagnostics [8], where both domain shift and label shift frequently co-occur. While semi/self-supervised learning [9, 10] reduces labeling demands, it still operates under closed-world constraints. Domain Adaptation (DA) and Domain Generalization (DG) [11, 12] address distribution shift but assume a fixed set of categories. Open-set DG [13, 14] allows test-time novelty but collapses all unknowns into a single rejection class, erasing semantic granularity.

Generalized Category Discovery (GCD) [15-17] seeks to identify both known and novel classes from unlabeled test data but requires joint access to labeled and unlabeled samples from the same domain. Cross-Domain GCD (CD-GCD) [18, 19] introduces domain shift but still assumes concurrent access to source-target domains during training. In contrast, Domain Generalization with GCD (DG-

Code Link : https://vaibhavrathore1999.github.io/HiDISC/

GCD) [1] represents a more realistic setting: the model is trained solely on labeled source data and must generalize to an unseen target domain containing both seen and novel categories.

Addressing DG-GCD requires (i) learning domain-invariant features and (ii) discovering novel semantic structures without supervision. The only existing solution tailored for DG-GCD, DG 2 CDNet [1] approaches this via episodic training with synthetic domains and task aggregation, but suffers from high computational cost and cumulative approximation errors that limit generalization.

From a different perspective, existing GCD and DG-GCD methods typically rely on Euclidean or hyperspherical geometry [1, 18], which struggle to capture semantic hierarchies. Hyperbolic geometry [20, 21], with its negative curvature and exponential volume growth, offers a natural alternative for modeling inter-class structure (Fig. 1). While hyperbolic embeddings have shown benefits in GCD (HypCD) [22] and DG [23] recently, their use in DG-GCD, where both domain and label shifts co-occur, remains unexplored. This raises our central question:

Can hyperbolic geometry provide a unified foundation for solving DG-GCD, addressing both distribution shift and novel-class discovery?

Our approach. We introduce HIDISC, the first hyperbolic geometry-aware framework for DG-GCD that learns semantically structured and domain-invariant embeddings in the Poincaré ball [20] without requiring target supervision. Unlike HypCD [22], which addresses standard GCD in single-domain settings, and DG 2 CD-Net [1], which operates in Euclidean space and relies on episodic simulation, HIDISC provides a unified, non-episodic solution using the representational advantages of hyperbolic space.

Since the hyperbolic space offers substantial domain invariance and focuses on shared semantics [23] (Fig. 1, Sup. Mat. ), we still chose to augment the training source domain with controlled stylistic variations and generate only 1-2 synthetic domains per image via a GPT-4o [24]-guided diffusion model, avoiding the computational over-

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head of task-based simulation in DG 2 CD-Net. A novel domain-diversity score ranks these augmentations by measuring source divergence and intra-pair variability, enabling a principled and scalable domain diversification strategy.

To ensure the model does not overfit the known classes and encourage semantic diversity, we propose Tangent CutMix , a curvature-aware interpolation method that mixes labeled features in the tangent space of the Poincaré ball to create pseudo-open samples. Unlike Euclidean mixing used in SimGCD [25] or CMS [26], our method preserves hyperbolic consistency and generates geometrically valid pseudo-novel embeddings that support open-set regularization.

To structure the latent space, we introduce a unified loss that combines three novel components not jointly explored in prior (DG)-GCD literature: (i) a penalized Busemann loss that aligns seen-class features to fixed prototypes at the hyperbolic boundary while reserving interior space for unknowns; (ii) a hybrid hyperbolic contrastive loss balancing angular and geodesic similarities to enable finegrained clustering across known and novel categories; and (iii) an adaptive outlier rejection loss that pushes synthetic cut-mix samples away from known-class regions, encouraging open-space generalization without relying on adversarial or domain-specific objectives. A learnable curvature parameter further adapts the geometry to dataset-specific complexity. Major contributions include:

-HIDISC, the first hyperbolic DG-GCD framework, jointly handles domain and category shift without target supervision or episodic simulation.

A unified loss formulation integrating Busemann alignment, hybrid contrastive regularization, and an adaptive outlier repulsion.

Tangent CutMix, the first open-set augmentation designed specifically for hyperbolic geometry.

-State-of-the-art results on PACS [2], Office-Home [3], and DomainNet [4], outperforming all the baselines consistently and reducing training FLOPs by over 96 × vs. DG 2 CD-Net.

2 Related Works

Domain Generalization. DG aims to train models on labeled data from one or more source domains to generalize effectively to previously unseen target domains [12, 27]. DG variants include closed-set, open-set, single-source, and multi-source settings [28]. Methods like MixStyle [29] and StyleHallucination [30] enhance robustness via feature-level style perturbations, while metalearning techniques [31, 32] simulate domain shifts episodically to improve adaptability. Open-set DG methods address novel test-time classes [33, 34, 14, 35], but typically collapse all unknowns into a single 'outlier' class, hindering fine-grained discovery needed in DG-GCD.

Category Discovery. Category Discovery seeks to partition unlabeled data into known and novel categories. While Novel Category Discovery (NCD) [36] assumes complete disjointness between training and test classes, GCD allows overlap and requires identifying both seen and unseen categories during inference [15-17, 25, 37, 38, 26]. Most GCD approaches assume joint access to source and target domains during training, limiting real-world applicability. CD-GCD methods like CDADNet [18] and HiLo [28] reduce domain gaps via adversarial alignment or style normalization but still depend on concurrent domain access. To remove this constraint, DG-GCD [1] simulates domain shifts through text-driven image manipulation (e.g., InstructPix2Pix [39]) and aggregates task-specific knowledge via task vectors [40]. However, these methods operate in Euclidean spaces, which struggle to encode the hierarchical and shared semantic structures crucial for robust domain and category generalization.

Hyperbolic Embedding Spaces. Hyperbolic geometry, defined by negative curvature and exponential volume growth, is well-suited for modeling hierarchical and part-whole semantic structures [20, 21]. Hyperbolic embeddings have improved performance in classification [41-43], few-shot learning [44], segmentation [45], and action recognition [46], supported by hyperbolic variants of standard network components [47, 48, 21, 49]. Recent Busemann-based techniques [23, 50] anchor ideal prototypes on the Poincaré boundary for directional alignment. HypCD [22] successfully applies this to GCD, but assumes joint source-target access. Beyond these, hyperbolic methods have been applied across diverse tasks: Ge et al. [51] explore contrastive learning for hierarchical scene-object representation, Yue et al. [52] study metric learning with hard negatives, Liu et al. [53] extend contrastive learning to EEG, Sun & Ma [54] investigate recommendation, while others address hashing [55] and face antispoofing with hierarchical prototypes [56]. To date, no work has explored hyperbolic representations for DG-GCD, which combines open-set discovery and domain shift without target supervision.

3 Methodology

3.1 The DG-GCD Problem Definition

In DG-GCD, we are given a labeled source-domain dataset:

where x s i represents source-domain inputs, and y s i denotes labels drawn from a set of known categories Y s . At test time, we encounter an unlabeled target-domain dataset:

where samples belong either to known categories ( Y old t = Y s ) or previously unseen, novel categories ( Y new t ), such that Y new t ∩ Y s = ∅ . Crucially, the data distributions across domains differ significantly, i.e., P ( X s ) = P ( X t ) , and the target dataset D T is inaccessible during training.

̸

Our objective is to construct an embedding space using only D S that generalizes across domains and categories, effectively clustering both known and novel-class samples from the unseen dataset D T .

3.2 Rationale Behind Using Hyperbolic Space for DG-GCD

Semantic structures in visual data-such as hierarchies, taxonomies, and part-whole relationships-are inherently suited to spaces with exponential capacity. Hyperbolic space, characterized

~Beta(α,β)

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by negative curvature and exponential volume growth, naturally encodes such structures, making it particularly beneficial for DG-GCD, where labeled classes typically reflect coarse semantic strata, while novel categories often reside in finer or more abstract regions.

In contrast to Euclidean or spherical embeddings [16, 57], which are constrained by polynomial growth, hyperbolic embeddings support both local compactness and global semantic separation. Moreover, hyperbolic geometry improves domain generalization by amplifying higher-level semantic distances and attenuating domain-specific low-level variations, thereby fostering robust, domaininvariant representations under substantial distributional shifts (more details provided in Sup. Mat ).

Poincaré Ball Geometry. We adopt the Poincaré ball [20] as our hyperbolic model. For curvature -c 2 , the n -dimensional ball is defined as:

where ∥ · ∥ denotes the Euclidean norm. Additional geometric details are provided in the Sup. Mat.

3.3 Navigating through HIDISC for DG-GCD

We propose HIDISC (Fig. 2), a hyperbolic framework that jointly addresses the dual challenges of DG-GCD: domain-invariant representation learning and unsupervised semantic disentanglement. The synthesis-driven components of our model include: (i) Synthetic Domain Augmentation , which introduces a compact set of diverse, diffusion-generated domains to simulate realistic distribution shifts without relying on target access; and (ii) Tangent CutMix , a curvature-aware interpolation mechanism operating in the tangent space of the Poincaré ball, generating pseudo-novel samples while preserving manifold fidelity. Complementing these are three loss-driven modules: (iii) Prototype Anchoring , which aligns seen-class embeddings to fixed ideal prototypes on the Poincaré boundary, reserving central space for novel classes; (iv) Adaptive Outlier Loss , which ensures synthetic samples are repelled from known-class clusters, promoting open-space regularization; and (v) Hybrid Hyperbolic Contrastive Loss , which combines geodesic and angular similarity to improve local cohesion and global separability. Each component is described in detail in the subsequent sections.

3.3.1 Lightweight Synthetic Domain Augmentation

To simulate domain variability without relying on expensive episodic training (as in DG 2 CD-Net [1]), we generate only one or two synthetic domains per experiment using a diffusion model guided by GPT-4o [24]-curated prompts (e.g., underwater , night-time variants of class instances) (see Sup. Mat. for qualitative visualizations). These synthetic domains serve as proxy distributions that expose the model to varied visual shifts and support generalization to unseen domains.

Unlike DG 2 CD-Net, which depends on numerous episodic tasks and synthetic domain permutations, our strategy is lightweight and avoids both computational overhead and error propagation across

episodes. Crucially, in hyperbolic space, even a small number of diverse augmentations can induce expansive representational changes due to the geometry's exponential capacity-effectively stretching the semantic space and encouraging separation between seen and unseen regions.

First, we introduce a domain-diversity score that ranks a given synthetic domain D ( s ) syn with respect to other synthetic domains {D ( l ) syn } M l =1 and the source domain D S based on the notion of mutual diversity calculated using the Fréchet Inception Distance (FID) [58] for M synthesized domains:

̸

This scoring promotes both source-domain divergence and intra-pair complementarity. We select the top-scoring 1 -2 domains to augment D S to obtain D train .

As shown in Fig. 3, excessive augmentation leads to overfitting on seen classes and degrades novel class discovery. Notably, training solely on D S yields competitive results, highlighting the inherent domain robustness of hyperbolic space, and using these augmentation provides marginal boosts. Effects of redundant augmentations are mentioned in Sup. Mat.

3.3.2 Mapping Visual Features into Curvature-Aware Hyperbolic Geometry

With the augmented training set, we learn representations using a frozen DINO [59]-pretrained ViT [60] followed by a 3-layer MLP. The resulting Euclidean feature z E ∈ R d is projected into the Poincaré ball D d c via the exponential map:

where c is a learnable curvature parameter in our case to approximate the data complexity more effectively. Let z i := z s i denote the hyperbolic feature. This projection facilitates the encoding of hierarchical semantics and ensures geometric consistency in the downstream tasks.

3.3.3 Tangent CutMix and Adaptive Outlier Loss

To hallucinate novel-category samples and regularize the open space in hyperbolic geometry, we introduce Tangent CutMix [61]-a curvature-aware variant of CutMix tailored for the Poincaré ball. Traditional CutMix interpolates feature representations in Euclidean space to synthesize outliers, which can violate the geometric constraints of hyperbolic space. In contrast, Tangent CutMix performs mixing in the tangent space at the origin, ensuring consistency with the underlying manifold structure.

Given two embeddings z i , z j ∈ D d c with different class labels, we:

Project to tangent space: v i = log c 0 ( z i ) , v j = log c 0 ( z j )

Linear mix: Compute v i,j mix = λv i +(1 -λ ) v j , where λ ∼ Beta(1 , 1) = Uniform(0 , 1)

Map back: z i,j mix = exp c 0 ( v mix )

The resulting embedding z mix represents a curvature-preserving interpolation of features with incompatible semantics, mimicking out-of-distribution behavior while remaining valid in the hyperbolic space. Furthermore, to prevent these synthetic features from collapsing into known class regions, we apply an adaptive outlier loss:

̸

where D H is the hyperbolic distance, and γ is a quantile-based adaptive margin over the distances from all class prototypes in { p k } |Y s | k =1 . This encourages pseudo-novel embeddings to remain outside the regions occupied by seen classes, effectively reserving space for novel category discovery. For further analysis regarding adaptive margin and the generated CutMix samples, see Sup. Mat.

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3.3.4 Prototype Anchoring with Penalized Busemann Loss

To enforce semantic structure among the known categories, we associate each class k ∈ Y s with a fixed ideal prototype p k ∈ ∂ D d c [23], placed uniformly on the boundary of the Poincaré ball. These prototypes serve as directional anchors and remain fixed throughout training, enabling compact clustering of seen-class features while leaving the interior volume of the ball available for unknown category discovery.

To align the features z i with their respective class prototypes, we adopt a penalized Busemann loss :

where p y i is the prototype corresponding to the class label of z i , and ϕ is a regularization coefficient. The first term guides directional alignment between features and their prototypes, preserving semantic proximity in the hyperbolic geometry. The second term penalizes embeddings that approach the boundary too aggressively, thereby maintaining stability during optimization and avoiding overconfidence.

3.3.5 Hybrid Hyperbolic Contrastive Loss

While the Busemann loss anchors known classes via directional alignment, it does not explicitly enforce local structure among unlabeled or novel samples. To address this, we incorporate a hybrid hyperbolic contrastive loss [22], designed to refine the latent space by encouraging consistency between augmented views and separating unrelated instances-even in the absence of explicit labels.

For each positive pair of embeddings z ′ i , z ′′ i , corresponding to different augmentations of the same input, we define the contrastive objective as:

̸

where τ is a temperature hyperparameter and B is the batch of samples. We use a hybrid similarity function δ ( ., . ) , which linearly combines distance-based and angle-based measures:

cos( · , · ) computes cosine similarity in the tangent space, thanks to the co-conformality of the Euclidean and Hyperbolic spaces. α d is the balancing factor (for more details see Sup. Mat. ).

This hybrid formulation leverages the metric structure of hyperbolic space to promote global semantic separation via geodesic distances, while retaining angular consistency within local neighborhoods. Fig. 3 shows the importance of the full δ over the individual distance metrics.

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3.3.6 Training Objective

Our final minimization objective integrates all components:

Test-time Protocol. After training, we extract hyperbolic features from target-domain samples and perform clustering using K-Means as in [1, 15]. See Sup. Mat. for detailed algorithm.

3.4 Theoretical Justification: Generalization in Euclidean vs. Hyperbolic Spaces

We analyze HIDISC under the lens of generalization theory in hyperbolic space. Given D S , D T , and synthetic augmentations {D ( l ) syn } M l =1 , the goal is to minimize the expected target risk:

Extending Rademacher-based analysis to the Poincaré ball D d c [21], we obtain:

where: L S ′ ( f ) : empirical loss over the augmented training set S ′ ; ∆ H ( S ′ , T ) : hyperbolic discrepancy between augmented source and target; R H ( H ) : Rademacher complexity of the hypothesis class H ; ϵ : a residual optimization error.

Compared to the Euclidean bound L E T ( f ) ≤ L S ′ ( f )+∆ E ( S ′ , T )+ R E ( H )+ ϵ , the hyperbolic version benefits from the exponential volume and hierarchical structure of D d c . This allows semantically distant concepts to be placed further apart with less distortion and curvature-driven compression around known classes-thereby making fewer, well-chosen augmentations sufficient to span the generalization space. As such, ∆ H ( S ′ , T ) < ∆ E ( S ′ , T ) holds under the same augmentation budget, yielding a tighter bound (see Sup. Mat. for a formal proof).

Each loss in HIDISC contributes to improving specific terms: (i) The Busemann loss L Buse aligns seen-class features to ideal prototypes at the boundary, stabilizing L S ′ ( f ) via directional compactness; (ii) The hybrid contrastive loss L u integrates angular and geodesic similarity to encourage semantically meaningful clusters and reduce model complexity R H ( H ) ; (iii) The outlier loss L out , applied on Tangent CutMix samples, helps partition the open space, reducing false positives on novel categories without explicit domain alignment; (iv) The curated synthetic domains {D ( l ) syn } enrich S ′ , approximating T 's support and reducing ∆ H ( S ′ , T ) in a geometry-consistent manner.

In Sup. Mat. , we show that FID-based estimates of ∆ H yield minimal improvement over the inherent domain-independence of hyperbolic geometry. We also compare our loss terms in Euclidean and hyperbolic spaces, demonstrating that hyperbolic geometry better reduces the generalization gap.

4 Experimental Evaluations

Dataset Details. We evaluate our method on three standard DG-GCD benchmarks: PACS [2], Office-Home[3], and Domain-Net[4]. We follow the protocol of [1] for constructing known/novel class-splits and source-target domain pairs. The dataset details are provided in the Sup. Mat .

Evaluation Metrics. Following [15, 18, 1], we evaluate clustering using three metrics: Old (accuracy on known classes Y old t ), New (accuracy on novel classes Y new t ), and All (overall accuracy on D T ). Hungarian matching is used to align predicted clusters with ground-truth labels. Scores are averaged over three runs and all source-target combinations. Further experimental details and hyper-parameter choices are mentioned in Sup. Mat.

4.1 Comparisons to the Literature

Table 1 compares our proposed HIDISC against state-of-the-art methods on the said datasets. Baselines are categorized into four groups: (i) Euclidean source-only GCD methods , including GCD [15], SimGCD [25], CMS [26], and SelfEx [64]; (ii) Synthetic augmentation-based GCD methods , such as SimGCD+Synthetic, CMS+Synthetic, and CDAD-Net+Synthetic [18], which incorporate domain-shifted images via diffusion-based generation; (iii) Hyperbolic GCD methods , including Hyp-GCD [22] and Hyp-SelfEx, which project features into hyperbolic space to improve clustering but do not generalize across domains. To ensure consistency with the DG-GCD setting, we retain only the components of these methods that rely on labeled data during training and omit terms involving unlabeled samples in all the above baselines, as recommended in [1]; and (iv) the DG-GCD baseline DG 2 CD-Net [1], which simulates multiple domains using diffusion models and aggregates task-level knowledge via episodic training and task vectors. For a fairer comparison, we also implement a hyperbolic variant, Hyp-DG 2 CD-Net, by replacing its embedding space with a Poincaré ball. As in [1], we report results for CDAD-Net [18] under joint access to source and target domains as an upper bound of our results.

Quantitatively, HIDISC achieves state-of-the-art performance across all metrics and datasets. It improves upon DG 2 CD-Net by +2.06% in average overall clustering accuracy and by +1.27% on novel class discovery. On DomainNet-the most diverse and challenging benchmark-HIDISC outperforms the best previous method by +1.21%. UMAP visualizations (Fig. 4) show HIDISC forms a compact embedding space. These gains are achieved without target access and with over

96 × lower training FLOPs than [1] while using the same number of synthetic domains (see Sup. Mat ). On the other hand, the performance of DG 2 CD-Net degrades drastically as the number of synthetic domains is reduced (see Sup. Mat. )

Furthermore, Table 2 compares the estimated number of clusters inferred by each method against the ground truth on PACS, Office-Home, and DomainNet. HIDISC is found to approximate the cluster counts more precisely than the counterparts.

The learnable curvature converges to dataset-specific values: 0.041 for Office-Home, 0.059 for PACS, and 0.38 for DomainNet. The curvature evolution plots are mentioned in Sup. Mat.

4.2 Ablation Analysis

Impact of Loss Components and Key Model Components. Table 3 evaluates the contribution of each loss component in HIDISC on Office-Home. The vanilla model, trained without any loss terms, yields only 26.17% overall accuracy. Introducing the Busemann loss alone improves performance substantially to 56.32%, while the hybrid hyperbolic contrastive loss independently achieves 50.95%. Combining both leads to further gains, particularly in old-class accuracy. Incorporating the outlier repulsion term yields the best overall result, with 56.78% total accuracy, 59.23% on known classes, and 53.21% on novel classes.

Table 4 presents ablations on key architectural components. Manual augmentations achieve 50.80% accuracy. Replacing the learnable curvature with static values ( c = 0 . 01 and 0 . 03 ) reduces accuracy considerably, as it fails to manage the data manifold effectively. Substituting Tangent CutMix with Euclidean CutMix lowers performance by 3.96%, confirming the benefits of curvature-consistent mixing. The complete HIDISC configuration consistently outperforms all variants, confirming the complementary benefits of its geometric and loss-driven design.

Ablation of Norm Radius and Slope in Hyperbolic Embedding. Westudy two key hyperparameters in our hyperbolic embedding setup: the ℓ 2 norm radius before exponential mapping and the slope ϕ in the penalized Busemann loss, both controlling embedding compactness and placement. As per Table 5, lower slopes (e.g., ϕ = 0 . 10 ) favor seen-class accuracy but hurt generalization, while higher slopes (e.g., ϕ = 0 . 90 ) improve novel-class performance by restricting dispersion. We choose ϕ = 0 . 75 for balance. For the norm radius, Table 5 shows that 1 . 5 best balances alignment to boundary-anchored prototypes and generalization, whereas smaller values (e.g., 1 . 0 ) overfit Y S .

Choice of Hyperbolic Model: Poincaré vs. Lorentz Model

Weadopt the Poincaré ball model, which we find performs more favorably than the Lorentz model [65] for DG-GCD on Office-Home in Table 6. Full theoretical details are in the Sup. Mat. The empirical comparison is below:

Hyperparameter Sensitivity for Loss Weights. We conducted an ablation study on the loss weights ( λ 1 , λ 2 , λ 3 ) and found our chosen configuration achieves near-optimal performance, demonstrating robustness Table 7. More details are in the Sup. Mat.

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5 Takeaways

We addressed the problem of DG-GCD, where novel categories emerge in unseen domains without target supervision. To this end, we proposed HIDISC, a hyperbolic representation learning framework that leverages penalized Busemann alignment, Tangent CutMix-based augmentation, and hybrid contrastive regularization to enable domain- and category-level generalization. Extensive experiments across PACS, Office-Home, and DomainNet show that HIDISC achieves state-of-the-art performance, particularly improving novel class discovery under domain shift. Our findings underscore the utility of hyperbolic geometry for scalable open-world recognition. Future directions include extending HIDISC to continual DG-GCD and integrating it with large-scale vision-language models.

Broader Impact and Limitations: While HIDISC advances open-world recognition under domain shift using geometry-aware learning, which is extremely practical, its reliance on synthetic augmentations guided by diffusion models may limit applicability in resource-constrained or safety-critical environments where generative artifacts could propagate bias.

Acknowledgments and Disclosure of Funding

We thank our colleague Shubranil B. for his assistance with the figures in this paper. We are also grateful to Adobe Research and the CMInDS department for providing the necessary resources and support.

References

Vaibhav Rathore, Shubhranil B, Saikat Dutta, Sarthak Mehrotra, Zsolt Kira, and Biplab Banerjee. When domain generalization meets generalized category discovery: An adaptive task-arithmetic driven approach, 2025. URL https://arxiv.org/abs/2503.14897 .

Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy M Hospedales. Deeper, broader and artier domain generalization. In Proceedings of the IEEE international conference on computer vision , pages 5542-5550, 2017.

Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In Proceedings of the IEEE conference on computer vision and pattern recognition , pages 5018-5027, 2017.

Xingchao Peng, Qinxun Bai, Xide Xia, Zijun Huang, Kate Saenko, and Bo Wang. Moment matching for multi-source domain adaptation. In Proceedings of the IEEE/CVF international conference on computer vision , pages 1406-1415, 2019.

Athanasios Voulodimos, Nikolaos Doulamis, Anastasios Doulamis, and Eftychios Protopapadakis. Deep learning for computer vision: A brief review. Computational intelligence and neuroscience , 2018(1):7068349, 2018.

Junyi Chai, Hao Zeng, Anming Li, and Eric WT Ngai. Deep learning in computer vision: A critical review of emerging techniques and application scenarios. Machine Learning with Applications , 6:100134, 2021.

Tao et al. Sun. Shift: a synthetic driving dataset for continuous multi-task domain adaptation. In CVPR , 2022.

Jee Seok Yoon, Kwanseok Oh, Yooseung Shin, Maciej A Mazurowski, and Heung-Il Suk. Domain generalization for medical image analysis: A survey. arXiv preprint arXiv:2310.08598 , 2023.

Jesper E Van Engelen and Holger H Hoos. A survey on semi-supervised learning. Machine learning , 109(2):373-440, 2020.

Ashish Jaiswal, Ashwin Ramesh Babu, Mohammad Zaki Zadeh, Debapriya Banerjee, and Fillia Makedon. A survey on contrastive self-supervised learning. Technologies , 9(1):2, 2020.

Mei Wang and Weihong Deng. Deep visual domain adaptation: A survey. Neurocomputing , 312:135-153, 2018.

Kaiyang Zhou, Ziwei Liu, Yu Qiao, Tao Xiang, and Chen Change Loy. Domain generalization: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence , 45(4):4396-4415, 2022.

Kuniaki Saito, Shohei Yamamoto, Yoshitaka Ushiku, and Tatsuya Harada. Open set domain adaptation by backpropagation. In Proceedings of the European conference on computer vision (ECCV) , pages 153-168, 2018.

Prathmesh Bele, Valay Bundele, Avigyan Bhattacharya, Ankit Jha, Gemma Roig, and Biplab Banerjee. Learning class and domain augmentations for single-source open-domain generalization. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages 1816-1826, 2024.

Sagar Vaze, Kai Han, Andrea Vedaldi, and Andrew Zisserman. Generalized category discovery. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 7492-7501, 2022.

Nan Pu, Zhun Zhong, and Nicu Sebe. Dynamic conceptional contrastive learning for generalized category discovery. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 7579-7588, 2023.

Sheng Zhang, Salman Khan, Zhiqiang Shen, Muzammal Naseer, Guangyi Chen, and Fahad Shahbaz Khan. Promptcal: Contrastive affinity learning via auxiliary prompts for generalized novel category discovery. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 3479-3488, 2023.

Sai Bhargav Rongali, Sarthak Mehrotra, Ankit Jha, Shirsha Bose, Tanisha Gupta, Mainak Singha, Biplab Banerjee, et al. Cdad-net: Bridging domain gaps in generalized category discovery. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 2616-2626, 2024.

Shuo Wen and Maria Brbic. Cross-domain open-world discovery. arXiv preprint arXiv:2406.11422 , 2024.

Maximillian Nickel and Douwe Kiela. Poincaré embeddings for learning hierarchical representations. Advances in neural information processing systems , 30, 2017.

Ines Chami, Aditya Wolf, Pierre Juan, Frederic Sala, Sujith Ravi, and Christopher Ré. Hyperbolic neural networks. In NeurIPS , pages 5345-5355, 2019.

Yuanpei Liu, Zhenqi He, and Kai Han. Hyperbolic category discovery. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2025.

Mina Ghadimi Atigh, Martin Keller-Ressel, and Pascal Mettes. Hyperbolic busemann learning with ideal prototypes. Advances in neural information processing systems , 34:103-115, 2021.

OpenAI. Chatgpt, 2024. https://chat.openai.com/.

Xin Wen, Bingchen Zhao, and Xiaojuan Qi. Parametric classification for generalized category discovery: A baseline study. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 16590-16600, 2023.

Sua Choi, Dahyun Kang, and Minsu Cho. Contrastive mean-shift learning for generalized category discovery. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 23094-23104, 2024.

Jindong Wang, Cuiling Lan, Chang Liu, Yidong Ouyang, Tao Qin, Wang Lu, Yiqiang Chen, Wenjun Zeng, and S Yu Philip. Generalizing to unseen domains: A survey on domain generalization. IEEE transactions on knowledge and data engineering , 35(8):8052-8072, 2022.

Hongjun Wang, Sagar Vaze, and Kai Han. Hilo: A learning framework for generalized category discovery robust to domain shifts, 2024. URL https://arxiv.org/abs/2408.04591 .

Kaiyang Zhou, Yongxin Yang, Yu Qiao, and Tao Xiang. Domain generalization with mixstyle. arXiv preprint arXiv:2104.02008 , 2021.

Yuyang Zhao, Zhun Zhong, Na Zhao, Nicu Sebe, and Gim Hee Lee. Style-hallucinated dual consistency learning for domain generalized semantic segmentation, 2022. URL https: //arxiv.org/abs/2204.02548 .

Ishaan Gulrajani and David Lopez-Paz. In search of lost domain generalization. In International Conference on Learning Representations , 2021.

Da Li, Yongxin Yang, Yi-Zhe Song, and Timothy Hospedales. Learning to generalize: Metalearning for domain generalization. In Proceedings of the AAAI conference on artificial intelligence , volume 32, 2018.

Xiran Wang, Jian Zhang, Lei Qi, and Yinghuan Shi. Generalizable decision boundaries: Dualistic meta-learning for open set domain generalization. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 11564-11573, 2023.

Ronghang Zhu and Sheng Li. Crossmatch: Cross-classifier consistency regularization for open-set single domain generalization. In International conference on learning representations , 2022.

Yang Shu, Zhangjie Cao, Chenyu Wang, Jianmin Wang, and Mingsheng Long. Open domain generalization with domain-augmented meta-learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 9624-9633, 2021.

Kai Han, Andrea Vedaldi, and Andrew Zisserman. Learning to discover novel visual categories via deep transfer clustering. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 8401-8409, 2019.

Florent Chiaroni, Jose Dolz, Ziko Imtiaz Masud, Amar Mitiche, and Ismail Ben Ayed. Parametric information maximization for generalized category discovery. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 1729-1739, 2023.

Dahyun Kang, Piotr Koniusz, Minsu Cho, and Naila Murray. Distilling self-supervised vision transformers for weakly-supervised few-shot classification & segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 19627-19638, 2023.

Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 18392-18402, 2023.

Gabriel Ilharco, Marco Tulio Ribeiro, Mitchell Wortsman, Ludwig Schmidt, Hannaneh Hajishirzi, and Ali Farhadi. Editing models with task arithmetic. In The Eleventh International Conference on Learning Representations , 2023.

Aleksandr Ermolov, Leyla Mirvakhabova, Valentin Khrulkov, Nicu Sebe, and Ivan Oseledets. Hyperbolic vision transformers: Combining improvements in metric learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 7409-7419, 2022.

Yunhui Guo, Xudong Wang, Yubei Chen, and Stella X Yu. Clipped hyperbolic classifiers are super-hyperbolic classifiers. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 11-20, 2022.

Valentin Khrulkov, Leyla Mirvakhabova, Evgeniya Ustinova, Ivan Oseledets, and Victor Lempitsky. Hyperbolic image embeddings. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 6418-6428, 2020.

Zhi Gao, Yuwei Wu, Yunde Jia, and Mehrtash Harandi. Curvature generation in curved spaces for few-shot learning. In Proceedings of the IEEE/CVF international conference on computer vision , pages 8691-8700, 2021.

Zhenzhen Weng, Mehmet Giray Ogut, Shai Limonchik, and Serena Yeung. Unsupervised discovery of the long-tail in instance segmentation using hierarchical self-supervision. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 2603-2612, 2021.

Luca Franco, Paolo Mandica, Bharti Munjal, and Fabio Galasso. Hyperbolic self-paced learning for self-supervised skeleton-based action representations. arXiv preprint arXiv:2303.06242 , 2023.

Ryohei Shimizu, Yusuke Mukuta, and Tatsuya Harada. Hyperbolic neural networks++. arXiv preprint arXiv:2006.08210 , 2020.

Ahmad Bdeir, Kristian Schwethelm, and Niels Landwehr. Fully hyperbolic convolutional neural networks for computer vision. arXiv preprint arXiv:2303.15919 , 2023.

Caglar Gulcehre, Misha Denil, Mateusz Malinowski, Ali Razavi, Razvan Pascanu, Karl Moritz Hermann, Peter Battaglia, Victor Bapst, David Raposo, Adam Santoro, et al. Hyperbolic attention networks. arXiv preprint arXiv:1805.09786 , 2018.

Martin Keller-Ressel. A theory of hyperbolic prototype learning. arXiv preprint arXiv:2010.07744 , 2020.

Songwei Ge, Shlok Mishra, Simon Kornblith, Chun-Liang Li, and David Jacobs. Hyperbolic contrastive learning for visual representations beyond objects. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages 6840-6849, 2023.

Yun Yue, Fangzhou Lin, Guanyi Mou, and Ziming Zhang. Understanding hyperbolic metric learning through hard negative sampling. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages 1891-1903, 2024.

Jiang Chang, Zhixin Zhang, Yuhua Qian, and Pan Lin. Multi-scale hyperbolic contrastive learning for cross-subject eeg emotion recognition. IEEE Transactions on Affective Computing , 2025.

Shengyin Sun and Chen Ma. Hyperbolic contrastive learning with model-augmentation for knowledge-aware recommendation. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages 199-217. Springer, 2024.

Rukai Wei, Yu Liu, Jingkuan Song, Yanzhao Xie, and Ke Zhou. Exploring hierarchical information in hyperbolic space for self-supervised image hashing. IEEE Transactions on Image Processing , 33:1768-1781, 2024.

Chengyang Hu, Ke-Yue Zhang, Taiping Yao, Shouhong Ding, and Lizhuang Ma. Rethinking generalizable face anti-spoofing via hierarchical prototype-guided distribution refinement in hyperbolic space. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 1032-1041, 2024.

Jona Otholt, Christoph Meinel, and Haojin Yang. Guided cluster aggregation: A hierarchical approach to generalized category discovery. In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV) , pages 2618-2627, January 2024.

Thomas Eiter and Heikki Mannila. Computing discrete fréchet distance. Technical Report CD-TR 94/64, Christian Doppler Laboratory for Expert Systems, TU Vienna, 1994.

Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In Proceedings of the IEEE/CVF international conference on computer vision , pages 9650-9660, 2021.

Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition at scale. In International Conference on Learning Representations , 2021.

Sangdoo Yun, Dongyoon Han, Seong Joon Oh, Sanghyuk Chun, Junsuk Choe, and Youngjoon Yoo. Cutmix: Regularization strategy to train strong classifiers with localizable features. In Proceedings of the IEEE/CVF international conference on computer vision , pages 6023-6032, 2019.

Leland McInnes, John Healy, and James Melville. Umap: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426 , 2018.

Peter J Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics , 20:53-65, 1987.

Sarah Rastegar, Mohammadreza Salehi, Yuki M Asano, Hazel Doughty, and Cees G M Snoek. Selex: Self-expertise in fine-grained generalized category discovery. In European Conference on Computer Vision , 2024.

Maximillian Nickel and Douwe Kiela. Learning continuous hierarchies in the lorentz model of hyperbolic geometry. In International conference on machine learning , pages 3779-3788. PMLR, 2018.

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{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper tackles Domain Generalization with Generalized Category Discovery (DG-GCD), which requires classifying samples into seen or novel categories under domain shifts at test time without target-domain access during training. The authors propose HIDISC, a hyperbolic representation learning framework featuring: 1) GPT-guided diffusion for efficient and diverse domain augmentation; 2) Tangent CutMix for open-set augmentation consistent with hyperbolic geometry; and 3) a unified loss integrating Busemann alignment, hybrid contrastive regularization, and adaptive outlier repulsion. Experiments on the PACS, Office-Home, and DomainNet datasets demonstrate state-of-the-art performance, with ablations rationalizing the contribution of each component.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n1. The paper is well positioned within the landscape of GCD, DG-GCD, and open-set DG, providing clear context and highlighting the gaps in existing methods. The writing and organization are commendable, with meaningful analysis and presentation.\n2. The components and architecture of HIDISC are well motivated, with design choices justified in relation to the challenges of DG-GCD and theoretical grounding that generalization bounds in hyperbolic space can be tighter than in Euclidean space.\n3. The results are impressive, with accuracy on known, novel, and overall categories across three datasets outperforming the CVPR'25 method DG$^2$CD-Net and its hyperbolic adaptation. Meanwhile, the training efficiency of the method is improved significantly.\n\nWeaknesses\n1. While the application of hyperbolic methods in DG-GCD is interesting, it may represent the incremental novelty, given that hyperbolic approaches have already been explored in GCD (HypCD, [22] in the main paper) and open-set DG (HyProMeta*, Peng et al.).\n2. The framework introduces an excess of components and hyperparameters (e.g., $\\phi$ for $\\mathcal{L}^\\text{Buse}$, $\\tau$ and $\\alpha_d$ for $\\mathcal{L}^u$, $\\gamma$ for $\\mathcal{L}^\\text{out}$, $\\ell_2$ radius constraint before exponential mapping, $\\lambda$ for linear mix, $\\lambda_{1,2,3}$ for $\\mathcal{L}^\\text{total}$), which increases the overall complexity and may impact the practicality of the method, as careful parameter tuning is required for optimal outcome.\n3. Although the use of GPT-guided diffusion for domain augmentation is effective, it may propagate domain-specific biases. Since GPT-generated images are constrained by the distributional priors of the underlying generative model, this approach does not constitute uniform sampling over the whole domain space, potentially limiting its generalizability.\n\n*Peng, Kunyu, et al. \"Mitigating Label Noise using Prompt-Based Hyperbolic Meta-Learning in Open-Set Domain Generalization.\" *arXiv preprint arXiv:2412.18342* (2024).\n\nQUESTIONS:\n1. Why does the hyperbolic adaptation of DG$^2$CD-Net lead to decreased overall performance compared to the original DG$^2$CD-Net?\n2. In Table 7 of the Sup. Mat., comparing the 40-25 and 50-15 old-new splits, why does using more known classes for training result in a 1% drop in old-category accuracy?\n3. While the paper emphasizes training efficiency, could the authors comment how much time does the GPT-based domain generation consume?\n4. As the number of source domains increases and the number of target domains decreases, can HIDISC still maintain its performance advantage over other baselines?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work tackles the challenge of domain shifts and novel-class discovery in DG-GCD, where no target-domain data is available—a scenario often overlooked by previous studies. The authors introduce HiDISC, a hyperbolic learning approach that uses curvature-aware embeddings and simple synthetic augmentation to build domain-invariant and semantically meaningful features. Extensive experiments show that HiDISC not only achieves state-of-the-art performance but also cuts computational cost by 96×.\n\nSTRENGTHS AND WEAKNESSES:\n**Strength:**\n- Novel perspect: Introduces hyperbolic space to DG-GCD, enabling better hierarchical representation and domain invariance compared to Euclidean baselines.\n- Computational efficiency: Achieves SOTA results with 96× fewer FLOPs than prior work by replacing episodic training with lightweight GPT-guided synthetic domains.\n- Good results: The figures and tables are clear and informative.\n\n**Weaknesses:**\n- Relies on Synthetic Data: Uses diffusion-generated augmentations, which could introduce unwanted biases or artifacts—especially risky for safety-critical use cases.\n- More parameters:  The framework relies heavily on tuning several hyperparameters—geometry (e.g., curvature, slope), loss weights ($\\lambda_1-\\lambda_3$), and augmentation settings ($\\lambda$)—which may limit its practicality without thorough validation.\n\nQUESTIONS:\n- Hyperbolic Consistency: Does Tangent CutMix truly preserve hyperbolic consistency? Linear interpolation in the tangent space (Eq. (2)) might not guarantee valid hyperbolic embeddings after reprojection.  Were there cases where synthetic samples violated geometric constraints?\n- Minimal Augmentation Justification: The claim that hyperbolic geometry’s “exponential capacity” reduces the need for augmentation (Sec. 3.3.1) is not intuitive. Is there theoretical or empirical support for this?\n- Dataset Clarity: The dataset used for Table 5 is unspecified. Please clarify.\n- Model Choice Justification: Why choose the Poincaré ball over alternatives like the Lorentz model? Prior work (e.g., Hyperbolic ViTs) suggests Lorentz may offer better stability—was this considered?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work presents HIDISC, a hyperbolic geometry-aware framework for Domain Generalization with Generalized Category Discovery (DG-GCD). The method leverages the properties of the hyperbolic geometry (negative curvature and exponential volume growth) to learn domain-invariant embeddings in the Poincare ball in a hierarchical and semantically meaningful structure. Unlike previous methods that rely on costly episodic sampling solutions, HIDISK uses GPT-guided diffusion to create 2-3 stylistic variations of the input sample. To hallucinate samples from novel-categories, Tangent CutMix is introduced as a curvature-aware adaptation of CutMix interpolation that mixes labeled examples in the tangent space of the Poincare ball to form a novel category embedding.\n\nA combination of 3 losses is used to train HIDISC. (I) A Busemann loss that aligns seen/known features to fixed prototypes at the boundary of the ball. (II) a hyperbolic contrastive loss that allows for fine-grained clustering for seen and novel categories. (III) an adaptive outlier rejection loss that pushes synthetic novel-category CutMix samples away from known categories.\n\nThe proposed method is evaluated empirically on 3 benchmark datasets and compared against several baseline and DG methods. HIDISC consistently beats other synthetic domain augmentation baselines with significantly reduced computational cost, as it does not require episodic sampling. Two ablation studies are performed to measure the impact of loss components (in the 3-part composite loss), and also the influence of the components of the model (using synthetic domains with CutMix, curvature). These studies show that each part of the loss and each component of the model have a role in successful generalization to new domains.\n\nSTRENGTHS AND WEAKNESSES:\nQuality and clarity: The paper is well organized and overall not hard to follow. The notation gets cumbersome in some sections, but the overall discussion remains clear and to the point. \n\nSignificance and originality: To the best of knowledge, the use of hyperbolic space for category embeddings in a DG-GCD framework is novel to this work. The paper claims (rightly) that this geometry provides a naturally structured and hierarchical space, with known prototypes on the boundary and novel categories on the inside. The particular mix of training losses and the Tangent CutMix algorithm are also novel to this work. All elements of the proposed methods are shown to be beneficial in the ablation studies.\n\nQUESTIONS:\nThe paper mentions that the second term in the Busemann loss (Eqn. 4) penalizes embeddings that are too close to the prototypes on the boundary (to avoid overconfidence). However these terms look somewhat ad hoc, and a similar effect can likely be achieved with other loss terms that penalize overconfidence. Is there a reason for the specific choice in the paper?\n\nLIMITATIONS:\nThe authors have adequately addressed the limitation of the proposed method.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes HIDISC, a hyperbolic representation learning framework for DG-GCD task. It that achieves domain and category-level generalization without episodic simulation. Penalized Busemann alignment, Tangent CutMix-based augmentation, and hybrid contrastive regularization are proposed to enable domain- and category-level generalization. Extensive experiments show HIDISC significantly outperforms previous methods on several challenging benchmarks.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The methodology is well-described, with clear diagrams and ablations highlighting the contribution of each module.\n\n2. The paper is among the first to study domain generalization with generalized category discovery in hyperbolic space, providing a sound insight .\n\nWeaknesses:\n\na) Concerns about the reproducibility. Due to the lack of any code in the supplementary material, the reviewers have concerns regarding the reproducibility of this work. The reviewer suggests that the authors supplement comprehensive implementation details in the current manuscript and formally commit to open-sourcing their code. This would greatly enhance the research transparency and facilitate validation of the proposed methodology.\n\nb) Concerns about the fairness of the experimental comparison. The authors said, “DG2CD-Net is the only prior DG-GCD method, ” and “We evaluate our method on three standard DG-GCD benchmarks:” However, the code and benchmark of DG-GCD (CVPR 2025) have not been open-sourced yet. How can the authors ensure that their experimental comparisons are fully fair or not?\n\nc) Concern about the novelty. Introducing the idea of hyperbolic feature learning for DG-GCD is interesting; however, the proposed method seems like a combination of various existing methods. Firstly, hyperbolic contrastive learning has been widely explored by previous published works [A]. What are the differences from these previous methods? What are the specific designs for DG-GCD task? Secondly,  Prototype Anchoring with Penalized Busemann Loss have also been studied by prior works. The authors need to make extensive discussions on the differences.\n\n[A] .Hyperbolic Contrastive Learning for Visual Representations beyond Objects, CVPR 2023;\n\n[B]. Understanding Hyperbolic Metric Learning through Hard Negative Sampling, WACV 2024L;\n\n[C].Multi-Scale Hyperbolic Contrastive Learning for Cross-Subject EEG Emotion Recognition, IEEE TAFFC;\n\n[D]. Hyperbolic Contrastive Learning with Model-Augmentation for Knowledge-Aware Recommendation, ECML 2024;\n\n[E].Hyperbolic Contrastive Learning for Cross-Domain Recommendation, CIKM 2024;\n\n[F] .Exploring Hierarchical Information in Hyperbolic Space for Self-Supervised Image Hashing, IEEE TIP 2024;\n\n[G]. Rethinking Generalizable Face Anti-spoofing via Hierarchical Prototype-guided Distribution Refinement in Hyperbolic Space, CVPR 2024\n\n3)Lack of important citations and experimental comparison. The paper [G] also studied DG in hyperbolic space; however, the authors don’t cite this paper or make any experimental comparisons. The reviewer suggests that the authors briefly review this paper in the related work section and compare it in a fully fair manner on the same benchmark.\n\n4)Lack of important experimental analysis. The authors do not show any experimental comparisons to show the superiority of learning in hyperbolic space to that in Euclidean space. Firstly, could the authors show the results that apply a similar idea in Euclidean space (HIDISC-Euc) to see whether the proposed HIDISC is better than HIDISC-Euc? Secondly, could the authors visualize the T-SNE feature distributions between HIDISC-Euc and HIDISC to make further analysis? Thirdly, there are no analysis experiments on the number of prototypes. How many prototypes are better for the DG-GCD?\n\nSome experimental results are confusing. In Table 3, the vanilla model is learned in the Euclidean space or in the hyperbolic space? The authors don’t mention the details in the paper, which is quite confusing for readers. In Fig. 4, the visualization results are not a tree-like architecture in the Poincaré ball, which is confusing.\n\nQUESTIONS:\nPlease see the weakness part above\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-07"}