HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery
Authors: Vaibhav Rathore
Divyam Gupta
Biplab Banerjee
Venue: NeurIPS 2025 poster ()
Keywords: Domain Generalization
Category Discovery
Hyperbolic Spaces
Primary area: applications
TL;DR: We solve an under explored setting of domain generalization in generalized category discovery, where the unlabeled target domain is unknown till inference.

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.

A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery
HIDISC:
Vaibhav Rathore'
Divyam Gupta' Biplab Banerjee'
Indian Institute of Technology Bombay'
(vaibhav. rathor. in, divs25. iitb, getbiplab)0gmail. com
Abstract
Generalized Category Discovery (GCD) aims to classify test-time samples into either seen avvalore during training-or novel ones, without relying on label supervision. Most existing GCD methods assume simultaneous access labeled and unlabeled data during training and arising from the same domain, limiting applicability in open- open-world scenarios involving distribution shifts. Domain Generalization with GCD (DG-GCD) lifts this constraint by requiring models generalize to unseen domains containing novel categories, without accessing target- domain data during training. The only prior DG-GCD method, CG* [. relies on episodic training with multiple synthetic domains and task vector aggre- gation, incurring high computational cost and error accumulation. We propose HIDISC, hyperbolic representation learning framework that achieves domain and category-level generalization without episodic simulation. To expose the model to minimal but diverse domain variations, augment the source domain using GPT- guided diffusion, avoiding overfitting while maintaining efficiency. To structure the representation space, we introduce Tangent CutMix, curvature-awary interpo- lation that synthesizes pseudo-novel samples tangent space, preserving manifold consistency. A unified boss-combining penalized Busemann alignment, hybrid hyperbolic contrastive regularization, and adaptive outlier repulsion-faal facilitates compact, semantically structured embeddings. learnable curvature parameter further adapts the geometry to dataset complexity. HIDISC achieves state-of- the-art results PACS 22, Office-Home [3], and DomainNet 4. consistently outperforming the existing Euclidean and hyperbolic (DG)-GCD baselines
1
Introduction
Deep neural networks have achieved impressive success visual recognition 5 6., yet typically assume shared domain and lahel space between training and test data. This assumption breaks down in real-world applications such as autonomous driving [7] and medical diagnostics g where both domain shift and label shift frequently co-occur. While
learning 9 [0 reduces
labeling demands, it still operates under closed-world constraints. Domain Adaptation (DA) and Domain Generalization (DG) [2] address distribution shift but assume fixed set of categories. Open-set DG 13 14 allows test-time novelty but collapses all unknowns into single rejection class, erasing semantic granularity.
Generalized Category Discovery (GCD) [7 seeks to identify both known and novel classes from unlabeled test data but requires joint access labeled and unlabeled samples from the same domain. Doosa- GCD (CD-GCD) [8] 19 introduces domain shift but still assumes concurrent access source target domains during training. In contrast, Domain Generalization with GCD (DG-
Code Link http://abbbaaaataoooo/.gggg..o.. 1999
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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GCD) [1 represents more realistic setting: the model is trained solety 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 Net [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 different perspective, existing GCD and DG-GCD methods typically rely on Euclidean or hyperspherical geometry [8) 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. D. While hyperbolic embeddings have shown benefits in GCD (HypCD) [22] and DG [23] recently, their use DG-GCD, where both domain and label shifts co-occur, remains unexplored. This raises our central question:
Can hyperbolic geometry provide 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 the Poincaré ball [20] without requiring target supervision. Un- like HypCD [22], which addresses standard GCD in single-domain settings, and DG M which operates in Euclidean space and relics on episodic simulation, HIDISC provides unified, non-episodic solution using the representational advantages of hyperbolie space.
Semunzic misaligmmen
Intencloo squaration
datsan, scnsatic alganneni
docals pairtig deneis
Hyperbolic Manifold
Spherical Manifold
(Poincaré Disk)
Since the hyperbolic space offers substantial do- main invariance and focuses shared semantics 23 (Fig. [ Sup. Mat.), we still chose to aug- ment the training source domain with controlled stylistic variations and generate only 1-2 synthetic domains per image via GPT-4o (24 -ggided dif- fusion model, avoiding the computational over- head of task-based simulation in DG-CN-Net. A novel domain-diversity score ranks these augmenta- tions by measuring source divergence and intra-pair variability, enabling a principled and scalable domain diversification strategy.
Figure 1: Spherical vs. hyperbolic (Poincaré) embeddings on PACS. Same-class samples from different domains (green/red) cluster more tightly in hyperbolic space, demonstrating im- proved class separation. Refer to Sup. Mat. for quantitative analysis.
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 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 enable fine- grained 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 adversarial or domain-specifi 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.

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oftte-o-tthe-rr results on PACS 22, Office-Home B1 and DomainNet 4 outperforming all the baselines consistently and reducing training FLOPs by over 96 vs. CD-NNt.
2
Related Works
Domain Generalization. DG aims to train models on labeled data from one or more source DG variants include
domains generalize effectively to previously unseen target domains 12 27
closed-set, open-set, single-source, and multi-source settings [28]. Methods like MixStyle [29] and StyleHallucination (30] enhance robustmess via feature-level style perturbations, while meta- learning techniques 32 simulate domain shifts episodically to improve adaptability. Open-set
DG methods address novel test-time classes [33] 34 [4] 335, but typically collapse all unknowns into
a single "outlier" class, hindering tine-graieed 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 17 25 37 26]. Most GCD approaches assume joint access to source and target domains during training, limiting real-world applicability. CD-GCD methods like CDAD- Net [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 [T] 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 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
Hyperbolic embeddings have improved performance in classification [41H43), few-shot learning
segmentation [45), and action recognition [46). supported by hyperbolic variants of standard network
components [47 48 [2 [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 -ojject 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 anti- spoofing 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 labeled source-domain dataset:
Ds {(1], vin x E E V/ E V.,
where zff represents source-domain inputs, and of denotes labels drawn from set of known categories y. At test time, we encounter an unlabeled target-domain dataset:
Dr = {>
21 E Ex,
where samples belong either to known categories ()rold Vv.) or previously unseen, novel categories ()new)) such that yonw n n) = 0. Crucially, the data distributions across domains differ significantly. i... P(X.) + P. and the target dataset Dr inaccessible during training.
Our objective is to construct an embedding space using only Ds that generalizes across domains and categories, effectively clustering both known and novel-class samples from the unseen dataset Dr.
3.2 Rationale Behind Using Hyperbolic Space for DG-GCD
Semantic structures in visual data-such as hierarchies, taxonomies, and part-whole relation- ships-are are inherently suited to spaces with exponential capacity. Hyperbolic space, characterized
3

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Beta(a, 5)
Person
Ds
Imsqe
MLLP
Thngan
Logi
Weight Stoeing
Giraffe
Guttar
D2ye Sym
earpl
Imagg Locoder
ML.
Horse
Fine Turing: Last block of Imagge Ubooder
Figure 2: Illustration the HIDISC pipeline for DG-GCD in hyperbolic space. The model trained using labeled source data Ds (green borders) and 1 1-2 GPT-guided synthetic domains D D2yn (orange borders) simulate domain shift. Features from the shared encoder are projected the Poincaré ball via expo- To mimic novel categories, Tangent CutMix performs interpolation in the tangent space and maps the result 2mix back to hyperbolic space. The embedding space is structured via: (i) penalized Busemann loss Lusee for aligning seen classes to boundary-fixed prototypes: (ii) hybrid contrastive loss Lu for clustering and separability; and (iii) adaptive outlier loss Laui to repel pseudo-novel points. Together, these shape curvature-awan space for generalization and discovery.
by negative curvature and exponential volume growth, naturally encodes such structures, making 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 -emaii--peecffc low-level variations, thereby fostering robust, domain- invariant representations under substantial distributional shifts (more details provided in Sup. Mat).
Poincaré Ball Geometry. We adopt the Poincaré ball -c², the n--iimensional ball defined as:
20 our hyperbolic model. For curvature
D {a E R"
c| |||a|| 2
<1},
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 hyperbolic framework that jointly addresses the dual challenges of DG-GCD: domain-invariant invariant representation learning and unsupervised semantic disentanglement. The synthesis-driven components of our model include: (i) Synthetic Domain Augmentation, which intro- duces a compact set diverse, diffusion-generatte
domains to simulate realistic distribution shifts without relying on target access; and (ii) Tangent CutMix, curvature-awwe 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 Outlerr Loss, which ensures synthetic samples 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 expensive episodic training (as in DG*CD-Ner M.. we generate only one or two synthetic domains per experiment using a diffusion model guided by GPT-4o 24 -urated 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 varied visual shifts and support generalization unseen domains.
Unlike D which depends on numerous episodic tasks and synthetic domain permutations, strategy is lightweight and avoids both computational overhead and error propagation across

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episodes. Crucially, in hyperbolic space, even a small number of diverse augmentations can induce expansive representational changes due the geometry's exponential capacity capacity- effectively stretching the semantic space and encouraging separation between seen and unseen regions.
First, introduce foomain-diversing score that ranks given synthetic domain Deyn with respect to other synthetic domains {D L.M, and the source domain Dy based on the notion of mutual diversity calculated using the Fréchet Inception Distance (FID) 58 for M synthesized domains:
M
Score (D(s) sym
FID D(g)) + FID(D(a) syn D
M-1
1
This scoring promotes both source-domain divergence and intra-pair complementarity. We select the top-scoring domains to augment Dy to obtain Drain-
As shown in Fig. excessive augmentation leads to overfitting on seen classes and degrades novel class discovery. Notably, training solely on Ds yields competitive results, highlighting the inherent domain robustness of hyperbolic spuce, 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 (5 preetrrrdd VIT [60] followed by 3-layer MIP. The resulting Euclidean feature zB E TR is projected into the Poincaré ball Dyd via the exponential map:
z (xp
(2)
vCl /
where e is learnable curvature parameter in our case to approximate the data complexity more effectively. Let 2₁ == z 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] 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 2,, 2y Dd with different class labels,
(I) Project to tangent space: i, (2:), by log)(zz)
(2) Linear mix: Compute
(i mix = Ao; + (1 A)ej, where A ~ Beta(1, Uniform(0, 1)
(3) Map back:
J. exp((vmmx) mix
The resulting embedding 2mix represents servature-preserviii interpolation of features with incom- patible semantics, mimicking out-of-distribttion 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:
Cost
Σ
max(0, min Da mix Ps)),
(x..g) ( F.
kEV.
where Dy is the hyperbolic distance, and 7 is quantile-based adaptive margin over the distances D'
from all class prototypes in [2 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.
5

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60
All Old New
Accuracy (%)
58
56,78
Accuracy (%)
70
56.09
55,95
56
60
54
50
52
50
40
Combination
0
3
4
Odd
Number of Synthetic Domains
Figure (Left) Effect of au 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.
3.3.4 Prototype Anchoring with Penalized Busemann Loss
To enforce semantic structure among the known categories, we associate each class it E V, with fixed ideal prototype Рą aD [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 with their respective class prototypes, we adopt penalized Busemann loss:
| Pys 12 1 - c||
Lusee log
+ #loog( - 1|
(4)
where Рy; is the prototype corresponding to the class label of z,. and Φ is regularization coeffi- cient. The first term guides directional alignment between features and their prototypes, preserving semantic proximity in the hyperbolic geometry. The second term penalizes embeddings that ap- proach 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 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/, 2,", corresponding to different augmentations of the same input, we define the contrastive objective as:
exp( xxp()(==,=))) =/)/T) Ej exp( 2,)TT)
Cu
log
B
JEB
where 7 a temperature hyperparameter and is the batch of samples. We use a hybrid similarity function 8(-,-), which linearly combines distance-bart basse and angle-based measures:
8(...) ad !-DE(..) +(1 aa) cos(...).
(6)
cos(:.) computes cosine similarity in the tangent space, thanks to the co-conformality of the Eu- clidean and Hyperbolic spaces. ar 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 ó over the individual distance metrics.

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Classes
House
Guizr
Horse
Person
Elephant
Hyp-GCD
Hyp-SelIEx
Hyp-DG*CD-Ne
HiDISC(Ours)
Figure 4: Poincaré-disk UMAP 62
embeddings of the target domain ("Photo") clusters, as
produced by Hyp-GCD 22 Hyp-Selffs SelfEx 22]. Hyp-DG'CD-Nee and HiDISC(Ours) for the PACS dataset, with "Sketch" as the source. HIDISC produces visually clean and compact embedding space, supported by silhouette scores 63 (E 1.1]. t), indicating improved cluster compactness
and separation: (Hyp-GCI:: -0.52, Hyp-SelfEx: -0.42, Hyp-DGPCD-Nett -0.29, HIDISC: -0.14)
3.3.6 Training Objective
Our final minimization objective integrates all components:
Liotal
A1
Cusse
+\2
Lu
+h3
Cout
where \1 + +2 11
Semantic alignment
Contrastive regularization
Outlier repulsion
Test-time Protocol. After training, we extract hyperbolic features from target-domain samples and perform clustering using K-Means as in 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 Ds. Dr, and synthetic augmentations (D (!) LM the goal is to minimize the expected target risk: 1==1
Cr(f) Ex~T [x))),
(8)
Extending Sudemacher-basees analysis to the Poincaré ball D' (2 we obtain: Cr(s) S Ls (f) An(S', T) Ru (H) +
where: Ls (f): empirical loss over the augmented training set S"; (S' T): hyperbolic discrepancy
between augmented source and target; RE(H):: Rademacher complexity of the hypothesis class H;;
a residual optimization error.
Compared the Euclidean bound ()) s benefits from the exponential volume and hierarchical structure of Drd This allows semantically distant concepts to be placed further apart with less distortion and curvature-driven compression around known classes-ther thereby making fewer, well-chosen augmentations sufficient to span the generalization space. As such, ( () < As(S", T) holds under the same augmentation budget, yielding tighter bound (see Sup. Mat. for a formal proof).
the hyperbolic version
Each loss in HIDISC contributes to improving specific terms: (i) The Busemann loss Lusee aligns seen-class features to ideal prototypes at the boundary, stabilizing (f) via directional compact- ness; (it) The hybrid contrastive loss L, integrates angular and geodesic similarity encourage semantically meaningful clusters and reduce model complexity Rn(H):: (iii) The outlier loss C 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)) enrich S' approximating I's support and reducing Ax T) in geometry-conste
manner.
In Sup. Mat., we show that FID-based estimates of Aa yield minimal improvement over the inherent fomain-independert of hyperbolic geometry. We also compare our loss terms in Euclidean and hyperbolic spaces, demonstrating that hyperbolic geometry better reduces the generalization gap.
Experimental Evaluations
Dataset Details. We evaluate our method on three standard DG-GCD benchmarks: PACS 2 Office-Home and Domain-Net(4). We follow the protocol of ① for constructing known/novel class-splits and source-target domain pairs. The dataset details provided in the Sup. Mat.
7

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Table 1: Comparison of clustering accuracy (%) for known (Old), novel (New), and overall (All) categories across PACS, Office-Home, and DomainNet. It can be seen that HIDISC beats other synthetic domain augmentation based baselines using significantly less number of synthetic domains (from 6/9 to 2). (Bold: best, underline: second best).
Method
Venue
PACS
Office-Home
DomainNet
Avg.
All
Old
New
All
Old
New
All
Old
New
All
Old
New
ICLR'21
41.98
50.91
33.16
26.17
29.13
21.62
25.35
26.48
22.41
31.17
35.51
25.73
GCD 15
CVPR'22
52.28
62.20
38.39
52.71
54,19
50.29
27.41
27.88
26.13
44.13
48.09
38.27
SimOCD 25
1CCV'23
34.55
38.64
30,51
36.32
49.48
13.55
2.84
2.16
3.75
24.57
30.09
15.94
CMS 26
C4
28.95
28.13
36.80
10.02
9.66
10.53
2.33
2.40
2.17
13.77
13:40
16.50
SelfEx 64
ECCV'24
71.82
73.37
71.55
48.59
52.16
24.78
24.99
24.21
48.93
48.98
CDAD-Net 18
CVPR-W'24 24
69.15
69.40
68.83
53.69
57.07
47.32
24.12
23.99
24.35
48.99
50.15
46.83
GCD+ Synth
CVPR'22
65.33
67.10
24.71
21.94
46.85
SimGCD+ Syath
1CCV
39.76
43.76
35,97
35.57
48.58
12.89
2.71
1,99
4.14
26.01
31.44
17.67
CMS+ 6 Synth
CVPR'24
28.01
26.71
29.04
12.09
12.66
11.13
3.22
3.28
3.03
14.44
14.22
14,40
CDAD+ Synth
CVPR. 2'
60.76
61.67
59.49
47.76
23.85
24.26
46.03
Hyp-CGD 22 Hyp-SelfEx
CVPR'25
65.33
67.11
64.42
50.13
49.36
48,08
22, 888
74
2.5 89
46.12
46.74
46.13
ECCV'24
72.44
74.70
71.20
52.91
52.65
52,96
29. 30
30 40.45
26.37
51.55
52.60
50.18
DG Syath)
CVPR'25
13,30
75.28
72.56
53.86
53.37
54.33
29.01
30.38
25,46
52.06
53.01
50.78
Hyp-DGCCD-Ne (9 Synth
CVPR'25
74.07
74.40
73.95
49.40
50.29
48.03
22.31
21. 12.52
24.29
48.59
48.74
48.76
HiDISC (Ours) Synth)
75.07
75.54
74.52
56.78
59.23
53.21
30.51
31.40
28.41
54.12
55.39
52.05
A
+1.00
+0.26
+0.57
+2.92
+2.16
-1.12
+1.21
+0.95
+2.04
+2.06
+2.38
+1.27
CDAD-Net (DA) JUB]
C'PR--W24
83.25
87.58
77.35
72.42
70.28
76.46
65.19
73.69
we evaluate clustering using three metrics: Old (accuracy on known classes )oold), New (accuracy on novel classes ), and All (overall accuracy on Dr). 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.
Evaluation Metrics. Following 15
18
4.1 Comparisons to the Literature
Table 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 methods, such as SimGCDDSymthetic CMS+Synthetic, and CDAD-Net+Snnthttt (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-GCI 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 M; and (iv) the DG-GCD baseline DGGCD-Net (1) which simulates multiple domains using diffusion models and aggregates lesel knowledge via episodic training and task vectors. For a fairer comparison, we also implement hyperbolic variant, Hyp-DG*CD-MN
GCD [5), SimGCD (25). CMS (26), and SelfEx [64]; (ii) Synthetic augmentation-bass
by replacing its embedding space with Poincaré ball. As M. we report results for CDAD-Net (18) under joint access to source and target domains an upper bound of our results.
Table 2: Estimated number of clusters. Correct estimates are in green, small errors in orange, and large deviations in red.
Quantitatively, HIDISC achieves state-of-the-art performance across all metries and datasets. It improves upon DG*CD-Net by +2.06% in aver- age overall clustering accuracy and by +1.27% on novel class discovery. On tom most diverse and challenging Senchmark-HiDIEr outperforms the best previous method by +..21% UMAP visualizations (Fig. 4 show HIDISC forms a compact embedding space. These gains are achieved without target access and with over 96x lower training FLOPS than 1 while using the same number of synthetic domains (see Sup. Mat). On the other hand, the performance of DG*CD-Net degrades drastically as the number of synthetic domains is reduced (see Sup. Mat.)
Method
PACS
Office-Home
DomainNet
Ground Truth
7
65
345
CD-
67
355
CDAD-Net (DG)
12
362
CDAD-Net (DA)
349
HIDISC (Ours)
7
66
351
8

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Table Impact loss components HIDISC on Office-Home
Table 4: Performance metrics demonstrating the influence of key model components of HIDISC for Office-Home.
Config.
Lausa
Lun
Office-Home
All
Old
New
Model Vortant
Office-Homee
Vanilla
x
26.17
29.13
21.62
OMil
New
Chas
56.32
59.74
50,32
manual anguaeatations
Pon
K
50.95
49.33
53.06
Without syuthetic domain
56.07
59.29
50.67
Lause Lanee
/
x
56.29
60.36
50.41
-Fised curvature (c=1.001, ckos to Euclidisan)
-Fioed curvature (c=1lit3)
56.
55.67
58.65
57.39
$2.69
52.68
Ctawt Leust
51.04
51.51
50,29
-CutMis Enelidean Space)
53.46
54.86
Full HiDISC
56.78
59.23
53.21
HiDISC
Furthermore, Table 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 mentioned in Sup. Mat.
4.2 Ablation Analysis
Impact Loss Components and Key Model Components. evvaluats 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 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% aceuracy. 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 Fuclidean CutMix lowers performance by 3.96%, confirming the benefits of curvature-consister mixing. The complete HIDISC configuration consistently outperforms all variants, confirming the complementary benefits its geometric and loss-driven design.
Ablation of Norm Radius and Slope in Hyperbolic Embedding. We study two key hyperparameters in our hyperbolic embedding setup: the & norm radius before exponential mapping and the slope o in the penalized Busemann loss, both controlling embedding compactness and placement. As 0.
per Table 5 lower slopes (e.g., 0.10) favor seen-class accuracy but hurt generalization, while higher slopes (c.g.. 6 = 0.90) improve novel-class performance by restricting dispersion. We choose = 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 )'s-
Table Ablation on hyperbolic embedding parameters on Office-Home. (Left) Effect slope coefficient ó in the penalized Busemann loss. Lower ó concentrates embeddings near the boundary, improving seen-class accuracy but reducing generalization. (Right) Effect of & radius constraint before exponential mapping. Radius 1.5 yields the best trade-off between known and novel
categories.
Slope
All
Old
New
Radius
All
Old
New
0.10
58.84
65.77
47.07
1.5
56.78
59.23
53.21
0.75
56.78
59.23
53.21
1.0
57.33
61.14
51.76
0.90
57.76
62.82
49.18
2.3
57.31
60.96
52.04
Choice of Hyperbolic Model: Poincaré vs. Lorentz Model
We adopt the Poincaré ball model, which we find performs more favorably than the Lorentz model [65 for DG-GCD Office-Home in Table 6 Full theoretical details in the Sup. Mat. The empirical comparison is below:
Hyperparameter Sensitivity for Loss Weights We conducted ablation study the loss weights (A1, Xg, X²) and found our chosen configuration achieves near-optimal performance, demonstrating robustness Table 7 More details are in the Sup. Mat.

---

Table 7: Ablation study on loss term weights
Table 6: Comparison of Poincaré ball and Lorentz models on Office-Home.
(A1, X2, As) on OfficeHome.
Loss Weights
Acc. (%)
Model
All
Old
New
Config.
A
2g
Ag
All
Old
New
Poincaré Ball 20
56.78
59.23
53.21
Config.
0.60
0.25
0.15
56,78
59.23
53.21
Lorentz Model 65
54.28
56.01
51.41
Config. 2
0.15
0.60
0.25
52.12
53.33
50.07
Config.
0.25
0.15
0.60
51.37
52.17
50.01
Figure Computational efficiency of
Total Training FLOPs Accuracy
#IDISC
HIDISC. Hyp-Busemann requires only 16.53 PFLOPs over 50 epochs with batch size of 128 x 2, representing ~ 2x reduction com- pared to GCD (33.06 PFLOPs), 12x vs. GCD+Synthetic (198.36 PFLOPs), and nearly 96 vs. DG*CD-Net (1,586 PFLOPs). De- spite this efficiency. Hyp-Busemann maintains superior accuracy without relying on episodic- training loops, simplifying the overall training pipeline.
52
CDNet
Accuracy (80)
hibIc
UCD
GiD-Syytheiir
40
DolaDke:
SCD-Syytheticc
44
50
250
500
750
1000
1250
1500
PFLOPS
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 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 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 reometry-awar learning, which is extremely practical, its reliance on synthetic augmenta- tions guided by diffusion models may limit applicability in resource-constrained safety-critical environments where generative artifacts could propagate bias.
10

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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.
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Reviews:
[{"review_id": "vaCRYssHLR", "reviewer": "Reviewer_SCgF", "summary": "This 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.", "questions": "Please see the weakness part above", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "Thank you for the authors' efforts in providing the rebuttal. Most of my concerns have been addressed, and I' 'd like to increase my rating and recommend acceptance.", "rebuttal": "We thank the reviewer for their thoughtful and constructive feedback. Below we address all concerns point-by-point, with supporting theoretical and empirical justifications. \n\n### 1. Reproducibility and Missing Code\n\n**Concern:** _No code provided; concerns about reproducibility._\n\n**Response:**  \nAs noted in the **footnote of Page 1 (main paper)**, we will release the full codebase upon paper acceptance. Implementation details are already provided in:\n\n- **Main Paper Sec. 4:** Training, datasets, optimization details.\n- **Supplement Sec. 8.2:** Hyperparameters, data splits, batch sizes.\n- **Supplement (Pseudocode):** Full pipeline breakdown.\n\nThe released repository will include config files, fixed seeds, scripts to regenerate tables/figures, and domain generation prompts. If permitted, we are willing to share an anonymized code link with the AC during review.\n\n---\n\n### 2. Fairness of Comparison with DG²CD-Net\n\n**Concern:** _DG²CD-Net is not public; how can comparisons be fair?_\n\n**Response:**  \nWe received DG²CD-Net code directly from its authors for academic benchmarking **(acknowledged below Table 1 (main paper))**. All experiments follow:\n\n- Identical datasets, splits, and evaluation protocols.\n- Matched environment and seeds.\n- Hyperparameters and loss settings from the original config.\n\nSupplement Sec. 8.1 details our setup for reproducing DG²CD-Net and its hyperbolic variant.\n\n---\n\n### 3. Novelty vs. Prior Hyperbolic Works [A–G]\n\n**Concern:** _HiDISC appears to combine existing methods—what's new?_\n\n**Response:**  \nWe appreciate the reviewer’s feedback and clarify the novelty of **HiDISC** in relation to prior hyperbolic contrastive learning and prototype anchoring works:\n\n- **[A] Ge et al. (CVPR 2023)** focus on hierarchical scene-object representation with hyperbolic contrastive learning, while **HiDISC** targets *Domain Generalization with Generalized Category Discovery (DG-GCD)*, jointly handling domain shifts and novel category discovery without target data.\n\n- **[B] Yue et al. (WACV 2024)** provide theoretical insights on hyperbolic metric learning and hard negative mining. In contrast, **HiDISC** integrates these into a *prototype anchoring framework* with penalized Busemann loss and adaptive outlier repulsion for open-set domain generalization.\n\n- **[C] Liu et al. (IEEE TAFFC)** apply hyperbolic contrastive learning to EEG data, differing fundamentally from our visual DG-GCD setting involving unseen domains and categories.\n\n- **[D] Sun & Ma (ECML 2024)** and **[E] Rongali et al. (CIKM 2024)** address recommendation systems with model-level augmentations, whereas **HiDISC** introduces *geometry-aware synthetic domain augmentation* and *Tangent CutMix* tailored for visual DG-GCD.\n\n- **[F] Choi et al. (IEEE TIP 2024)** explore hierarchical self-supervised hashing, while **HiDISC** offers a supervised framework explicitly addressing domain and category shifts via unified loss and prototype anchoring.\n\n- **[G] Hu et al. (CVPR 2024)** focus on generalizable face anti-spoofing with hierarchical prototypes. **HiDISC** instead targets open-world visual recognition with simultaneous domain and category generalization, incorporating *Tangent CutMix* for pseudo-novel sample synthesis.\n\n\n**Key innovations of HiDISC** include a unified hyperbolic framework for DG-GCD, penalized Busemann prototype anchoring that reserves space for unknown categories, curvature-aware tangent space augmentation for pseudo-novel samples, and lightweight synthetic domain augmentation via GPT-guided style transfer.\n\n---\n\n### 4. Citation and Comparison with Hu et al. (CVPR 2024)\n\n**Concern:** _Hu et al. also uses hyperbolic prototypes—why not cited/compared?_\n\n**Response:**  \nWe thank the reviewer and will cite Hu et al. (CVPR 2024) in the revised version. Hu et al. (CVPR 2024) address domain generalization for face anti-spoofing—a binary classification task—by leveraging hyperbolic prototypes to enhance robustness across visual domains. While their work employs hyperbolic embeddings for domain robustness, it does **not** address the _open-set_ or _generalized category discovery (GCD)_ setting. In contrast, our work targets the **DG-GCD** task, which is fundamentally more challenging and general: it requires discovering _novel categories_ in an _unseen domain_ at test time without access to any unlabeled target data during training.\n\nTo further ground this distinction empirically, we re-implemented the embedding learning component of Hu et al. within our DG-GCD framework. As shown in the table below, their method (denoted HPDR) performs significantly worse than our approach (HiDISC) on the Office-Home benchmark.\n\n| Method | All ↑ | Old ↑ | New ↑ |\n|--------|-------|--------|-------|\n| HPDR   | 15.05 | 16.55  | 12.58 |\n| HiDISC | 56.78 | 59.23  | 53.21 |\n\n**Explanation of performance gap:**\n\n- **Closed‑set binary vs. open‑set multi‑class discovery.** HPDR is trained to separate two classes (live vs. spoof) using hyperbolic prototypes, with no mechanism to create or refine prototypes for unseen classes in an unseen domain.\n\n- **Lack of clustering/discovery losses.** HPDR optimizes a closed‑set classification loss and distribution‑refinement regularizer but does not encourage cluster‑friendly embeddings for novel classes. Simply clustering HPDR’s embeddings yields near‑random groupings among new classes, explaining the low “New” accuracy.\n\n- **Domain shift without adaptation.** HPDR generalizes across source spoof examples but never sees or models target‑domain distributions of new categories. In contrast, HiDISC integrates domain‑generalization regularizers with discovery losses to align source and unseen‑domain distributions while structuring novel‑class geometry.\n\n---\n\n### 5. Experimental Analysis Requests\n\n**Concern:** _Please compare HiDISC vs. HiDISC-Euc, show t-SNEs, analyze prototypes, and clarify Fig/Table._\n\n**Response:**  \n\nWe appreciate these suggestions and will include the following in the revision:\n\n- **Euclidean vs. Hyperbolic (HiDISC-Euc vs. HiDISC):**  \n  We already evaluated Euclidean analogues of our modules (Supp. Sec. 6.2, Table 8). We will move the core comparison into the main text, e.g.:\n\n| Method             | All ↑ | Old ↑ | New ↑ |\n|--------------------|-------|-------|-------|\n| HiDISC-Euc (Office-Home) | 49.46 | 52.08 | 45.66 |\n| HiDISC (Office-Home)     | 56.78 | 59.23 | 53.21 |\n| HiDISC-Euc (PACS)        | 68.78 | 69.13 | 68.64 |\n| HiDISC (PACS)            | 75.07 | 75.54 | 74.52 |\n\n- **t-SNE visualizations:**  \n  We have generated side-by-side t-SNE plots comparing embedding spaces from HiDISC-Euc and HiDISC, which show qualitatively improved cluster separation under hyperbolic geometry. While we cannot include these visualizations here due to conference policy, they will be included in the revised Supplementary Material (Sec. 6.2) and final paper upon acceptance.\n\n- **Prototype count analysis:**  \n  We ablated the number of prototypes per class $(\\(P \\in \\{1, 2, 4\\}\\))$ on Office-Home. Results:\n\n| Prototypes / Class | All   | Old   | New   |\n|--------------------|-------|-------|-------|\n| 1                  | 56.78 | 59.23 | 53.21 |\n| 2                  | 54.40 | 57.85 | 48.68 |\n| 4                  | 56.23 | 59.75 | 50.27 |\n\nPerformance peaks at $\\(P=1\\)$, suggesting one discriminative prototype per class suffices in hyperbolic space. Larger values sometimes hurt generalization, possibly due to overfitting or redundancy. This will be discussed in the Supplement.\n\n- **Clarification:**  \n  `\"Vanilla\"` in Table 3 = no proposed losses, Euclidean ViT.  \n  Fig. 4 distortion arises from UMAP projection; radial tree-like hierarchy is preserved in native Poincaré space but appears flattened due to 2D projection.\n\n---\n\n### 6. Theoretical Justification\n\nIn Supplement Table 11, we compare generalization gap $\\(\\Delta\\)$:\n\n- PACS: +73% gain with hyperbolic head  \n- Office-Home: +215%  \n- DomainNet: +243%\n\nWe also show (Sec. 3.4 main paper, Sec. 6 Supplement) that for hierarchical data:\n\n$$\n\\Delta_{\\mathbb{H}} \\leq \\mathcal{O}\\left(\\frac{\\log N}{K}\\right) < \\Delta_{\\mathbb{E}} \\approx \\mathcal{O}\\left(N^{1/d}\\right)\n$$\n\nwhere $\\(N\\)$ = number of classes, $\\(K\\)$ = prototypes, $\\(d\\)$ = latent dimension. This favors hyperbolic models under category expansion, typical in DG-GCD.\n\n---\n\n### Conclusion\n\nWe appreciate the reviewer's detailed feedback. Our revised paper will include:\n\n- Detailed comparisons to [A–G] and Hu et al.  \n- Euclidean ablations, t-SNEs, prototype analysis.  \n- Clarifications on visualization and tables.\n\nWe believe these additions establish the novelty, rigor, and broad relevance of our work. We respectfully request the reviewer to reconsider and support acceptance."}, {"review_id": "KjLQCsACC6", "reviewer": "Reviewer_658A", "summary": "This 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.", "questions": "The 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?", "limitations": "The authors have adequately addressed the limitation of the proposed method.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Quality 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.", "was_revised": true, "final_justification": "Based on the new results and discussions provided in the rebuttal (multiple new requested studies added to the paper), I'm updating the overall score to accept.", "rebuttal": "## Ablation Study: Overconfidence Regularizers\n\nTo rigorously evaluate the effectiveness of our proposed **Penalized Busemann Loss** (Eq. 4), we perform a controlled ablation comparing it against three widely used overconfidence mitigation strategies. Each variant substitutes only the penalty term in the Busemann component of the HiDISC loss while keeping all other elements *identical*. This isolates the contribution of the regularizer in controlling overconfident or radially saturated embeddings in hyperbolic space.\n\n### Alternative Regularizers Considered\n\n- **Penalized Busemann Loss (HiDISC)**  \n  $$\n  \\mathcal{L}_{\\mathrm{Buse}}\n    = \\log\\Bigl(\\tfrac{\\|z - p\\|^2}{1 - c\\|z\\|^2 + \\epsilon}\\Bigr)\n      + \\phi\\log\\bigl(1 - \\|z\\|^2\\bigr).\n  $$  \n  This term penalizes radial overconfidence while maintaining geometric consistency in the Poincaré ball.\n\n- **Entropy Regularization**  \n\n  We replace the penalty term in Eqn. 4 with the following term:  \n  $$\\mathcal{L}_{\\mathrm{Ent}} = -\\sum_i p_i \\log p_i$$, where $$p = \\mathrm{softmax}(-d(z, (p_k)))$$.\n\n  Encourages high‐entropy (uncertain) predictions.\n\n- **Confidence Penalty (KL to Uniform)**  \n$$\n\\mathcal{L}_{\\mathrm{Conf}} = \\mathrm{KL}\\bigl(p \\\\Vert\\ \\mathrm{Uniform}_C\\bigr),\n$$\nwhere $\\(p = \\mathrm{softmax}(-d)\\).$\n\n  Penalizes confident deviation from a uniform prior.\n\n**Logit Margin Penalty**  \n\n  Loss is : $\\mathcal{L}_{\\mathrm{Margin}} = \\max(0, S)$, \n\n\nwhere $S = s_{\\mathrm{y}} - s_{\\mathrm{2nd}} - \\delta$ ,  $s = -d(z, (p_k))$  and $\\delta = 0.5$.  \n\n  Enforces separation between the top‐1 and runner‐up logits.\n\n### Experimental Protocol\n\nAll settings were kept constant across variants:\n\n- **Backbone:** ViT‑DINO with learned hyperbolic curvature  \n- **Head:** identical projection layers, no auxiliary classifier  \n- **Training:** same optimizer, learning rate, batch size, epochs  \n- **Loss weights:** $\\{0.60,\\,0.25,\\,0.15\\}$ for (regularizer, contrastive, outlier)  \n- **Logits:** negative hyperbolic distances to prototypes  \n\n### Results and Discussion\n\n| Regularizer                       | All   | Old    | New    |\n|-----------------------------------|-------|--------|--------|\n| Entropy                           | 51.63 | 57.31  | 41.86  |\n| Confidence Penalty (KL→Uniform)   | 56.69 | **61.15** | 49.10  |\n| Logit Margin                      | 54.49 | 56.54  | 51.02  |\n| **Penalized Busemann (Ours)**     | **56.78** | 59.23  | **53.21** |\n\nAs shown, our Penalized Busemann Loss yields the best trade‑off, especially on novel‐class discovery, while KL and margin penalties tend to over‐penalize valid novel assignments and entropy struggles under domain shift.\n\n### Geometric Motivation & Theoretical Properties\n\n1. **Busemann‐based Penalty Aligns with Hyperbolic Geometry.**  \n   The Busemann function  \n   $$\n   B_p(z) = \\log\\\\frac{\\|z - p\\|^2}{1 - c\\|z\\|^2}\n   $$  \n   measures signed distance to the horosphere at prototype \\(p\\). Penalizing \\(B_p(z)\\)  \n   - aligns with true geodesic bisectors,  \n   - adapts to curvature \\(c\\) via the denominator,  \n   - yields uniform radial repulsion without directional bias.\n\n2. **Theoretical Properties.**  \n   - *Isometry‐invariance:* horosphere distances are invariant under hyperbolic isometries.  \n   - *Convexity in Busemann coordinates:* reparametrizing $\\(u = B_p(z)\\)$ makes the penalty convex, aiding optimization.  \n- *Unified geometric form:*  \n$$\n\\underbrace{\\log\\frac{\\|z - p\\|^2}{1 - c\\,\\|z\\|^2}}_{\\text{Busemann}} + \\phi\\,\\log(1 - \\|z\\|^2) {\\text{[Radial Repulsion]}};\\longrightarrow\\ \\text{single, curvature-aware loss.}\n$$\n\n\nUnlike Euclidean entropy or margin penalties, our loss is *intrinsically hyperbolic*, principled by geometry, and thus more effective at controlling overconfidence in Poincaré embeddings."}, {"review_id": "8xf9jjVGLH", "reviewer": "Reviewer_zY4n", "summary": "This 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×.", "questions": "- 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?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**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.", "was_revised": true, "final_justification": "1. The authors mathematically and empirically demonstrate that there is no violation of hyperbolic constraints throughout training.\n2. The authors justify that the \"exponential capacity\" described in Section 3.3.1 reduces the need for augmentation providing support from Theoretical Justification, Empirical results, and the Generalization Bound in Section 3.4.\n3. The authors empirically show that the Poincaré ball outperforms Lorentz models.", "rebuttal": "We thank the reviewer for highlighting these points\n\n**Reviewer Concern:** _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\n**Rebuttal:**  \nWe appreciate the reviewer’s insightful concern regarding the geometric validity of Tangent CutMix under the Poincaré ball model of hyperbolic space. We clarify below with precise mathematical justification.\n\nLet $\\mathbb{D}^d_c = { z \\in \\mathbb{R}^d : |z| < 1/\\sqrt{c} }$ denote the $d$-dimensional Poincaré ball with curvature $-c$. Given two hyperbolic embeddings $z_i, z_j \\in \\mathbb{D}^d_c$, we first map them to the tangent space at the origin $T_0 \\mathbb{D}^d_c \\cong \\mathbb{R}^d$ using the logarithmic map (see Sec. 3.3.3):\n\n$$\nv_i = \\log_0^c(z_i) = \\frac{2}{\\lambda_{z_i}} \\tanh^{-1}(\\sqrt{c}\\|z_i\\|) \\cdot \\frac{z_i}{\\|z_i\\|}, \\quad \\text{where } \\lambda_{z_i} = 1 - c\\|z_i\\|^2.\n$$\n\nThis results in \\(v_i, v_j \\in \\mathbb{R}^d\\), ensuring they lie in a flat Euclidean space where linear interpolation is valid.\n\nTangent CutMix proceeds by linearly interpolating these vectors:\n\n$$\nv_{\\text{mix}} = \\lambda v_i + (1 - \\lambda) v_j, \\quad \\lambda \\sim \\text{Uniform}(0,1).\n$$\n\nWe then project the mixed vector back to the hyperbolic manifold via the exponential map:\n\n$$\nz_{\\text{mix}} = \\exp_0^c(v_{\\text{mix}}) = \\tanh(\\sqrt{c} \\|v_{\\text{mix}}\\|) \\cdot \\frac{v_{\\text{mix}}}{\\sqrt{c} \\|v_{\\text{mix}}\\|}.\n$$\n\nSince $\\(\\tanh(x) < 1\\)$ for all $\\(x > 0\\)$, it follows that $\\(\\|z_{\\text{mix}}\\| < 1/\\sqrt{c}\\)$, and thus $\\(z_{\\text{mix}} \\in \\mathbb{D}^d_c\\)$. Therefore, Tangent CutMix guarantees that the interpolated sample remains a *valid hyperbolic embedding*.\n\nIn addition to geometric correctness, we also regularize the embeddings using the penalized Busemann loss (Eq. (4)), which includes a term $\\(\\log(1 - \\|z\\|^2)\\)$ that discourages embeddings from drifting too close to the boundary, thereby maintaining numerical stability and preventing degeneracy.\n\nEmpirically, we observed no violation of hyperbolic constraints throughout training. Moreover, substituting Tangent CutMix with Euclidean CutMix led to a significant performance drop (-3.96% on Office-Home; Table 4), further confirming that preserving hyperbolic consistency is essential for effective generalization.\n\nWe hope this mathematical clarification addresses the reviewer’s concern. We will incorporate this discussion into the final version to improve clarity.\n\n---\n\n**Reviewer Concern:** _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\n**Rebuttal:**  \nWe thank the reviewer for raising this important question. The statement is supported both by geometric theory and by ablation studies provided in the paper.\n\n- **(1) Theoretical Justification:**  \n  In hyperbolic space with curvature $\\(-c\\)$, the volume of a ball grows exponentially with radius, i.e., $\\(V_{\\text{Hyp}}(r) \\sim \\exp(\\sqrt{c}r)\\)$, unlike the polynomial growth $\\(V_{\\text{Euc}}(r) \\sim r^d\\)$ in Euclidean space. This exponential growth yields greater *representational capacity* for semantic separation, requiring fewer samples to cover the space with minimal distortion. As a result, even sparse or low-coverage augmentations are sufficient to populate the embedding space for robust generalization.\n\n- **(2) Empirical Evidence:**  \n  As shown in Table 4, training without any synthetic domains still achieves 56.07% accuracy on Office-Home—surpassing several Euclidean and hyperbolic baselines that use 6–9 augmentations. Adding only 1–2 GPT-guided augmentations leads to further gains (56.78%), while additional domains degrade novel-class performance due to overfitting (see Fig. 3, right). This empirically supports that hyperbolic embeddings generalize better with fewer but diverse augmentations.\n\n- **(3) Generalization Bound (Sec. 3.4):**  \n  Equation (9) presents a Rademacher-based generalization bound in hyperbolic space, where the hyperbolic discrepancy term $\\(\\Delta_{\\mathbb{H}}(S', T)\\)$ is provably tighter than its Euclidean counterpart $\\(\\Delta_{\\mathbb{E}}(S', T)\\)$ under identical augmentation budgets. This supports the theoretical claim that fewer augmentations are needed to approximate the target domain’s support in hyperbolic geometry.\n\nWe will revise the final paper to explicitly highlight this geometric intuition and cite formal results from hyperbolic geometry and volume theory.\n\n---\n\n**Reviewer’s concern:** The dataset for Table 5 is unspecified.  \n**Response:**  \nThank you for pointing this out. We will revise both the caption and the corresponding reference in the main text to explicitly state that Table 5 reports results on the **OfficeHome** dataset. While this is consistent with Tables 3 and 4, we agree that it should be clearly indicated to avoid ambiguity and ensure clarity for the reader.\n\n---\n\n**Reviewer Concern:** _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\n**Rebuttal:**  \nThank you for the insightful question. We chose the Poincaré ball model over the Lorentz model based on its compatibility with our core design elements, both mathematically and empirically.\n\n- **Tangent CutMix and Closed-Form Mappings:**  \n  Our Tangent CutMix strategy (Sec. 3.3.3) relies on linear interpolation in the tangent space and exponential/logarithmic maps. The Poincaré model offers closed-form, numerically stable expressions for these operations. In contrast, the Lorentz model requires projection onto the hyperboloid and normalization constraints, increasing implementation complexity.\n\n- **Conformal Geometry for Contrastive Learning:**  \n  The Poincaré ball is conformal (angle-preserving), which makes cosine similarity in the tangent space well-defined and compatible with the angular term in our hybrid contrastive loss (Eq. 6). This is crucial for combining local angular coherence and global geodesic structure.\n\n- **Empirical Stability:**  \n  While we did an experiment with a Lorentzian version early on, we encountered unstable gradients and poorer convergence when optimizing Busemann-aligned or contrastive losses. The optimization constraints (e.g., maintaining Minkowski norm) in Lorentz space were harder to manage under our regularization and sampling framework.\n\n- **Visualization and Interpretability:**  \n  The Poincaré disk allows intuitive and bounded 2D visualization (e.g., Fig. 4), which is preferable for cluster analysis and qualitative evaluations in DG-GCD.\n\nWhile Lorentz models (e.g., Hyperbolic ViTs) have benefits in certain contexts, the Poincaré ball aligned better with our goals of closed-form interpolation, angular reasoning, and geometric interpretability. We will include this justification and relevant citations in the final version.\n\nBelow, we present a comparison between the Lorentz model and the Poincaré ball using the OfficeHome dataset:\n\n| **Model**  | **Avg. (All)** | **Avg. (Old)** | **Avg. (New)** |\n|-------------------|--------------------|--------------------|--------------------|\n| **Poincare Ball**            | 56.78                       | 59.23                      | 53.21                       |\n| **Lorentz**            | 54.28                      | 56.01                    | 51.41                      |\n\nAs evident from the table, the Poincaré ball outperforms the Lorentz model across all splits in our DG-GCD setting.\n\n---\n**Addressing the weaknesses mentioned by the reviewer:** \n\n**W1** As noted in Line 327 of the main paper, we acknowledge the potential risks of using diffusion-based augmentations, particularly for safety-critical applications, and plan to explore mitigation strategies in future work.\n\n**W2** We appreciate the concern about hyperparameter complexity. In fact, we conducted a comprehensive ablation over all key knobs—curvature c, slope ϕ, radius before mapping, contrastive weight α_d, and loss‐term weights (λ₁, λ₂, λ₃) on the OfficeHome dataset —and found that only the penalized‑Busemann slope and mapping radius materially affect results, with robust defaults (ϕ = 0.75, radius = 1.5) generalizing across benchmarks. For the remaining loss weights, setting (λ₁, λ₂, λ₃) = (0.60, 0.25, 0.15) balances our alignment, contrastive, and outlier terms and yields 56.78% overall accuracy (59.23% old, 53.21% new). Swapping to (0.15, 0.60, 0.25) or (0.25, 0.15, 0.60) only reduces overall accuracy to 52.12% and 51.37%, respectively—drops of ~4–5 points—demonstrating that our defaults achieve near‑optimal performance without exhaustive tuning.\n\n|**Configuration** | **λ₁** | **λ₂** | **λ₃** | **Avg. (All)** | **Avg. (Old)** | **Avg.(New)** |\n|---------------|--------------------|--------------------|--------------------|--------------------------|--------------------------|--------------------------|\n|**Config 1**| 0.60               | 0.25               | 0.15               |    56.78                 | 59.23                       | 53.21                    |\n|**Config 2**| 0.15               | 0.60               | 0.25               |    52.12                       | 53.33                       | 50.07                        |\n|**Config 3**| 0.25               | 0.15               | 0.60               |   51.37                       | 52.17                       | 50.01                       |"}, {"review_id": "QhWIrlMoLx", "reviewer": "Reviewer_68ad", "summary": "This 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.", "questions": "1. 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?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\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).", "was_revised": true, "final_justification": "The rebuttal makes progress in addressing most of my initial raised concerns. However, the weakness that *'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'* remains. Therefore, I keep my initial rating.", "rebuttal": "---\n\n**Reviewer Concern:** _Why does the hyperbolic adaptation of DGCD-Net lead to decreased overall performance compared to the original **DG²CD-Net**?_\n\n**Rebuttal:**  \nWe appreciate the reviewer’s observation. While hyperbolic geometry is beneficial for semantic modeling, a naive substitution of the embedding space is insufficient. Below, we explain the performance drop in Hyp-**DG²CD-Net** relative to the original **DG²CD-Net**:\n\n- **(1) Task Vector Arithmetic Mismatch:** **DG²CD-Net** performs episodic training and aggregates task vectors via Euclidean averaging. In hyperbolic space, arithmetic operations (e.g., vector addition) do not preserve associativity or commutativity, leading to distortion when such operations are naively retained. The adapted Hyp-**DG²CD-Net** preserves these Euclidean components, which conflict with the curved geometry.\n\n- **(2) Episodic Prototype Drift:** Synthetic novel classes introduced episodically may cause representation drift. In hyperbolic space, repeated feature injection without curvature-aware constraints can result in embeddings accumulating near the boundary, degrading class separability and inducing overconfidence.\n\n- **(3) Lack of Geometry-Aware Losses:** Hyp-**DG²CD-Net** reuses the original **DG²CD-Net**'s loss functions, which were not designed to operate on hyperbolic manifolds. In contrast, HIDISC leverages curvature-aligned supervision via Busemann loss, geodesic-aware contrastive regularization, and adaptive outlier repulsion. The absence of these elements in Hyp-**DG²CD-Net** limits its effectiveness.\n\n- **(4) Empirical Evidence:** As shown in Table 1, Hyp-**DG²CD-Net** performs worse than both **DG²CD-Net** and our proposed HIDISC across all benchmarks. This highlights the importance of full-stack geometric alignment—not merely embedding substitution—for successful adaptation to hyperbolic space.\n\nWe will clarify this in the final version and emphasize that hyperbolic adaptation must be end-to-end, not just at the representation level.\n\n---\n\n**Reviewer Concern:** In Sup. Tab. 7, why does more known classes (50–15 vs. 40–25) drop Old accuracy by ~1%?\n\nThis drop arises from two interacting effects:\n\n- **Boundary crowding:** Adding more “Old” classes packs additional prototypes near the Poincaré boundary, slightly increasing overlap and confusion among old categories. However, this boundary density actually *benefits* discovery of “New” classes—by pushing unfamiliar samples more decisively toward the interior—resulting in the observed tradeoff (Old ↓, New ↑).\n\n- **Per-class sample dilution:** Under a fixed data budget, increasing the number of known classes means fewer samples per class. This mildly raises per-class variance, which may contribute to the slight drop in Old accuracy.\n\nWe will clarify these effects in the Supplement Sec 6.4.\n\n---\n\n**Reviewer Concern:** Wall-clock cost of GPT-based generation.\n\nThe image synthesis process (via InstructPix2Pix + GPT-guided prompts) is performed *once offline* and does not affect model training or inference. On our setup using an NVIDIA A100 GPU, image generation averaged **1-2 seconds per image**.\n\nTo support reproducibility and reduce compute barriers, we commit to publicly releasing the entire set of synthetic images—so future work can reuse our domain expansions without needing to regenerate them.\n\n---\n\n**Reviewer Concern:** _If source domains ↑ and target domains ↓, does HiDISC still hold its lead?_\n\n**Response:**  \nYes, HiDISC remains robust and effective even as the number of target domains decreases. Because our training paradigm is source-only and domain-agnostic, HiDISC inherently generalizes well to shifts in the source-to-target distribution. To thoroughly validate this, we conduct a controlled ablation study where we systematically vary the number of source and target domains while keeping the total image budget fixed. For each setting, the remaining domains are treated as target domains, and we report the average performance over all possible target domain combinations.\n\nThe results, shown in the table below, demonstrate that HiDISC consistently holds or exceeds the performance of the baseline DG$^2$CD-Net across all scenarios. We will include a detailed comparison and additional analysis in the Supplementary material.\n\n| Training  Domains | Method     | Average All ↑ | Average Old ↑ | Average New ↑ |\n|------------------------|------------|-------------|-------------|-------------|\n| Art                       | DG$^2$CD-Net  | 54.47       | 53.65       | 55.54       |\n|                        | HiDISC     | 54.33       | 54.75       | 53.53       |\n| Art + Clipart                      | DG$^2$CD-Net  | 66.67       | 65.78       | 67.99       |\n|                        | HiDISC     | 67.34       | 70.78       | 62.02       |\n| Art + Clipart + Product                     | DG$^2$CD-Net | 66.83       | 66.89       | 66.75       |\n|                        | HiDISC     | 69.86       | 79.17       | 54.24       |\n\n**Addressing the weaknesses mentioned by the reviewer:** \n\nWe thank the reviewer for highlighting these points\n\n**W-1** We thank the reviewer and respectfully clarify that **HiDISC is not a minor extension of prior hyperbolic methods**, but introduces key innovations tailored to the unique challenges of **Domain Generalized Generalized Category Discovery (DG-GCD)**—a setting unaddressed by HypCD or HyProMeta.\n\n**Novel Task Scope:** HiDISC is the first hyperbolic method for DG-GCD, which simultaneously addresses open-set recognition, domain generalization, and label shift *without access to target domains*. In contrast, prior works handle only subsets of these challenges in isolation.\n\n**Architectural Contributions:** HiDISC introduces (i) **Tangent CutMix**, a geometry-aware augmentation strategy in hyperbolic space, (ii) a **hybrid contrastive loss** that fuses angular and geodesic similarities, (iii) **penalized Busemann regularization** to prevent radial saturation and overconfidence, and (iv) an **adaptive outlier repulsion loss** that pushes pseudo-novel samples away from known prototypes.\n\n**Empirical Strength:** HiDISC significantly outperforms both Euclidean and prior hyperbolic baselines. For instance, HPDR achieves 15.05% overall accuracy, while HiDISC achieves 56.78% on the same benchmark—demonstrating its superior generalization under the DG-GCD setting.\n\nWe will revise the manuscript to emphasize these distinctions more clearly and cite all relevant prior works.\n\n**W-2**\nWe conducted a comprehensive ablation over all key knobs—curvature c, slope ϕ, radius before mapping, contrastive weight α_d, and loss‐term weights (λ₁, λ₂, λ₃) on the OfficeHome dataset—and found that only the penalized‑Busemann slope and mapping radius materially affect results, with robust defaults (ϕ = 0.75, radius = 1.5) generalizing across benchmarks. For the remaining loss weights, setting (λ₁, λ₂, λ₃) = (0.60, 0.25, 0.15) balances our alignment, contrastive, and outlier terms and yields 56.78% overall accuracy (59.23% old, 53.21% new). Swapping to (0.15, 0.60, 0.25) or (0.25, 0.15, 0.60) only reduces overall accuracy to 52.12% and 51.37%, respectively—drops of ~4–5 points—demonstrating that our defaults achieve near‑optimal performance without exhaustive tuning.\n\n| **Configuration** | **λ₁** | **λ₂** | **λ₃** | **Avg. (All)** | **Avg.  (Old)** | **Avg.  (New)** |\n|-------------------|--------------------|--------------------|--------------------|--------------------------|--------------------------|--------------------------|\n| **Config 1**      | 0.60               | 0.25               | 0.15               |    56.78                 | 59.23                       | 53.21                    |\n| **Config 2**      | 0.15               | 0.60               | 0.25               |    52.12                       | 53.33                       | 50.07                        |\n| **Config 3**      | 0.25               | 0.15               | 0.60               |   51.37                       | 52.17                       | 50.01                       |\n\n**W-3** \nGPT-4o is used exclusively to generate text prompts, while the InstructPix2Pix diffusion model synthesizes images—mirroring the DG$^2$CD-Net (CVPR ’25) baseline and original DG-GCD setup. This separation ensures augmentations leverage InstructPix2Pix’s strengths rather than GPT’s priors.\n\nThough GPT-guided diffusion relies on pretrained generative priors and doesn’t sample uniformly over the domain space, uniform coverage is neither well-defined nor necessary for effective DG-GCD generalization. Our justification:\n\n- **Task-Aware Domain Coverage:** Let $\\mathcal{D} \\subset \\mathcal{X}$ be the latent domain manifold. Uniform sampling $P(x) \\sim \\mathcal{U}(\\mathcal{D})$ is intractable in high-dimensional spaces. Instead, we use a conditional distribution $P_G(x|t)$ from prompts $t$ semantically aligned with domain shifts, producing diverse, task-relevant perturbations that increase domain discrepancy (Eq. 1).\n\n- **Empirical Diminishing Returns:** Fig. 3 (right) shows that adding more synthetic domains yields diminishing returns. The generative loss $\\mathcal{L}_{\\text{gen}}$ satisfies\n\n  $$\n  \\frac{\\partial^2 \\mathcal{L}_{\\text{gen}}}{\\partial N^2} > 0 \\quad \\text{for } N > 2,\n  $$\n\n  indicating potential overfitting and validating our selective augmentation strategy.\n\n- **Hyperbolic Geometry Benefits:** Key gains arise from hyperbolic learning. Without synthetic domains, HiDISC attains 56.07% on OfficeHome, outperforming Euclidean and augmented baselines. As per Sec. 3.4,\n\n  $$\n  \\Delta_{\\mathbb{H}} \\leq \\Delta_{\\mathbb{E}},\n  $$\n\n  implying fewer samples suffice under hyperbolic curvature.\n\nIn sum, our GPT-guided augmentation introduces *diverse yet semantically structured* domain shifts, and combined with a *geometry-aware learning framework*, achieves strong generalization without uniform domain sampling. We will expand this in the revised paper."}]

Author rebuttal:

Meta-review: This paper introduces HiDISC, a hyperbolic representation framework for DG-GCD that couples penalized Busemann prototype anchoring, Tangent CutMix in tangent space, and a hybrid hyperbolic contrastive/outlier loss to handle unseen target domains with both known and novel classes, achieving strong results on PACS, Office-Home, and DomainNet.

Reviewers' primary concerns revolved around the method's novelty compared to prior work in hyperbolic learning, its reproducibility due to the lack of code, the fairness of experimental comparisons, and the complexity introduced by its many components and hyperparameters. The authors' rebuttal successfully addressed these points by providing detailed justifications for their design choices, clarifying the novelty and distinctions from previous methods, explaining their fair evaluation protocol, and presenting new ablation studies that demonstrated the robustness of the model's hyperparameters. 

Overall, the paper is recommended for acceptance; however, the authors should integrate the link of code, insightful clarifications, additional ablation studies on hyperparameter sensitivity, and the new comparative experiments (e.g., Poincaré vs. Lorentz models, Euclidean vs. Hyperbolic performance) from their rebuttal into the final manuscript to further strengthen the paper and address the reviewers' suggestions.
Decision: Accept (poster)