Generalized Category Discovery under Domain Shift: A Frequency Domain Perspective
Authors: Wei Feng
Zongyuan Ge
Venue: NeurIPS 2025 poster ()
Keywords: Generalized Category Discovery
Domain Shift
Primary area: general_machine_learning

Abstract: Generalized Category Discovery (GCD) aims to leverage labeled samples from known categories to cluster unlabeled data that may include both known and unknown categories. While existing methods have achieved impressive results under standard conditions, their performance often deteriorates in the presence of distribution shifts. In this paper, we explore a more realistic task: Domain-Shifted Generalized Category Discovery (DS\_GCD), where the unlabeled data includes not only unknown categories but also samples from unknown domains. To tackle this challenge, we propose a \textbf{\underline{F}}requency-guided Gene\textbf{\underline{r}}alized Cat\textbf{\underline{e}}gory Discov\textbf{\underline{e}}ry framework (FREE) that enhances the model's ability to discover categories under distributional shift by leveraging frequency-domain information. Specifically, we first propose a frequency-based domain separation strategy that partitions samples into known and unknown domains by measuring their amplitude differences. We then propose two types of frequency-domain perturbation strategies: a cross-domain strategy, which adapts to new distributions by exchanging amplitude components across domains, and an intra-domain strategy, which enhances robustness to intra-domain variations within the unknown domain. Furthermore, we extend the self-supervised contrastive objective and semantic clustering loss to better guide the training process. Finally, we introduce a clustering-difficulty-aware resampling technique to adaptively focus on harder-to-cluster categories, further enhancing model performance. Extensive experiments demonstrate that our method effectively mitigates the impact of distributional shifts across various benchmark datasets and achieves superior performance in discovering both known and unknown categories.

Generalized Category Discovery under Domain Shift: A Frequency Domain Perspective
Wei Fengl.2. Zongyuan 1.2
MMonash University, Clayton, VIC 3800, Australia 2 AAirooc-Monash Research, Monash University, Clayton, VIC 3800, Australia uf024298gmail.cm zongyuan zongyuan-ge@monach. wet.gnash.emeeeeeeeeeee
Abstract
Generalized Category Discovery (GCD) aims to leverage labeled samples from known categories to cluster unlabeled data that may include both known and unknown categories. While existing methods have achieved impressive results under standard conditions, their performance often deteriorates in the presence of distribution shifts. In this paper, we explore a more realistic task: Domain- Shifted Generalized Category Discovery (DS GCD), where the unlabeled data includes not only unknown categories but also samples from unknown domains. To tackle this challenge, we propose a Frequency- covery framework (FREE) that enhances the model's 's ability discover categories under distributional shift by leveraging frequency-dome -omaan information. Specifi- cally, first propose frequency- -bsse domain separation strategy that partitions samples into known and unknown domains by measuring their amplitude differ- ences. We then propose two types of frequency-doman a cross-domain strategy, which adapts to new distributions by exchanging ampli- tude components across domains, and an intra-domain strategy, which enhances robustness to intra-domaie variations within the unknown domain. Furthermore, we extend the supervvee contrastive objective and semantic clustering loss to better guide the training process. Finally, we introduce a siasterinnndifffullyyy aware resampling technique adaptively focus on harder-to-cluster categories, further enhancing model performance. Extensive experiments demonstrate that our method effectively mitigates the impact of distributional shifts across various benchmark datasets and achieves superior performance in discovering both known and unknown categories.
--udded guided Generalized Category Dis-
perturbation strategies:
Introduction
Deep learning has achieved remarkable success in visual recognition tasks under closed-world assumptions [25] [3]. However, visual concepts in the real world are infinite, open-ended, and constantly evolving, while traditional deep learning models are limited to recognizing a predefined of categories and cannot handle unseen concepts. In contrast, humans can recognize new concepts based on existing knowledge. Inspired by this, Generalized Category Discovery (GCD) [33] [3 has been proposed to enable models to simultaneously recognize both known and new categories. However, existing GCD methods typically assume that labeled and unlabeled data come from the same domain, which is often not the case in real-world scenarios. practice, data often exhibit both label and domain shifts. For instance, in clinical applications, medical images collected from different sources may differ significantly in both appearance and statistical properties, and new disease categories may emerge unexpectedly. Current GCD methods suffer substantial performance
"Correspondigg author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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as new Labeled Enean Categanis
Labeled Known Gotegery (bamein A)
6CD
Urkbeled Crown Getegary
Unitblled Knowen Cottggory (Damelk A)
Unkbeled Crews Oetegary (bonon $)
Unlmnonn Gategery
Unkrews Catlgeryy
A)
Unkozen Gotagory (Dansin B)
(0] Tracitional GCD Setting
(b) Domoin-Shifted GCD (DS_6CD)
Figure 1: Illustration of Homain--Sifteet GCD setting (DS_CCD) and the traditional GCD setting. In the DS_GCD setting, the model needs to categorize known and unknown categories from both known and unknown domains.
degradation when faced with both unknown categories and domain shifts 35 This work addresses more realistic and challenging problem setting, referred as Nomain-Shifee Generalized Category Discovery DSGGC,, where unlabeled data may belong to both unseen categories and entirely new domains, as illustrated in Fig. I DS DS_G requires models to identify novel categories and domains using only labeled data from known categories, while generalizing across both semantic and distributional variations. This setting poses major challenges for existing methods. First, most unsupervised domain adaptation (UDA) approaches cannot be directly applied to categories lack label supervision, and relying on unlabeled data often leads to poor performance. Second, current GCD methods lack mechanisms to address domain shifts, resulting in significant performance drops with novel domains.
Reul-Painting (Real)
Seal-Painting (Painting)
Real-Skeich (Real)
Real-Skeich (Skelch)
Clustering accuracy of all categories using FREE, SimGCD+FDA, and SimGCD. It can be observed that FREE outperforms SimGCD+FDA both final clustering accuracy and convergence speed. In contrast, random transformation in SimGCD+FDA may even hinder the learning of unknown domains, potentially leading to negative transfer effects.
Figure 2:
To address the aforementioned challenges, we propose reequency-guided Generalized Category Discovery framework (FREE), a method that tackles the DS GCD task from a frequency-domai perspective. Our work is inspired by Fourier Domain Adaptation (FDA) 42 which bridges domain gaps by leveraging Fourier Transform to exchange low-frequency components (typically associated with image style) across different domains in the frequency domain. However, directly applying the FDA to the GCD task poses two key challenges. First, FDA assumes that randomly exchanging amplitude components between images from different domains can enhance performance on the target domain. However, in the DS LCDD setting, where domain labels for individual samples are unavailable and the direction style transfer cannot be controlled, randomly swapping amplitude components between images may lead to unstable training and negative transfer, as shown in Figure 2 especially in the unknown domain. This is because transforming unknown domain samples into the style of the known domain may distort their original structure or semantic content. Unlike the known domain, the unknown domain lacks any supervision and relies solely on pseudo-labels to learn clustering, making the learning process more vulnerable to such instability. Furthermore, this strategy primarily focuses on global domain adaptation while overlooking intra-class style variations across domains. To address these issues, propose a divide-and concuure strategy that overcomes these limitations in

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more controlled and class-aware manner. Specifically, we first design frequency-based domain separation strategy, which separates known-domain and unknown-domain samples based on the amplitude differences across different sample sets. We then propose a cross-domain frequency perturbation strategy that integrates amplitude components from different domains in a class-aware manner to generate hybrid samples and bridge distribution gaps. Additionally, for unknown domains, we introduce an intra-domain frequency perturbation strategy to enhance the model's s robustness to domain-specific variations. Furthermore, we extend the self-supervised contrastive objective and semantic clustering loss to better guide the training process. These enhancements enable the model to effectively leverage cross-domain frequency knowledge and discover novel categories from unlabeled images, even under domain shift conditions. Finally, we propose a clustering ceriogddifffltty-aae awware resampling strategy, which dynamically evaluates the clustering difficulty of different categories and encourages the model to focus more on the harder ones. In summary, our contributions are as follows: 1) We introduce novel frequency-doman approach address the GCD task under domain separation and perturbation strategies to
domain shifts. 2) We propose frequency-basee improve domain robustness and cross-domain generalization. 3) We enhance learning with extended contrastive learning and clustering objectives. 4) We develop a
resampling mechanism to focus learning on challenging categories. 5) Extensive experimental results show that our method is able to remarkably discover new categories while minimizing the effects of domain shift, and performs far better than state-of-the -frtt---tttttttt methods on all datasets.
2 Related Works
Category Discovery Category discovery tasks are typically categorized into Novel Class Discovery
(NCD) [5] and Generalized Category Discovery (GCD) 8 settings. NCD was initially introduced by
[12] with the goal of clustering unlabeled samples from novel categories using only labeled data
from known categories. Early methods primarily relied on ranking statistics and self-supervised
contrastive learning to transfer discrininative knowledge from known to unknown categories [12
44. Subsequently, UNO [9] utilized a self-labeling strategy based on the Sinkhorn-Knopp (SK) algorithm, integrating multiple objectives into a unified framework to significantly enhance discovery performance. Later works further explored category-level semantic relationships to improve clustering accuracy for unknown categories 18 M.. GCD extends the NCD setting by allowing unlabeled samples to contain both known and unknown categories. Vaze et al. [33] proposed to learn unified feature representations via a combination of self-supervised and supervised contrastive learning, and applied semi-supervised K-means algorithm for clustering. Cao et al. [1] proposed ORCA, a framework that explicitly addresses class distribution mismatch by introducing an uncertainty- adaptive margin to balance learning between seen and novel classes. Wen al. [38 introduced parametric classifier with self-distillation and entropy regularization, enabling joint optimization of representation learning and clustering. Wang al. (36] proposed SPTNeet, two-stage adaptation framework that jointly optimizes model parameters through fine-tuning and data parameters via spatial prompt tuning, effectively aligning representations with pre-trained models. Liu al. [19 proposed RLCD a reciprocal learning framework with an auxiliary branch for base classification and class-wise distribution regularization, enabling mutual refinement between branches and mitigating base-class bias in generalized category discovery. Recent studies have also extended the GCD problem to more complex scenarios such as active learning (1 and federated learning (24] Although existing GCD methods have achieved promising results, most neglect domain shifts in unlabeled data. To address this limitation, Hil.o (55] tackles distributional shift by minimizing mutual information between semantic and domain features, using PatchMix [6 for augmentation and curriculum learning for training. However, its layer-wise disentanglement assumption and random patch mixing may cause noise and instability. CDAD-Net [29] further explores cross-domain category discovery by aligning source and target prototypes via entropy-driven adversarial and neighborhood-baat contrastive learning, though adversarial optimization can still introduce instability.
Unsupervised Domain Adaptation Current Unsupervised Domain Adaptation (UDA) approaches for cross-domain knowledge transfer are mainly categorized into two strategies. The first aims to narrow the distribution gap between source and target domains to improve generalization. Common techniques include moment matching 2 23
10 to learn nomain-invarian features. The second strategy focuses on employing larger and more expressive models to mitigate domain shifts. For example, TVT 4] injects transferability information into
32
7 6 and adversarial training K0, 31
3

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multi-head attention modules to guide learning of transferable and domain-specinf features, MTTrans 45 utilizes multi-level feature alignment and pseudo-labeling to enable cross-domain knowledge 37 enhances target domain performance through multi-consistency constraints at the attention level. In addition, recent research has explored frequency- -based domain adaptation strategies [4] These studies have found that domain-specifer style information is typically encoded in the now-freuenccy and amplitude components of images, while semantic content is primarily captured in the phase components. By perturbing and aligning features in the frequency domain, such methods improve robustness to domain shifts. Despite these advancements, most UDA methods focus improving performance target domains sharing the same categories the source and not designed to discover new unknown categories, making them ineffective for the challenges posed by DS GCD.
transfer. CDAC
3 Preliminaries
Problem Formulation In the DS_ S_GCD setting, we have a labeled dataset Dj = {al, 3/ where each image xi E "Cxx"CCC is drawn from a known domain Ta, and y is its corresponding label. In addition, we have an unlabeled dataset D., {x] JEi, where images may originate from either the known domain TA or an unknown domain TB- Note that unknown domains may also consist of multiple domains. Let C' denote the set of classes in the labeled dataset, and C" denote the set of classes in the unlabeled dataset. The labeled dataset contains only the known classes, i.c. C Cold while the unlabeled dataset contains both known and unknown classes, i.c., C = Coold L C The number of categories in the unlabeled dataset can either be a known prior or estimated in advance using an offline class number estimation algorithm 33 The goal of DS GCD is to leverage the knowledge contained in the labeled dataset Dj to cluster the images Da, regardless of whether they originate from known unknown domains.
the first parametric classifier that jointly optimizes multiple objectives in end-to-end manner. It leverages two synergistic losses: contrastive loss and clustering loss. Specifically, for an input image z, the contrastive loss consists of an unsupervised contrastive loss applied to all samples and supervised contrastive loss applied to labeled samples, formulated as:
Revisiting SimGCD SimGCD (38
exp (z: 2p/T)
(rep(t) = P(())
Σ log PEP())
ECEA()) exp (2: Ze/T)'
where 2 = G(E(z)), E and denote the feature extractor and projection head respectively. T is the temperature parameter. P(i) denotes the set of positive samples for x; in A(i). For the unsupervised part, P(i) contains only the augmented views of the same image. For the supervised part (on labeled data), P(i) also includes samples with the same ground-truth label of 24.-
The clustering loss consists of two components: a cross-entropy loss on labeled samples, a self- distillation loss all samples, which is given by:
C"
(x) =- - (m()))ogp
where p = F(E())) where F is the prototype classifier. For self-distillation loss on all samples, the supervised signal q is the pseudo-label of the prediction from another view after temperature sharpening; For supervised learning on labeled samples, on the other hand, q is its corresponding ground truth label. The overall optimization objective of SimGCD is thus formulated as:
LSimGCD (1 :3) Σ (p)))()) + L (c)(())) + + > (CTep(()) + L (x)(()))) +GA,
2EB
ZEBI
where A an entropy regularization loss to prevent inactive classifier prototypes. 3 and c are balance hyperparameters. B and B3' represent the current batch and the labeled subset of the current batch, respectively. Although SimGCD performs well on GCD tasks within known domains, its performance drops significantly when facing unseen domain shifts due to a lack of consideration for distributional discrepancies. Next, we introduce the FREE framework, which incorporates four key innovations to effectively address domain shift in GCD tasks.

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Figure 3: The overall framework of our proposed FREE method.
Trequency-guider Generalized Category Discovery Framework
The overall framework of our proposed FREE method is illustrated in Fig. We first introduce frequency-guided domain separation strategy to effectively distinguish between known and unknown domains. Then, design domain-specific frequency perturbation strategies tailored for known and unknown domains, respectively, and jointly optimize the model using contrastive loss and clustering loss. Finally, further propose clustering diffieulty-awas aware sampling strategy to enhance the model's ability to cluster challenging categories more effectively.
4.1 Frequency-Based Domain Separation (FDS)
Previous studies have demonstrated that the amplitude component predominantly captures the style information of an image [42 33]. Motivated by this insight, we exploit the amplitude discrepancies between unlabeled samples and labeled anchor samples to facilitate domain separation. Specifically, given an image 2; E xgXxxxx where C, H, and W denote the number of channels, height, and width, respectively. We apply the Fast Fourier Transform (FFT) 4 to each channel to convert the image into the frequency domain: iy(u, v) = F(z,). Here, F denotes the FFT operator. The frequency representation then be decomposed into amplitude component A; and phase component P, defined as:
A (R(E) + I(x.) (u, v), P; arctan
I(i.))u. ((E.)(u,,))
where u and are the corresponding frequency coordinates in the spectral domain. R(t;) and I(;;) represent the real and imaginary parts of the frequency representation æ. To enhance interpretability, we centralize the amplitude spectrum by shifting low-frequency components the center of the spectrum. To determine whether unlabeled sample originates from a known unknown domain, we analyze the discrepancy between its amplitude component and the anchor set of amplitude representations from labeled known-domale samples. Specifically, we define density-based function between the unlabeled amplitude feature A; and the anchor set D::
A,
d(),,Da)= =
Σ
(5)
| |
A,E
where Q(A,, DA) denotes the set of K-nearest neighbors (KNN) of the amplitude representation A,, retrieved from the anchor set D where each element in DA corresponds to the amplitude component of labeled sample from the known domain.
To model the distribution of this density score, we employ a Gaussian Mixture Model (GMM)
28 with two components, corresponding known and unknown domains. Let Ç E Z
5

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(known, unknown] be a latent variable representing domain membership. The GMM parameters are denoted as y flt. Eg, =c kcke where Mç, m. and The denote the mean, covariance, and mixture weight of component Ç, respectively. The posterior probability P5(S x, Da) can be decomposed where (S DA) = *ę representing the ownership probability of C, and (z DA) being normalisation factor. Py (2r D,) is modeled using
into: PC x, Da) = (a)
Pr (a(a)A)
Gaussian distribution:
Pr (.DA) = N (d(A, Mg. Eg).
(6)
The parameters Y are estimated via the prpectation-Mxxiizzattie (EM) algorithm [3] This proba- bilistic modeling enables a soft partitioning of unlabeled samples into known and unknown domains based on their amplitude similarity profiles.
4.2 Cross-Domain Frequency Perturbation (CDFP)
Given that the model is more familiar with the known domain and benefits from partial label supervision, training on the known domain can help the model learn domain-invariant feature representations. We propose a class-aware cross-domain frequency perturbation strategy to bridge the domain gap. Specifically, we first generate pseudo-labels for both known and unknown domain samples. Then, for each known-domain sample 27,6 of class k. we randomly select sample znd from the unknown domain that is also predicted class k and obtain perturbed known-domain sample by replacing the low- wwwffreuenncy amplitude components:
-.t = F- (f((()))))))))) F(x
where ff represents the low frequency swapping operation in 422 To mitigate the impact of noisy pseudo-labels, we perform class-aware low- low-frequency amplitude spectrum exchange only between samples whose predictions have confidence exceeding a predefined threshold 17. To address the case where pseudo-labeled class may be absent within a mini-batch, we maintain memory bank M using a first-in-fistt-out (FIFO) mechanism to store the most recent M unknown-domain samples. During the early training stage, when class coverage is limited, we randomly sample from the unknown domain to perform frequency perturbation. As training progresses, the memory bank gradually accumulates samples from all classes. Once the perturbed samples are generated via cross-domain frequency manipulation, we train the model using the same loss formulation as in Eq. 3 now adapted for the perturbed inown-domain samples. The modified contrastive and clustering losses for cross- dooss- training are denoted as:
Lkd = (1 - 3)
Σ JKd
(CTT + (x)) + Σ (CTa (x)) + Cele (I)),
(8)
ZEBI
where B denotes the known domain samples within the unlabeled dataset. Note that we also apply perturbation to the labeled known domain samples fully leverage the available label information.
4.3 Intra-Domain Frequency Perturbation (IDFP)
To further improve the model's recognition performance on unknown domains, we propose an intra- domain frequency perturbation strategy to enhance the model's 's invariance to variations within the unknown domain. Specifically, for each unlabeled sample in the unknown domain, we apply two independent random data augmentations to generate two distinct views. We then apply the FFT to convert both views into the frequency domain, exchange their low-frequency amplitude components, and use the inverse Fast Fourier Transform F to reconstruct the perturbed samples:
2 = [ (z:)), (xx))
(9)
where S and S represent different data augmentations. Note that there are two augmented samples at this stage, and we randomly select one of them for training. To encourage the model to focus on learning semantically meaningful features while remaining invariant to domain-specific styles, we employ the loss defined in Eq. (3). The key difference is that treat the sisuuency-perturben views as additional positive pairs in contrastive learning, thereby promoting robust representations. For the clustering loss, we replace the soft assignment q with lseudo-labels obtained by sharpening the

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predictions from the trequency-augmented counterpart. The modified contrastive and clustering loss for intra-domain learning is defined as:
Lud
Σ #gBud
(Cud + Lad (a)()))
(10)
where Bud denotes the unknown domain samples within the unlabeled dataset.
Finally, by combining the losses from known-domain and unknown-domain, the overall training objective of our framework is defined as: Liota! = Ltd + Lad 6 AA.
4.4 Clustering Difficulty-Awar Sampling (CDAS)
While the above approaches have effectively alleviated the impact of domain distribution shift in GCD, it overlooks the varying levels of clustering difficulty across categories. This limitation may lead to suboptimal representation learning and clustering performance. To address this issue, we propose clustering difficulty-aware sampling strategy, which adaptively samples data according to the difficulty level of each class. By focusing more on hard-to-cluster categories, the model can better allocate learning capacity where it is most needed. To quantify clustering difficulty, introduce new metric based on the class prototypes O = [oi;.... oc- learned by the prototype classifier. The metric integrates two complementary components: intra-class compactness and inter- class separability. The intra-class compactness is measured by evaluating the variance of feature embeddings within each predicted class: detura N. (E.:.(((x;)) (B)r())))) oz) where
#: arg max. ( denotes the predicted label for sample I;, E(x;) denotes the feature embedding of sample vs, and Ne the number of samples assigned class higher variance di indicates greater dispersion of features within the class, suggesting increased clustering difficulty. The inter- class separability is designed assess the degree of distinction between different class prototypes. Classes with closer prototype distances are more prone to confusion. This is formally defined as: dinler - " Ej=1.j sim(o.. 0j), where sim(:,) :) is the cosine similarity, a larger di implies reduced inter-class margin and higher difficulty in distinguishing class from others. Based on intra-class variance and inter-class similarity, we compute a comprehensive learning difficulty score and convert it into sampling probability for each category:
exp(dinn + dinter)
Paifficulty
(11)
Σ C j=1 exp(dj + di
where c = 1, is the category index. During training, a category cs drawn from the categorical distribution Pameuuty where Purniuutty indicates the relative clustering difficulty of each class. Feature embeddings predicted by the model as belonging to the selected category then retrieved and used in subsequent classification or contrastive learning to refine the feature space. By assigning higher sampling probabilities to more challenging categories, the model is encouraged to focus difficult clusters, thereby improving overall clustering performance.
5 Experiments
5.1 Experimental Setup
Data Preparation Too validate the effectiveness of the proposed method, we conduct experiments on DomainNet (23) and the Corrupted Semantic Shift Benchmark (SSB-C) (35). DomainNet consists of approximately 600,000 images across 345 categories, distributed over six distinct domains: Real, Clipart, Infograph, Painting, Quickdraw, and Sketch. SSB-C is built upon the Semantic Shift Benchmark (SSB), which includes three fine-grained datasets: CUB (4), Stanford Cars [15]. and FGVC-Aircraft [22]. SSB-C introduces nine types of corruption to each sub-dataset to simulate domain shifts, namely: Gaussian noise, shot noise, impulse noise, zoom blur, snow, frost blur, fog, speckle noise, and spatter. Each corruption type is applied at five levels of severity, resulting in a challenging benchmark for evaluating robustness under semantic and visual distribution shifts.
Following the protocol in [35,, for the DomainNet dataset, we designate the Real domain as the known domain TA, and treat each of the remaining domains in turn the unknown domain TB (or
7

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alternatively, combine all remaining domains as unified unknown domain TB). For the SSB-C benchmark, we follow similar setup [3]] for each dataset, we use its original (clean) version as the known domain TA, and its corrupted variant as the unknown domain TB. Regarding category partitioning, we adopt the same practice as randomly select a subset of categories as the known classes. Then, 50% of the samples from these known classes are used to construct the labeled dataset D,, while the remaining samples (along with all samples from the unknown domain TB) form the unlabeled dataset D... Detailed data splits are summarized in Table in the Appendices.
3 35
Specifically, for the known domain Ta. we
Implementation Details and Evaluation Metries Following [35] 33 We used clustering ac- curacy as the main metric to evaluate clustering performance. For the DomainNet and SSB- C datasets, report clustering accuracy across different subsets of the unlabeled data from the known domain Ta and unknown domain TB. including accuracy over all classes (All), Old classes only (Old), and New classes only (New). Clustering aceuracy is computed
follows: ClusterAcc = Σ {3/ (fx) where y4 denote the ground-truth labels, D denote the model predictions. and 2 be the optimal permutation that aligns the predicted labels with the ground- truth labels using the Hungarian algorithm [16]
we adopt the DINO 2 pretrained ViT-B/16 as our backbone network. Both the projection head and classification head are implemented multi-layer perceptrons (MLPs). We fine-tune only the last layer of the ViT-B/16 backbone. The learning rate is initialized to 0.1 and adjusted throughout training using a cosine annealing schedule. The model is trained for 200 epochs using the SGD optimizer with batch size of 256. The hyperparameters 3, 1j.and e are set to 0.35, 0.9, and 0.1 respectively (38, and the memory bank size M is
Following 33 33
1024. The number of nearest neighbors K is set to 3. To accelerate K-nearest neighbor computations, we utilize the Faiss library [4]. All algorithms are run three times with different random seeds, and we report the averaged results, All models were implemented in PyTorch and trained using eight NVIDIA RTX 4090 GPUs. Please refer the Appendices for additional training details and full hyperparameter settings of our method.
Table 1: Clustering performance different methods on the DomainNet benchmark. For each task, we use Real as the known domain Ta and sequentially select one domain from Painting, Sketch, Quickdraw, Clipart, and Infograph as the unknown domain TB. Clustering accuracies are reported for both Ta and TB-
Mellhh
Paating
RESFEEIHHT AE
Kall
Moe
AII
OM
Nay
OM
Ner
OLI
AII
OM
Noy
0M
Nev
OL
131
670
197
181
183
31
610
10%
71
111
171
R75
RF5
41
15
313
614
163
311
R.7
147
071
15.
11.5
31.7
R11
1906
417
343
113
055
9.9
120
111
610
16:
63
1.8
86.5
8611
113
31.4
15.
16:1
1611
SMOKD
11.3
315
624
164
474
545
314
13
31A
772
358
229
133
123
652
463
154
53
SPINa
81.5
269
342
331
293
31
83
T1
83
A7
260
313
411
m38
254
69
57
13
525
765
354
347
319
188
345
635
222
119
194
19
BLCD
385
361
83
270
364
332
491
835
362
33
525
7h1
367
245
358
135
483
MLe
944
25.
364
535
88
538
776
566
253
166
213
76.
FIRE
600
761
683
056
16
015
016
71
01
355
358
369
611
761
551
89
74
664
761
011
363
373
363
(8.1
754
063
161
156
154
Table 2: Clustering performance of different methods on the SSB-C benchmark. For each dataset (CUB, Scars, and FGVC), we use the original clean version as the known domain Ta and its corresponding corrupted version as the unknown domain TB. Clustering accuracies are reported for both Ta and TB.
Scurs-C
FGVCC
Methods
Original
Commptee
Original
Cormpted
Original
Computdd
All
Old
New
All
Old
New
All
Old
New
All
Old
New
All
Old
New
All
Old
New
RankSttate
19.3
22.0
15.4
13.6
23.9
4.5
14.8
20.8
7.8
11.5
22.6
1.0
14.4
16.4
14.5
8.3
15.6
5.0
UND-
25.9
40.1
21.3
21.5
33.4
8.6
22.0
41.8
7.0
16.9
29.8
4.5
22.0
33.4
15.8
16.5
25.2
8.8
ORCA
18.2
22.8
14.5
21.5
23,1
18.9
19.1
28.7
11.2
15.0
22.4
8.3
17.6
19.3
16.1
13.9
17.3
10.1
27.5
28.7
22.1
21.6
10.5
23.0
SimGCD
33.9
28.8
31.6
26.7
39.6
25.6
22.1
30.5
14.1
26.1
25.1
23.2
21.4
SPTNet
33.0
34,5
31.2
30.1
33,1
26.1
28.0
40.2
27.9
24.2
32.1
16.3
28.7
30.2
27.9
24.8
25.7
23.9
RLCD
35.9
35.1
35.2
32.3
34.8
28.5
29.8
41.2
30.4
25.3
33.4
18.1
27.9
30.1
26.8
24.4
26.8
22.7
CDAD-Net
40.4
38.9
39.3
37.7
39.1
34.2
32.1
42.9
32.2
28.8
35.6
21.4
33.8
35.5
31.2
27.8
29.6
25.6
54.0
52.0
53.6
39.5
44.8
35.6
28.4
47.4
29.0
33.4
FREE
60.4
58.5
63.2
58.7
S7.1
53.7
43.6
48.1
40.8
38,9
46.1
32.6
48.5
54.9
$1.2
35.0
32.4
38,9
8

---

5.2 Comparison with Other SOTA Algorithms
We compare our method with several state-of-ther approaches for GCD, including ORCA M
GCD [33], SimGCD [38]. SPTNet [36]. and RLCD [19], as well as advanced methods originally designed for NCD such RankStats+ [2] and UNO+ (9) which we adapt to fit the GCD setting. Additionally, we compare our approach against CDAD-Net [29] and Hilo [55. recent methods tailored for DS DS_GCD Table and T clustering performance on the DomainNet and SSB- C datasets, respectively, with detailed per-domain results provided in Appendix. Notably, existing GCD methods suffer significant performance degradation under domain shift, and the presence of unlabeled samples from unknown domains can even impair clustering accuracy within the known domain. In contrast, our method consistently achieves performance gains across most scenarios. For instance, the SSB-C benchmark, our method consistently outperforms the strongest baseline, HiLo. Specifically, it achieves improvements in all categories on the corrupted domains of CUB-C, Scar-C, and FGVC-C by 3.7%, 3.3%, and 3,8%, respectively. In addition to the gains the unknown (corrupted) domains, our approach also leads to noticeable improvements in clustering accuracy within the known (clean) domains, demonstrating its ability maintain robustness while effectively bridging domain gaps. On the more challenging DomainNet dataset, our method yields improvements in nearly all domain pairings. For example, when using Real the known domain and Painting as the unknown domain, the proposed method outperforms HiLo by 3.5% in clustering accuracy on all categories in the Painting domain and by 3.3% the Real domain. These results further demonstrate the robustness of our method under substantial domain discrepancy.
Table 3: Ablation study of different components.
The real domain from DomainNet is used as the known domain Ta. and painting the unknown domain TB. Clustering performance is reported for both domains under various component con- figurations.
Real-Painting
Real-Sketch
Real
Fainting
Figure 4: Density histograms for different task combinations. A two-component Gaussian mix- ture model is fitted to distinguish between known and unknown domain samples (domain labels used here for visualization only).
FLS
IDFP
CDFF
LDAS
All
012
NEW
All
New
61.3
71.8
52.9
34.3
35.6
33.5
35.5
77.9
66.1
73.0
43.1
42.0
67.7
78.1
61.2
45.6
46.1
44.8
5.3 Analysis and Ablation Study
Effectiveness of different components To better understand the contributions of each ponent, we conduct extensive ablation studies on the DomainNet dataset. Using SimGCD as baseline, incrementally add each module observe its individual impact model per- formance. As shown Table 3] it can be observed that baseline methods that ignore do- main shift struggle achieve good performance on the unknown domain and lack robustness on the known domain. In contrast, our proposed domain separation strategy combined with domain-specific frequency perturbation effectively improves clustering performance on both known and unknown domains (Rows 2 and 3). Finally, we find that clustering difficulty-aware re- sampling further boosts clustering performance, particularly the unknown domain (Row 4). We further visualize the results of our frequency-basee domain separation. As shown Fig. 4 most samples from the known domain exhibit higher density values and appear on the right side of the histogram, while samples from the unknown domain tend to have lower density values and are located on the left. This indicates that samples with higher density are likely from the known domain, whereas those with lower density are likely from the unknown domain, thereby validating the effectiveness of our approach.
Table 4: Ablation study different transformation strategies.
Method
Real
Painting
New
Random
62.7
76.5
54.3
35.2
34.5
32.5
who class
65.6
77.6
58.3
43.5
44.6
42.1
Ablation study on different transformation strategies We further investigate the impact of different frequency transformation strategies by comparing our proposed FREE method with random

---

and class- alass-agnostic transformations. As shown in Table without domain separation, simply applying random frequency perturbations fails to improve performance on both known and unknown domains, and may even lead to negative transfer (Row 1). This suggests that blindly swapping amplitude components, without accounting for the directionality of style transfer, introduces unwanted noise that hinders model learning. Moreover, we observe that class-agnostic transformations perform worse than our class-aware method (Rows and 3), indicating that FREE effectively mitigates inter-class style discrepancies and further enhances clustering performance.
6 Conclusion and Limitations
In this paper, we propose a novel learning framework to address the GCD task under domain shift. By introducing four key innovations, our method enhances the robustness of clustering against distributional shifts. Extensive experiments on multiple domain-shifted benchmarks validate the effectiveness of the proposed approach. However, our method also has certain limitations. For instance, it primarily focuses on image classification tasks; extending this framework to more challenging scenarios such as open-set semantic segmentation and object detection remains an interesting direction for future research. Moreover, our approach requires access to both known and unknown domain data during training. An important avenue for future work is to adapt the method to domain generalization settings, where data from the unknown domain is not available during training.
7
Acknowledgments
This work was supported by the Center of Excellence for Antimicrobial Therapeutics Discovery and Innovation (CEATDI), Grant No. 8002003,
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A Technical Appendices
A.1 Preliminaries
Fourier-Based Interpretation of Phase and Amplitude Spectra
Given grayscale image E NNN, its complex-valued Fourier coefficient at frequency (u, v) is defined as:
N
Fu,,, v)
Σ
Σ
x(n, m) ( m2n(uunum) Σ axn, ()) (cos 0 i sin 0), (12)
n=
m=1
where 0 = n (un + em)/N.
The real and imaginary parts thus be rewritten
(u v) = Σ x(n, m) cos
(13)
(, Σ z(n, m) sin
(14)
Following the lemplate-basee interpretation 17 we decompose the cosine and sine components based on their signs:
Tali(x) R+
= Σ
I(n, m. cos 8
Thi (x) = Σ
æ(n, m) (- cos 0),
(15)
cos 820
cos B<0
Σ
m) sin 0,
(x)
Σ
s(n, mm) (-
sin 0).
(16)
sin 820
siu e<0
The real and imaginary components can thus be written as:
Ru -)= T - T Tu." (x),
(17)
In (u, = T T (x).
(18)
Phase Spectrum (Semantic/ Structural Encoding)
The phase spectrum is defined as:
[u v)) R₂ (u,
T (1) T (x)
Pa(u, v) arctan
arctan
(19)
T (r) - nh, (x)
13

---

This representation shows that the phase spectrum encodes the relative strength between different directional templates. Since it retains the positional and structural layout of features, it captures the semantic and structural information of the image, even in the absence of amplitude [17].
Amplitude Spectrum (Style/ / Domain Encoding)
The amplitude spectrum given by:
Au( RR, LI, (T (x) TT--TR---- ( (T (T TT' (20)
This expression shows that the amplitude spectrum measures the absolute energy of the frequency response. is sensitive to image-level traits such texture, contrast, and lighting, and is thus considered to capture the domain style or appearance of the image.
Summary. The phase spectrum encodes structural and semantic information via the relative tem- plate responses, while the amplitude spectrum encodes domain-specific appearance through energy distributions. This decomposition provides theoretical basis for frequency-based domain manipula- tion and adaptation strategies.
Table 5: Detailed statistics of data split.
Labelled
Unlabelled
Dataset
#lmage
#Class #Domain #lmage #Class #Domain
DomainNet
39.1K
172
547.5K
345
CUB-C
1.5K
100
I
45K
200
10
Scars-C
2.0K
98
I
61K
196
10
FGVC-C
1.7K
50
1
50K
100
10
B More Empirical Results
B.1 Detailed Description of the Dataset
DomainNet. DomainNet 23 is one of the largest and most challenging benchmark datasets for domain adaptation and generalization tasks. consists of approximately 800,000 images covering 345 object categories across six distinct domains, each representing different visual style or modality. The domains are:
Real: Natural images collected from online sources (e.g., photos).
Clipart: Cartoon-style clipart graphics.
Sketch: Hand-drawn sketches.
Painting: Artistic paintings with various styles.
Infograph: Informative icons and charts, often stylized and abstract.
Quickdraw:
Simplified sketches collected via the Google Quick, Draw! project.
SSB-C Dataset. SSB-C 351 is perturbed version of the Semantic Shift Benchmark (SSB). SSB
consists of three fine fine-grained visual recognition datasets:
CUB-200-2011 (CUB): A bird species classification dataset with 200 categories.
Stanford Cars (SCAR): A fine-grained car model classification dataset containing 196 categories.
FGVC Aircraft (FGVC): An aircraft model classification dataset with 100 categories.
In SSB-C, each of these datasets is augmented with nine types of perturbations, each applied five severity levels, resulting in a dataset that is 45 times larger than the original SSB.
Table presents the detailed splits of the different datasets.
14

---

B.2 Multiple unseen domains for Domainnet
We further explored the scenario where the unknown domain consists of multiple domains more comprehensively validate the effectiveness of the proposed method. Specifically, we combined the five domains in DomainNet-excludeee TB. and then re-ran all the experiments under this setting. As shown in Table 6 even when the unknown domain is composed of multiple diverse subdomains, our proposed FREE framework consistently outperforms all competing baseline methods. This result not only demonstrates the robustness of our approach in more complex, multi-domain unknown settings but also highlights its strong generalization capability across varied domain shifts.
the real domain- into single aggregated unknown domain
Table 6: Clustering performance when Ta contains multiple unknown domains. We construct Ta by combining the five domains from DomainNet excluding the Real domain, and report clustering accuracy separately for each domain.
Methods
Painting
Sketch
Quickdraw
Clipart
Infograph
Old
New
Old
Old
New
Old
New
New
StnkStutst
34.0
62.3
19.9
30.3
50.1
11.1
17.9
31.5
2.4
2.0
2.5
25.1
46.4
6.3
12.0
22.1
5.5
UNO+
43.1
72.0
28.6
30.3
43.7
17.4
12.0
16.3
8.9
2.1
2.3
1.8
22.8
37.4
9.5
12.4
20.3
6.5
ORCA
32.1
49.9
23.5
23.0
38.8
17.0
11.6
14.7
7.6
2.8
3.6
2.1
20.1
33.4
10.3
8.4
17.8
6.8
GCD
47.8
53.5
45.1
32,9
40.3
26.9
17.0
22.7
11.3
1,9
2,4
1.8
24.3
31.2
13.1
10.5
12.0
9.9
SimGCD
62.2
77.3
54.3
36.6
42.9
30.3
18.2
22.6
15.0
2,2
2.0
244
25.0
34.7
16.4
11.8
13.8
10.5
SPTNet
63.1
77.4
55.5
38.4
32,5
23.3
2.7
2.5
25.3
34.1
15.9
11.7
RLCD
64.3
77.6
57.0
39.7
33,8
27.5
2.5
26.7
35,9
13.0
CDAD-Net
64.6
76.5
59.5
40.1
45.6
36.4
18.6
22.1
16.0
2.6
26.3
33.2
19.9
12.7
15.0
12.8
Hila
65.8
77.8
58.9
43.4
49.0
42.9
20.0
23.6
17.4
3.1
4.0
2.5
27.6
34.7
21.4
13.9
16.5
12.1
FREE
67.4
78.5
61.3
48.9
54.6
48.6
22.7
25.1
19.1
4.5
5.2
3.1
29.7
35.4
25.7
16.1
20.1
14.5
B.3
Additional experimental results SSB-C
We additionally report the performance of our method on each corrupted dataset in the SSB-C bench- mark. As shown in Table 7 Table [8 and Table our proposed approach consistently outperforms baseline methods on most of the corrupted datasets, demonstrating its robustness and effectiveness various challenging scenarios.
Table 7: Detailed clustering performance CUB-C. We report the clustering accuracy each corrupted domain.
Ceasias Niise
Sho Neioo
Trqudin Naioo
Zoer
Suzu
Fioe
Rig
Specile
Sperner
Now
Nex
Nee
A3
Nev
HancState
22.1
36.
133
4.7
32.4
302
212
RiCh
344
368
254
254
264
563
355
366
346
CAAD-Ne
352
111
26.
355
111
359
414
34
110
556
Bia
348
-14
367
123
165
119
513
155
516
515
479
512
412
517
FREE
457
449
48.
465
413
413
471
435
475
363
481
542
53.
403
859
513
467
F4.
534
483
97.1
983
4677
531
838
512
569
Table 8: Detailed clustering performance Scars-C, We report the clustering accuracy each corrupted domain.
Mitiab
Canstaa Nova
GMd
Netee
AE
Tranew Nome
Nox
ZONY BLY
New
Sorr
QE
New
Fire
A3
Tog
All
Nev
Spuree
HancStates
35.0
22
11.2
1:4
213
153
18
SurdCD
SPTNe
253
171
389
300
253
183
151
RiCn
363
368
33.
36
86
891
161
CDADAN
22.5
29.3
21.
232
230
213
193
248
26.7
3.5
122
31.
25.1
31A
335
453
1111
361
216
574
490
1811
HL,
31.2
35.0
243
31.
313
243
382
365
233
15.
43.1
310
463
160
355
43.
295
417
49.3
322
37.1
31.1
236
37.5
45A
305
FIEE
438
278
364
420
278
369
4L9
276
413
302
368
41.
486
145
41.
412
335
454
SKL
359
412
413
333
43.1
499
345
B.4 Additional experimental results on domainnet
We further conducted additional experiments on the DomainNet dataset to comprehensively evaluate the generalization ability of our proposed method. Specifically, we first selected Real as the known
15

---

Table Detailed clustering performance on FGVC-C. We report the clustering accuracy on each
corrupted domain.
Metbod
All
Carudias Neve
(3)
Nov
Al
Siee Neiaa
ON
Nev
AE
Irqves Noie
ON
New
AE
Zoee Berr
0
Nee
A1
Suar
Nec
A1
Free
Nee
A4
Ire
Nee
ANI
Seecee
ON
Nov
All
Sturer
ON
New
1.5
13.6
3.5
00.7
55
5.0
083
55
161
12.3
4.
62
123
31
83
110
61
125
36.8
63
16
140
53
06.3
22:1
4.3
UNO
053
13.5
23.1
132
28.
83
28.1
28.3
130
156
013
98
136
253
193
268
1.3
165
586
39.8
15.6
12.3
DBCA
01.
163
15.1
176
16.
193
16.8
6.3
134
264
260
548
153
284
384
353
324
358
345
368
35.8
domain Ta and then, one by one, selected each of the remaining five domains as the target domain TB. For each such pair, evaluated the model's clustering performance the four remaining domains not involved in training. As shown in Table [T] Table Table [2] Table 13] Table [4]
Table Table T6. Table 17 method consistently achieves performance gains in most scenarios and outperforms other competing approaches. These results demonstrate the effectiveness of our method in learning bomain-invariaan semantic representations, enabling better generalization across diverse visual domains.
Table 10: We Real as the known domain (TA) and Sketch the unknown domain (TB), and report clustering performance on Ta, TB. as well as all other domains.
Real
Sketch
others
Methods
All
Old
New
All
Old
New
All
Old
New
RankStats+
34.2
62.0
19.8
17.1
31.1
6.8
17.3
30.0
6.1
UNO+
43.7
72.5
28.9
12.5
17.0
9.2
17.4
26.4
9.5
ORCA
32.5
50.0
23.9
11.4
14.5
7.2
13.3
23.1
9.1
GCD
48.0
53.8
45.3
16.6
22.4
11.1
20.7
25.8
15.8
SimGCD
62.4
77.6
54.6
16.4
20.2
13.6
20.4
25.4
16.1
SPTNet
62.7
77.8
54.9
16.9
20.8
13.9
21.2
25.9
16.9
RLCD
63.0
77.6
55.6
17.4
20.3
15.6
21.4
26.4
16.7
CDAD-Net
62.5
77.4
55.1
16.6
20.2
14.1
22.1
27.1
16.9
HiLo
63.3
77.9
55.9
19.4
22.4
17.1
21.3
25.8
17.4
FREE
65.8
78.4
57.2
22.5
25.1
19.8
24.0
27.0
19.8
Table Detailed clustering performance on other domains when using Real as TA and Sketch as
TB-
Painting
Quickdraw
Clipart
Infograph
Methods
All
Old
New
All
Old
New
All
Old
New
All
Old
New
RankStats+
29.7
49.2
10.2
2.3
2.1
2.4
24.6
45.9
5.9
12.5
22.6
5.9
UNO+
30.8
44.0
17.6
2.4
2.4
2.3
23.1
38.0
10.1
13.2
21.2
7.9
ORCA
23.1
39.1
2.5
3.0
2.0
19.7
33.1
10.0
8.9
18.1
GCD
32.6
40.1
31.5
1.6
1.9
1.5
24.1
31.1
14.9
14.1
16.2
10.2
SimGCD
38.7
44.7
32.7
1.9
1.2
2.5
25.2
35.3
16.3
15.8
20.3
12.8
SPTNet
37.9
44.2
32.2
2.0
1.5
2.1
25.7
35.8
16.9
16.2
20.9
13.1
RLCD
39.0
44.4
33.1
1.6
1.1
2.2
26.2
35.8
17.2
16.2
20.8
13.2
CDAD-Net
38.0
44.1
32.8
2.0
1.3
2.3
25.8
36.1
16.7
17.1
21.3
14.8
HiLo
39.8
44.7
34.9
1.9
2.0
1.7
27.2
35.9
19.6
16.2
20.5
13.4
FREE
41.9
45.8
37.2
2.5
2.9
2.3
29.8
36.5
21.8
18.1
22.8
15.5
16

---

Table 12: We use Real as the known domain (TA) and Quickdraw as the unknown domain (TB), and report clustering performance on TA, TB, well all other domains.
Real
Quickdraw
others
Methods
All
Old
New
All
Old
New
All
Old
New
RankStats+
34.1
62.5
19.5
4.1
4.4
3,9
21.0
37.4
7.2
UNO+
31.1
60.0
16.1
6.3
5.8
6.8
18.6
32.2
7.0
ORCA
19.2
39.1
15.3
3.4
3.5
3.2
15.6
28.4
8.1
GCD
37.6
41.0
35.2
5.7
4.2
6.9
21.9
34.3
12.2
SimGCD
47.4
64.5
37.4
6.6
5.8
7.5
22.9
33,8
13.8
SPTNet
47.8
64.9
37.6
6.8
5.9
7.8
23.1
33.6
14.5
RLCD
49.2
67.1
38.2
6.9
5.6
8.5
25.1
34.3
15.1
CDAD-Net
51.3
66.7
49.4
7.1
6.2
7.9
25.3
35.8
15.9
HiLo
58.6
76.4
52.5
7.4
6.9
8.0
25.9
32.5
20.4
FREE
62.3
78.9
56.3
8.1
8.1
8.9
27.6
33.9
22.1
Table 13: Detailed clustering performance other domains when using Real as Ta and Quickdraw
as TB.
Painting
Sketch
Clipart
Infograph
Methods
All
Old
New
All
Old
New
All
Old
New
All
Old
New
RankStats+
29.6
49.0
10.2
17.1
32.1
6.1
24.8
45.4
6.7
12.6
23.1
5.7
UNO+
26.8
43.7
9.9
14.7
25.6
6.6
20.7
38.4
5.1
12.2
21.0
6.4
ORCA
22.2
40.9
10.1
11.9
22.4
7.1
17.5
35.6
5.7
10.3
18.7
6.6
GCD
32.9
45.7
21.4
18.5
30.5
10.8
23.5
39.0
10.7
13.8
22.1
7.6
SimGCD
33.8
45.1
22.5
19.4
30.1
11.5
24.0
38.5
11.4
14.5
21.6
9.8
SPTNet
34.5
46.1
24.2
21.3
32.1
11.7
26.2
39.5
11.8
15.6
23.1
9.9
RLCD
36.2
46.0
25.1
21.8
31.8
12.5
26.0
39.1
11.7
16.5
22.4
10.9
CDAD-Net
36.8
46.9
24.3
21.9
30.8
14.6
26.8
38.7
14.2
15.7
22.3
11.8
HiLo
38.6
45.1
32.2
22.9
28.8
18.5
26.0
36.4
16.9
16.2
19.8
13.9
FREE
42.1
46.5
36.5
25.1
31.9
20.1
29.2
38.9
20.7
19.1
21.5
15.7
Table 14: We use Real as the known domain (TA) and Clipart the unknown domain (TB), and report clustering performance on TA, TB. as well as all other domains.
Real
Clipart
others
Methods
All
Old
New
All
Old
New
All
Old
New
RankStats+
34.0
62.4
19.4
24.1
45.1
6.2
15.8
27.0
6.4
UNO+
44.5
66.1
33.3
21.9
35.6
10.1
16.2
23.2
10.5
ORCA
32.0
49.7
23.9
19.1
31.8
4.3
13.7
19.9
8.6
GCD
47.7
53.8
44.3
22.4
34.4
16.0
18.0
24.1
12.1
SimGCD
61.6
77.2
53.6
23.9
31.5
17.3
19.2
23.6
15.6
SPTNet
63.0
77.7
53.9
24.4
31.8
17.9
21.2
24.5
16.7
RLCD
63.1
77.8
54.1
24.9
32.3
18.5
22.0
25.1
17.0
CDAD-Net
62.9
77.6
53.8
25.8
33.0
18.1
22.2
25.7
16.1
HiLo
63.8
77.6
56.6
27.7
34.6
21.7
19.8
23.6
16.8
FREE
66.1
78.3
60.1
29.4
37.1
24.9
23.4
23.9
20.1

---

Table 15: Detailed clustering performance on other domains when using Real as Ta and Clipart as
TB.
Painting
Quickdraw
Sketch
Infograph
Methods
Old
New
All
Old
New
Old
New
All
Old
New
RankStats+
30.0
50.3
9.7
2.6
2.3
2.9
17.4
31.9
6.8
13.1
23.6
6.2
UNO+
31.5
43.3
19.6
2.8
2.1
3.6
17.3
26.8
10.2
13.3
20.6
8.5
ORCA
29.3
36.9
9.2
1.3
1.5
1.2
13.7
21.9
8.3
10.3
19.4
6,3
GCD
33.4
40.4
22.2
3.6
5.7
2.2
19.5
27.7
12.7
15.5
22.7
11.1
SimGCD
39.0
45.9
32.1
0.8
0.5
1.1
21.1
27.3
16.5
15.9
20.8
12.7
SPTNet
40.2
46.4
33.1
0.6
0.4
1.0
22.3
27.9
17.1
16.1
20.1
13.5
RLCD
41.7
47.4
34.7
1.2
0.9
1.3
23.5
28.8
18.5
16.2
20.4
13.1
CDAD-Net
41.0
46.8
33.8
1.0
0.8
1.1
22.6
27.0
17.2
15.8
20.1
11.2
HiLo
40.7
46.3
35.1
1.3
0.4
2.3
21.2
26.9
17.0
15.9
20.6
12.8
FREE
42.3
47.1
37.2
2.1
0.9
3.2
23.1
27.5
18.9
16.5
20.9
13.0
Table 16: We use Real as the known domain (TA) and Infograph as the unknown domain (TB), and
report clustering performance on Ta, TB, as well as all other domains.
Real
Infograph
others
Methods
All
Old
New
All
Old
New
All
Old
New
RankStats+
34.2
62.4
19.6
12.5
21.9
6.3
18.5
32.1
6.4
UNO+
42.8
69,4
29.0
10.9
15.2
8.0
18.2
28.0
9.6
ORCA
29.1
47.7
20.1
8.6
13.7
7.1
13.8
24.8
5.4
GCD
41.9
46.1
39.0
10.9
17.1
8.8
19.0
29.1
11.1
SimGCD
52.7
67.0
44.8
11.6
15.4
9.1
20.8
28.4
14.2
SPTNet
53.4
67.9
45.1
12.1
16.2
8.9
20.9
28.6
14.4
RLCD
53.9
68.3
45.8
12.5
16.7
21.5
29.4
14.6
CDAD-Net
53.5
65.6
47.2
13.6
17.2
9.8
22.0
29.1
16.2
HiLo
64.2
78.1
57.0
13.7
16.4
11.9
23.0
28.5
18.3
FREE
66.5
80.4
60.3
15.9
17.2
13.8
24.1
29.4
19.5
Table 17: Detailed clustering performance on other domains when using Real as TA and Infograph as
TB-
Painting
Quickdraw
Sketch
Clipart
Methods
All
Old
New
All
Old
New
All
Old
New
All
Old
New
RtnkStats+
29.6
49.2
10.0
2.5
1.6
3.4
17.4
32.2
6.5
24.4
45.5
UNO+
30.8
44.8
16.8
2.7
2.3
3.1
17.0
27.0
9.7
22.3
37.8
8.7
ORCA
20.0
40.2
8.1
1.6
1.8
1.2
13.2
21.1
8.0
20.5
36.0
4.1
GCD
30.8
45.1
18.4
3.6
4.7
2.5
18.8
26.4
11.2
22.9
40.0
12.3
SimGCD
35.9
45.6
26.3
2.1
1.7
2.5
20.8
29.3
14.5
24.5
36.9
13.6
SPTNet
36.3
46.1
26.4
2.3
1.8
2.7
21.2
29.7
14.8
24.9
37.2
14.1
RLCD
37.2
46.8
26.9
2.5
1.9
2.9
22.3
30.5
15.3
25.1
37.3
14.7
CDAD-Net
39.3
46.5
29.6
2.5
1.7
3.4
21.8
30.5
16.1
25.6
36.5
16.4
HiLoo
40.1
46.1
35.8
2.0
2.2
1.5
22.6
29.4
17.6
26.6
36.3
18.1
FREE
44.5
47.2
39.7
2.8
2.9
2.3
24.1
30.2
19.3
28.7
37.1
20.2
18

---

B.5 Performance of different backbones
We further investigated the impact of using different backbone architectures on model performance. In particular, we adopted the pre-trained CLIP model [27] as our backbone and re-ran all the experiments accordingly. As shown in Table [8 the more advanced backbone consistently led to noticeable improvements across various evaluation metries. Importantly, even with this stronger backbone, our proposed FREE framework continued to outperform other competing methods by significant margin. This not only demonstrates the robustness of our approach but also provides additional evidence of its effectiveness and generalizability when combined with cutting-edge feature extractors.
Table 18: Clustering performance using different backbone architectures on DomainNet. We use Real the known domain (Ta) and Painting the unknown domain (TB).
Real
Painting
Methods
Backbone
All
Old
New
All
Old
New
HiLo
DINO
64.4
77.6
57.5
42.1
42.9
41.3
FREE
DINO
67.7
78.1
61.2
45.6
46.1
44.8
HiLo
CLIP
74.5
78.1
64.2
47.1
49.5
45.4
FREE
CLIP
78.2
78.3
69.5
51.0
54.2
49.3
Table 19: Clustering performance using the estimated number of categories.
Original
Corrupted
Methods
C*1
All
Old
New
All
Old
New
Hil.o
GT. (200)
56.8
54.0
60.3
52.0
53.6
50.5
FREE
GT. (200)
60.4
58.5
63.2
55.7
57.1
53.7
Hilo
Est. (257)
55.9
52.9
59.2
51.2
52.8
49.5
FREE
Est. (257)
59.3
56.1
62.0
54.4
56.1
52.3
B.6 Unknown category number
In previous experiments, assumed that the number of categories was known in advance. Here, extend our study to the more realistic scenario where the number categories is unknown beforehand. To address this, first employ the category estimation algorithm proposed in B3 35 to perform an offline estimation of the number of categories. Based on these estimates, we rerun all experiments accordingly. As shown in Table 19 on CUB dataset, categories, our proposed FREE framework consistently outperforms the strongest baseline method, HiLo. This result further validates the robustness and adaptability of our approach in practical settings where prior knowledge of the category count is unavailable.
when using the estimated number of
B.7 Parameter sensitivity analysis
Our proposed FREE framework involves several key hyperparameters: For certain parameters such as 3 and 6, we follow the settings adopted in prior work [3). For the temperature coefficients used representation learning and clustering objectives, we follow the settings in [38] 335. Specifically, the temperature 7 is set to 0.07 for the self-supervised contrastive loss and 0. for the supervised contrastive loss. For the clustering loss, the temperature т, is 0.07 and gradually warmed up to 0.04 during the first 30 epochs using a cosine scheduling strategy. Following [42,, we define square window with side length 2L min H, W) to select low-frequency components in the frequency domain. We conduct a sensitivity analysis on L. We use the Real domain as the known domain and Painting as the unknown domain. As shown Table the best performance is achieved when L is set to 0.04. Moreover, we observe that the model maintains stable performance even with slight variations in this parameter, indicating that the proposed method robust and relatively insensitive to the choice of L.
0. and т, is initialized at
19

---

Next, we investigate the effect of the memory bank size M, which stores style information for con- trastive and clustering objectives. As shown in Table increasing the memory bank size generally improves model performance, as it allows the model to access more diverse and representative set of style features. However, excessively large memory banks may incur additional computational and memory overhead. Based on empirical results, we find that size of 1024 strikes good balance between performance and efficiency.
Finally, we further investigate the impact of the number of nearest neighbors K used in the domain separation strategy. As shown in Table 22 the performance of our model remains stable across reasonable range of K values.
Table 20: Parameter analysis of L
Real
Painting
L
All
Old
New
All
Old
New
0.01
67.4
77.8
61.1
45.3
46.0
44.3
0.04
67.7
78.1
61.2
45.6
46.1
44.8
0.06
67.6
78.0
61.0
45.5
45.9
44.7
0.10
67.5
77.9
61.2
45.4
46.0
44.5
Table 21: Parameter analysis of memory bank size M
Real
Painting
M
All
Old
New
All
Old
New
512
67.5
78.0
61.1
45.5
46.1
44.6
1024
67.7
78.1
61.2
45.6
46.1
44.8
2048
67.8
77.9
61.5
45.8
46.2
44.9
Table 22: Parameter analysis of nearest neighbors K
Real
Painting
All
Old
New
All
Old
New
1
67.5
78.0
61.0
45.5
46.0
44.7
3
67.7
78.1
61.2
45.6
46.1
44.8
5
67.4
77.8
61.1
45.4
46.0
44.6
B.8 Visualization of the attention map
To gain deeper understanding of the advantages of our proposed FREE framework, we visualize the attention patterns within the final block of the VIT backbone. Specifically, we extract attention maps corresponding to the [CLS] token from all attention heads and highlight the top 10% most attended patches in red across the 12 attention heads. As shown in Fig. 5 our method consistently attends to samples come from known or unknown domains, and whether they belong to seen or unseen categories. This focused attention demonstrates that our method effectively suppresses distractions from background style variations, which often domain-speciff and irrelevant to semantic understanding. These observations further validate the effectiveness the FREE framework learning robust and domain-invarian invariant representations.
semantically meaningful foreground regions, regardless of whether
B.9 Incorporating various UDA techniques for DCDD
To explore whether recent advances unsupervised domain adaptation (UDA) can benefit DS_ DS_GCD, we integrate several state-of-the-art UDA techniques-sun such as Mixup 40) FACT 39) and MixStyle 45
into the SimGCD framework. shown Table 23] these additions result in only marginal performance improvements, indicating that directly applying existing UDA methods is insufficient for
20

---

Known domain
Unknown domain
Khown classes
Unknown classes
HiLo
FREE
HiLo
FREE
Figure 5: Attention visualization from the final block of the VIT backbone on the CUB-C dataset. The top 10% most attended patches from different heads are highlighted in red. Our method shows stronger focus on foreground regions across both known and unknown domains, demonstrating improved robustness to background style variations.
Table 23: Clustering performance of other UDA methods.
Real
Painting
Method
All
Old
New
All
Old
New
SimGCD
61.3
77.8
52.9
34.5
35.6
33.5
Mixup
62.7
76.5
54.3
34.9
37.2
32.5
Mixstyle
62.3
76.8
54.0
35.0
36.1
34.0
FACT
62.9
76.9
55.1
36.1
37.5
34.9
FREE
67.7
78.1
61.2
45.6
46.1
44.8
Table 24: Clustering performance of other separation strategy.
Real
Painting
Method
All
Old
New
All
Old
New
Semi-supervised K-means
65.8
77.7
58.1
42.8
45.7
42.1
FREE
67.7
78.1
61.2
45.6
46.1
44.8
solving DS GCD. This further underscores the necessity and effectiveness of our proposed approach.
B.10
Incorporating other separation strategy
We further compare our frequency-based domain separation strategy with alternative separation methods. Specifically, we adopt the semi-supervised K-means algorithm from (35] to divide the data into known and unknown domains, and then rerun the experiments. As shown in Table 24 our frequency-guide domain separation strategy achieves better performance across different domains, demonstrating its superiority.
B.11 Stability analysis
To further assess the robustness and reproducibility of our framework, we evaluate the stability of model performance under different random initialization seeds. Specifically, each experiment independently repeated three times with distinct random seeds, and the mean and standard deviation
21

---

of clustering accuracy are reported in Table and Table 26 The results demonstrate that our method maintains highly stable performance across runs. This indicates that the proposed optimization procedure and domain-awar components do not introduce sensitivity to stochastic factors such as weight initialization or data sampling, confirming the consistency and reliability of our approach.
Table 25: Clustering performance of different methods on the SSB-C benchmark. Results are reported as mean + std.
TOYCL
URged
Campaa
Usgra
BarkSuuse
1033223
223422
154411
116424
350.2.1
45:05
141:23
TA420
115626
16452
144123
1456:3
83a13
156-24
5066T
IIS0+
23.6225
48:425
213420
285523
154224
14412
23422
418423
TALLS
169635
283420
45688
225424
BA4A1
158123
JAS126
233420
M8-13
18:2111
23
145415
213128
188423
181222
3:114
112414
136224
224121
B31:3
10412
163221
112418
211422
Sa0CD
315623
333119
200120
20124
1A421
20121
25519
21112
385121
J4122A
35620
125121
231133
214200
343611
312115
381424
BL-1A
283333
20L15
40311
36213
163613
20322
235122
365115
23111
239124
BLCD
35 111112
22111
323A1A
2211
412133
MALLS
23115
314121
IRILIA
301123
201
20111
222120
ILLe
34311.3
90311
22111
8111
WALLS
431122
MAL1
441117
MALLS
112114
20113
11411A
004335
153121
353130
151222
303244
64:10
40.133
05377
35013
06:11
BALE
483:20
30L18
3131
10113
324013
30115
Table 26: Clustering performance of different methods the DomainNet benchmark. Results reported as mean std.
MEL
2011 S001 11611
C Potential societal impact
This work focuses on Generalized Category Discovery (GCD) under distribution shift, a critical yet underexplored scenario where models must identify novel categories in unlabeled data while encountering significant domain changes. From a societal perspective, this line of research advances our ability to build adaptive Al systems that can reliably operate in evolving previously unseen environments, which is essential in many real-world applications such as environmental monitoring, autonomous systems, medical diagnostics, and security surveillance.
By encouraging models to continuously discover and adapt to new concepts under domain shifts, our approach enhances the robustness and longevity of deployed machine learning systems, especially in non-stationary environments. For example, in healthcare, models must adapt to data from different hospitals demographics without requiring exhaustive annotations. In safety-critica domains, failure to adapt to new distributions could lead to severe consequences, such as misdiagnosis or false alerts. However, with the ability autonomously learn and categorize new concepts comes the risk of amplifying spurious correlations present in source domains. If the source domain data carries latent biases, these biases may propagate during the discovery process, particularly under domain shift, where spurious features may become more dominant. Thus, future work should explore bias detection and mitigation strategies tailored to open- ppen-world and chifting-domain settings. In summary, while our work enables more generalizable and context-aware AI, careful attention must be paid to ethical deployment, bias transfer, and accountability mechanisms, especially high-stakes applications where model decisions evolve beyond initial human supervision.
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Reviews:
[{"review_id": "TNWzjLXV9X", "reviewer": "Reviewer_Jovx", "summary": "This paper introduces a novel framework, \"Free,\" to tackle Domain-Shifted Generalized Category Discovery (DS-GCD), a challenging setting where unlabeled data contains both new categories and samples from unseen domains. The method is built on the core insight that an image's Fourier amplitude spectrum captures domain-specific style, while the phase spectrum retains semantic content. \"Free\" leverages this by first probabilistically separating samples into known and unknown domains based on amplitude similarity. It then employs class-aware frequency perturbation strategies to align distributions and enhance robustness, further guided by a difficulty-aware sampling mechanism. Extensive experiments on DomainNet and SSB-C benchmarks show that the proposed method significantly outperforms prior state-of-the-art approaches.", "questions": "1. Regarding Baselines: The paper's motivation hinges on the premise that standard GCD methods struggle under domain shift. To make this point more compelling, could you add more recent and powerful GCD methods like ProtoGCD [1], CMS [2], and SPTNet [3] into your main table? Demonstrating that these stronger methods also fail in the DS-GCD setting would significantly strengthen the paper's central motivation.\n2. Regarding Hyperparameter Sensitivity: The proposed 'Free' framework is methodologically complex. While the sensitivity analysis in Section B.7 is helpful, it appears to omit a key hyperparameter. Could you please elaborate on the model's sensitivity to the confidence threshold $\\mu$ used in CDFP? A more complete analysis would increase confidence in the method's robustness.\n3. Regarding Statistical Significance: The main results in Tables 1 and 2 report the mean accuracy over three runs but omit standard deviations or other measures of variance. Could you provide these values? This information is crucial for assessing the statistical significance and stability of the reported performance gains, especially for a complex, multi-component method.\n\n[1] Protogcd: Unified and unbiased prototype learning for generalized category discovery\n\n[2] Contrastive mean-shift learning for generalized category discovery. \n\n[3] Sptnet: An efficient alternative framework for generalized category discovery with spatial prompt tuning.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n* S1: Novel and Effective Approach for an Important Problem. The paper tackles the highly relevant and challenging problem of Generalized Category Discovery under a domain shift (DS-GCD). The core technical contribution—using the Fourier amplitude and phase spectra to disentangle domain-specific style from semantic content—is an elegant, well-motivated, and novel approach.\n* S2: State-of-the-Art Empirical Performance. The empirical evaluation is extensive and demonstrates state-of-the-art performance. The proposed 'Free' method consistently and substantially outperforms all baselines, including the specialized DS-GCD method HiLo, across the challenging DomainNet and SSB-C benchmarks (Tables 1 & 2). The magnitude of the gains convincingly validates the method's effectiveness.\n* S3: High-Quality and Rigorous Presentation. The paper is well-written and easy to follow. The authors' claims are supported by detailed ablation studies (Table 3) that clearly justify the contribution of each component. The inclusion of a comprehensive appendix with additional analyses further strengthens the quality and completeness of the work.\n\nWeaknesses:\n* W1: Limited Comparison to Recent GCD Methods. A key premise of the paper is that standard GCD methods are not suitable for the DS-GCD setting. However, the baselines used to demonstrate this (e.g., GCD, SimGCD) are not the most recent. Including stronger, contemporary GCD methods (such as ProtoGCD [1], CMS [2], or SPTNet [3]) and showing that they also struggle under domain shift would provide a more powerful motivation for the necessity of a specialized approach like Free.\n* W2: Incremental Novelty of Some Components. While the overall framework is novel, the novelty of some individual components is limited. For instance, the frequency-based perturbation is a well-designed, class-aware extension of the technique from FDA[4], and the clustering-difficulty-aware sampling is a relatively common strategy for handling hard examples. The paper would be strengthened by a clearer discussion of these connections.\n* W3: High Methodological Complexity and Incomplete Analysis. The proposed framework is composed of four main modules, resulting in a system with high methodological complexity and lots of hyperparameters that could be a practical drawback for adoption. The hyperparameter sensitivity analysis in the appendix is appreciated but incomplete; it omits several key parameters introduced by the method, such as the confidence threshold $\\mu$. A more complete analysis would increase confidence in the method's robustness.\n\n[1] Protogcd: Unified and unbiased prototype learning for generalized category discovery\n\n[2] Contrastive mean-shift learning for generalized category discovery. \n\n[3] Sptnet: An efficient alternative framework for generalized category discovery with spatial prompt tuning. \n\n[4] Fda: Fourier domain adaptation for semantic segmentation.", "was_revised": true, "final_justification": "The authors’ detailed rebuttal has addressed my remaining questions. This confirms my initial positive assessment, and therefore, my score remains unchanged.", "rebuttal": "### **Q1:Regarding Baselines:**\nWe have included comparisons with recent GCD methods, including ProtoGCD, CMS, and SPTNet, as shown in Table 1 and Table 2. While these methods bring some improvements, they still struggle under domain shift. In contrast, our method consistently outperforms them, further validating the need for a specialized solution like Free.\n\n### Table 1: Performance on the SSB-C Dataset\n| Method     | CUB-O All | CUB-O Old | CUB-O New | CUB-C All | CUB-C Old | CUB-C New | Scars-O All | Scars-O Old | Scars-O New | Scars-C All | Scars-C Old | Scars-C New | FGVC-O All | FGVC-O Old | FGVC-O New | FGVC-C All | FGVC-C Old | FGVC-C New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| ProtoGCD   | 33.2±1.8  | 35.9±1.3  | 32.3±2.2  | 31.7±1.9  | 33.8±1.5  | 27.2±2.3  | 29.1±1.4     | 41.9±2.0     | 28.2±1.6     | 24.8±2.1     | 33.6±1.7     | 16.4±1.9     | 29.8±2.0    | 31.5±1.1    | 28.2±2.2    | 25.7±1.6    | 26.6±2.4    | 24.6±1.5    |\n| CMS        | 33.0±1.7  | 34.5±1.1  | 31.2±1.9  | 30.1±2.0  | 33.1±1.4  | 26.1±2.2  | 28.0±1.5     | 40.2±2.0     | 27.9±1.6     | 24.2±2.3     | 32.1±1.8     | 16.3±1.3     | 28.7±2.0    | 30.2±1.7    | 27.9±2.2    | 24.8±1.5    | 25.7±1.1    | 23.9±2.4    |\n| SPTNet     | 35.9±1.9  | 35.1±1.2  | 33.2±2.1  | 32.3±1.4  | 34.8±2.0  | 28.5±1.1  | 29.8±1.8     | 41.2±2.2     | 30.4±1.5     | 25.3±1.0     | 33.4±2.1     | 18.1±1.6     | 27.9±1.3    | 30.1±2.3    | 26.8±1.4    | 24.4±2.2    | 26.8±1.2    | 22.7±2.0    |\n| FREE | 60.4±1.1  | 58.5±1.4  | 63.2±1.3  | 55.7±1.6  | 57.1±1.7  | 53.7±1.5  | 43.6±1.1     | 48.1±1.5     | 40.8±1.2     | 38.9±1.7     | 46.1±1.6     | 32.6±1.5     | 48.5±1.3    | 54.9±1.4    | 51.2±1.1    | 35.0±1.5    | 32.4±1.3    | 38.9±1.2    |\n### Table 2a: Real+Painting Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Painting All   | Painting Old   | Painting New   |\n|-|-|-|-|-|-|-|\n| ProtoGCD   | 61.8±1.5       | 77.3±1.4       | 54.9±2.2       | 36.8±1.5       | 36.5±1.4       | 35.6±1.8       |\n| CMS        | 61.6±1.5       | 76.9±2.3       | 54.7±2.0       | 35.2±1.8       | 35.9±1.2       | 35.1±1.2       |\n| SPTNet     | 62.1±1.9       | 78.3±1.2       | 53.8±1.1       | 36.9±2.3       | 35.7±2.4       | 36.2±2.1       |\n| FREE | 67.7±1.4       | 78.1±1.7       | 61.2±1.2       | 45.6±1.1       | 46.1±1.3       | 44.8±1.6       |\n### Table 2b: Real+Sketch Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Sketch All   | Sketch Old   | Sketch New   |\n|-|-|-|-|-|-|-|\n|ProtoGCD   | 63.1±1.5       | 77.9±1.6       | 55.2±2.1      | 17.8±1.2       | 21.5±1.3       | 14.5±1.3    |\n| CMS      | 63.3±1.1        | 77.8±2.2        | 55.3±1.8        | 16.7±1.0        | 26.0±1.0        | 11.3±1.4        |\n| SPTNet   | 62.8±1.4        | 77.4±1.1        | 55.7±2.0        | 17.0±1.4       | 20.4±1.2        | 15.2±1.1        |\n| FREE | 67.8±1.5        | 78.2±1.4        | 61.6±1.3        | 22.5±1.4        | 25.8±1.3        | 20.9±1.1        |\n### Table 2c: Real+Quickdraw Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       |Quickdraw All   | Quickdraw Old   | Quickdraw New   |\n|-|-|-|-|-|-|-|\n| ProtoGCD   | 51.3±1.6       | 69.2±1.7       | 40.2±2.5       | 7.2±0.9       | 6.1±0.8       | 8.1±0.8       |\n| CMS      | 47.1±2.2        | 65.6±1.3        | 35.4±1.3        | 6.9±1.0         | 5.7±1.1         | 7.7±0.7         |\n| SPTNet   | 49.1±1.0        | 67.8±2.3        | 38.0±1.4        | 7.0±1.1         | 5.8±0.6         | 7.8±0.8         |\n| FREE | 61.4±0.9        | 78.1±1.6        | 55.1±1.8        | 8.9±0.7         | 7.8±0.5        | 9.0±0.9         | \n### Table 2d: Real+Clipart Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Clipart All   | Clipart Old   | Clipart New   |\n|-|-|-|-|-|-|-|\n| ProtoGCD   | 63.1±1.3       | 77.3±1.7       | 55.8±2.4       | 25.8±1.6       | 38.7±1.4       | 14.8±1.5       |\n| CMS    | 62.5±1.6        | 76.5±1.4        | 55.4±1.9        | 24.7±1.2        | 30.9±1.4        | 18.8±1.5        |\n| SPTNet   | 62.3±1.8        | 77.1±1.3        | 54.7±2.4        | 24.5±2.1        | 38.0±2.3        | 13.9±2.3        |\n| FREE | 66.4±1.0        | 78.1±0.9        | 60.1±0.9        | 29.3±1.5        | 37.2±1.6        | 26.3±1.6        |\n### Table 2e: Real+Infograph Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Infograph All   | Infograph Old   |Infograph New   |\n|-|-|-|-|-|-|-|\n| ProtoGCD   | 55.6±2.4       | 68.8±1.7       | 46.8±2.6       | 12.8±1.7       | 16.6±1.5       | 9.9±1.2       |\n| CMS      | 54.5±1.6        | 67.9±2.1        | 46.2±1.3        | 11.9±1.7        | 19.4±1.8        | 7.9±1.1         |\n| SPTNet   | 57.2±1.8        | 68.3±2.3        | 48.1±1.1        | 12.0±1.3        | 15.9±1.1        | 9.8±1.5         |\n| FREE| 68.1±1.4        | 78.9±1.3        | 60.2±1.6        | 16.1±1.4        | 18.6±1.2        | 13.4±0.9        |\n\n### **Q2:Regarding contribution of each component:**\nWe appreciate the reviewers’ recognition of the practical value and challenges associated with our proposed problem setting. Indeed, our formulation—which combines labeled and unlabeled data from distinct domains and categories for category discovery—is a natural yet underexplored generalization of UDA and GCD. While prior work has tackled GCD under domain homogeneity or UDA under closed-label space, few have addressed both semantic and domain shift simultaneously. Our work is to bridge this gap with a unified and principled solution. While we acknowledge that some components draw inspiration from previous work, we would like to emphasize that our method is not a trivial composition of existing modules, but rather introduces key innovations specifically tailored to the dual-challenge of domain and category shifts. \n\nFirst, we observed that directly applying previous frequency-based adaptation methods (e.g., FDA) to the GCD setting is problematic, as randomly mixing frequency components from different domains may introduce spurious correlations and semantic noise. This is especially detrimental for novel categories, which rely solely on pseudo-label supervision. To address this, we propose an FDS mechanism that explicitly separates samples by domain before applying perturbation, preventing harmful signal contamination and ensuring more stable representation learning and better discrimination between known and novel categories. Building on this, our class-aware cross-domain frequency perturbation uses the more familiar known-domain data to guide feature learning and mitigate domain gaps without disrupting category structure. To further improve the model’s robustness within the unknown domain, we introduce an intra-domain frequency perturbation module. This enhances the model’s invariance to intra-domain variations, addressing the lack of supervision and diversity in unlabeled novel categories. Existing GCD or UDA approaches typically assume uniform difficulty across categories during training. However, in practice, some categories (especially in the unknown domain) are harder to cluster due to greater intra-class variance or domain shifts. Our proposed CDAS module adaptively reweights the sampling process based on per-category clustering difficulty, allowing the model to focus its capacity on harder categories, improving both representation learning and final clustering quality. To our knowledge, this is the first work to incorporate such difficulty-awareness into domain-adaptive category discovery.\n\n### **Q3:Regarding Hyperparameter Sensitivity:**\nWe have further conducted a parameter analysis on \\\\(\\eta\\\\), as shown in Table 3. We observe that smaller \\\\(\\eta\\\\) values tend to introduce noisy pseudo-labels and degrade performance, while larger \\\\(\\eta\\\\) can effectively filter out noisy samples, leading to more accurate category-aware perturbation.\n### Table 3: Parameter Analysis of \\\\(\\eta\\\\)\n\n| \\\\(\\eta\\\\)    | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|\n| 0. 1  | 65.6     | 77.6     | 58.3    | 43.5         | 44.6          | 42.1         |\n| 0.5 | 66.2     | 77.8     | 59.1    | 44.1          | 45.2           | 42.8           |\n| 0.9  | 67.5    | 78.0     | 60.9    | 45.4          | 45.9          | 44.6           |\n| 0.95  | 67.7     | 78.1     | 61.2     | 45.6          | 46.1           | 44.8           |\n### **Q4:Regarding Statistical Significance:**\nWe thank the reviewer for pointing this out. We have added standard deviation results in Table 1 and Table 2, which show the performance is stable across runs. The error bars for other methods, such as GCD, SimGCD, and ORCA, can be referenced from Appendix Figure 8 in the HiLo paper. Due to space limitations, we will include the full error statistics in the final version."}, {"review_id": "ZrW8E6OvCn", "reviewer": "Reviewer_rRLy", "summary": "This paper introduces *Frequency-guided Generalized Category Discovery (Free)*, a novel framework for Domain-Shifted Generalized Category Discovery (DS\\_GCD), which aims to categorize both known and unknown classes from unlabeled data spanning both seen and novel domains. In contrast to existing approaches, *Free* takes a frequency-domain perspective by leveraging the amplitude and phase of the Fourier transform to model style and semantic content, respectively. Experiments on DomainNet and the newly proposed SSB-C benchmark demonstrate that *Free* achieves superior results compared to prior GCD and NCD methods.", "questions": "Please refer to the weakness part.", "limitations": "Please refer to the weakness part.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. The proposed *Free* framework consistently outperforms a wide range of state-of-the-art methods on challenging domain-shifted benchmarks.\n2. The paper is clearly written and well-structured, making it accessible and easy to follow.\n\n**Weaknesses**\n\n1. While the use of Fourier-based techniques is innovative in the GCD context, such methods are well-studied in Domain Adaptation (DA) and Domain Generalization (DG). Given that the datasets are well-examined in DA/DG literature, it is not entirely surprising that *Free* achieves improved results.\n2. Although the paper explains how frequency manipulation may help mitigate domain shifts, it lacks a deeper analysis of how such manipulation specifically aids the discovery of unknown classes. For example, does the Intra-Domain Frequency Perturbation (IDFP) affect intra-class compactness or inter-class separability?\n3. The *Free* framework comprises four main components, resulting in a relatively complex pipeline. The reliance on Fourier transforms and extensive data augmentations may introduce considerable computational overhead. The paper does not provide an analysis of this computational cost (e.g., training time, FLOPs) relative to the baseline methods.\n4. Minor issue: Lines 458, 460, 463, and 465 contain Markdown syntax.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns.", "rebuttal": "### **Q1:contribution of each component:**\nWe appreciate the reviewers’ recognition of the practical value and challenges associated with our proposed problem setting. Indeed, our formulation—which combines labeled and unlabeled data from distinct domains and categories for category discovery—is a natural yet underexplored generalization of UDA and GCD. While prior work has tackled GCD under domain homogeneity or UDA under closed-label space, few have addressed both semantic and domain shift simultaneously. Our work is to bridge this gap with a unified and principled solution. While we acknowledge that some components draw inspiration from previous work, we would like to emphasize that our method is not a trivial composition of existing modules, but rather introduces key innovations specifically tailored to the dual-challenge of domain and category shifts. First, we observed that directly applying previous frequency-based adaptation methods (e.g., FDA) to the GCD setting is problematic, as randomly mixing frequency components from different domains may introduce spurious correlations and semantic noise. This is especially detrimental for novel categories, which rely solely on pseudo-label supervision. To address this, we propose an FDS mechanism that explicitly separates samples by domain before applying perturbation, preventing harmful signal contamination and ensuring more stable representation learning and better discrimination between known and novel categories. Building on this, our class-aware cross-domain frequency perturbation uses the more familiar source domain data to guide feature learning and mitigate domain gaps without disrupting category structure. To further improve the model’s robustness within the unknown domain, we introduce an intra-domain frequency perturbation module. This enhances the model’s invariance to intra-domain variations, addressing the lack of supervision and diversity in unlabeled novel categories. Existing GCD or UDA approaches typically assume uniform difficulty across categories during training. However, in practice, some categories (especially in the unknown domain) are harder to cluster due to greater intra-class variance or domain shifts. Our proposed CDAS module adaptively reweights the sampling process based on per-category clustering difficulty, allowing the model to focus its capacity on harder categories, improving both representation learning and final clustering quality. To our knowledge, this is the first work to incorporate such difficulty-awareness into domain-adaptive category discovery.\nAs shown in Table 1, directly applying frequency transformations without domain separation often leads to negative transfer, especially in the unseen domain where pseudo-labels are noisy. This is because the model relies entirely on pseudo-labels to supervise clustering in these unfamiliar domains, which may result in noisy guidance and degraded performance. \nThis motivated us to first perform domain separation and leverage the more familiar source domain to learn domain-invariant feature representations. Then, we apply In-Domain Frequency Perturbation (IDFP) within the target domain to avoid collapse of semantic structures.\nAs shown in Table 2, IDFP consistently improves performance across all/known/unknown classes in the unseen domain, indicating that it helps enhance intra-class compactness and inter-class separability. Moreover, the Cross-Domain Frequency Perturbation (CDFP) significantly improves generalization, suggesting that it promotes learning of domain-invariant representations.\n\n#### **Table 1: Ablation study on different transformation strategies**\n\n| Method     | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|------------|----------|----------|----------|---------------|---------------|----------------|\n| SimGCD     | 61.3       | 77.8       | 52.9       | 34.5      | 35.6      | 33.5   |\n| Random     | 62.7     | 76.5     | 54.3     | 33.2          | 34.5          | 32.5           |\n| FREE  | 67.7     | 78.1     | 61.2     | 45.6          | 46.1          | 44.8           |\n\n#### **Table 2: Ablation study of different components.**\n\n| FDS | IDFP | CDFP | CDAS | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|:---:|:----:|:----:|:----:|:--------:|:--------:|:--------:|:-------------:|:------------:|:-------------:|\n| ✗   | ✗    | ✗    | ✗    | 61.3     | 77.8     | 52.9     | 34.5          | 35.6         | 33.5          |\n| ✓   | ✓    | ✗    | ✗    | 62.0     | 77.8     | 53.3     | 36.6          | 37.8         | 35.5          |\n| ✓   | ✗    | ✓    | ✗    | 65.6     | 77.9     | 58.2     | 41.6          | 41.9         | 40.7          |\n| ✓   | ✗    | ✗    | ✓    | 63.1     | 77.9     | 54.8     | 37.6          | 38.0         | 36.9          |\n| ✓   | ✓    | ✓    | ✗    | 66.1     | 78.0     | 59.5     | 42.8          | 43.1         | 42.0          |\n| ✓   | ✓    | ✓    | ✓    | 67.7     | 78.1     | 61.2     | 45.6          | 46.1         | 44.8          |\n\n### **Q2:Computational Complexity**\nWe evaluate the computational efficiency of our method relative to baseline approaches. Although our framework introduces additional operations—namely spectral decomposition via Fast Fourier Transform (FFT), K-nearest neighbor similarity estimation, and Gaussian Mixture Model (GMM)–based domain modeling—these are implemented using highly optimized tools. Specifically, we utilize torch.fft for frequency transformations and FAISS for efficient KNN retrieval on GPU.\nAs shown in the table below, we report the FLOPs of a single forward step and the elapsed time per iteration on the CUB-C dataset with a batch size of 128 on an NVIDIA A100 GPU. Our method maintains a comparable computational profile in terms of both FLOPs and per-iteration training time:\n\n#### **Table 3: FLOPs and training time cost**\n\n| Method  | FLOPs (G) | Time Cost per Iteration (s) |\n|---------|-----------|------------------------------|\n| SimGCD  | 2159.3    | 1.079    |\n| FREE | 2160.8    | 1.132 |\n\nThese results demonstrate that the proposed enhancements introduce minimal overhead, while enabling more effective domain-aware learning.\n\n### **Q3:Markdown syntax**\nThanks for the suggestion. We will properly fix it in our final version."}, {"review_id": "xAQavSpEum", "reviewer": "Reviewer_ivLL", "summary": "This paper presents a frequency-based approach to Generalized Category Discovery (GCD) that is designed to be robust under domain shift. The method consists of four main components. First, it separates known and unknown samples using a Gaussian Mixture Model (GMM). Next, it introduces Cross-Domain Frequency Perturbation (CDFP), which applies Fourier-based augmentations to samples of the same category across different domains, encouraging the model to generalize across domain boundaries. The third component, Intra-Domain Frequency Perturbation (IDFP), enhances robustness by applying similar augmentations within a single domain. Lastly, the method incorporates Difficulty-Aware Sampling, enabling the model to focus more on challenging samples during clustering.", "questions": "1- Regarding Table 6 in the appendix, GMM is set to two modes in the main paper, which aligns with separating known and unknown categories. However, in the context of the appendix, there appear to be more than just two relevant categories, and the distributions seem to differ significantly. Since there are no experiments directly demonstrating the impact of this GMM setup with different mode numbers, does this table suggest that using GMM in this way may not be effective?\n\n2- Since the proposed difficulty-aware clustering and Fourier augmentation are not inherently limited to scenarios involving domain shift, what would be their impact when applied to a standard GCD baseline? It would be interesting to see if these components also benefit generalized category discovery in the absence of domain adaptation.", "limitations": "While the authors acknowledge that their work is currently limited to image classification, it would also be valuable to discuss some method-specific limitations. For example, the use of FFT introduces additional computational overhead, which may impact scalability. Additionally, the effectiveness of the GMM component relies on its ability to accurately separate known and unknown categories, which may not always hold in practice. Addressing these potential limitations would provide a more balanced perspective on the approach.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n1- The method leverages Fourier-based frequency perturbations for both inter-domain (same class across domains) and intra-domain (within-domain) settings, which enhances the model’s ability to generalize under domain shift.\n\n2- The introduction of Difficulty-Aware Sampling is a useful addition, helping the model focus on more challenging categories and potentially improving clustering performance across a range of scenarios.\n\n3- The approach demonstrates effectiveness across multiple state-of-the-art baselines and includes extensive ablation studies (detailed in the appendix), supporting the robustness of the proposed contributions.\n\n\n**Weaknesses:**\n\n1- Although the paper claims five key contributions, several of them do not appear to be particularly major novel contributions:\n\nFDS (Frequency-based Domain Separation): The use of a Gaussian Mixture Model (GMM) to separate known and unknown domains is introduced without clear justification or analysis of its necessity. It remains unclear how much this component contributes to the overall performance. While a semi-supervised K-means variant is briefly mentioned, it is not thoroughly explored or compared. Furthermore, it is not specified whether this clustering was performed in the frequency domain or on raw images, an important distinction, as K-means might perform better than GMM in image space.\n\nIDFP (Intra-Domain Frequency Perturbation): This is essentially a basic augmentation strategy that has been explored in prior work. It is not clearly tied to the specific goals of Generalized Category Discovery, limiting its significance as a standalone contribution.\n\n2- The related work section is lacking in important citations, both in the context of Generalized Category Discovery and frequency-based methods. For example, in line 112, the phrase \"recent research has explored frequency-based domain adaptation strategies\" is vague and does not cite any specific papers. Related work should explicitly reference prior studies to provide proper context, and prior methods such as ORCA are missing entirely from the related works section while being reported in experiments. \n\n3- For a method composed of multiple components, the ablation studies in the main paper are limited, and the experiments in the appendix are introduced without sufficient explanation or discussion. This makes it difficult to understand the individual contribution of each module or justify design choices.\n\n4- The writing could be improved for clarity. While the general structure is understandable, figures and tables are not always well explained, and several new terms and notations are introduced without clear definitions, which makes the paper more difficult to follow and interpret.\n\n*Minor:*\nConsider using an acronym (e.g., FREE) or consistently formatting the method name in bold or italics throughout the paper. Using “Free” in plain text makes it harder to distinguish from regular words.\n\nThe distinction between losses introduced by SimGCD and standard GCD losses is unclear. For clarity, it would help to explicitly label which components originate from prior GCD frameworks and which are specific to SimGCD.\n\nThe method mentions swapping low-frequency amplitudes, but it does not clearly define what constitutes \"low frequency.\" Specifying a threshold or frequency range would provide a better understanding. Although there is some mention of low frequency in the appendix, it would be helpful to explicitly state in the main text how low-frequency components are identified and how the swapping is implemented, or to clearly direct readers to the relevant section in the appendix.\n\nThere are several notations introduced that are used only once, which adds unnecessary complexity. Simplifying these would improve readability.\n\nLine 239: The notation $E(x_i)$ is used without definition; please clarify what this refers to.\n\nLines 261 and 264: It may be helpful to explicitly mention “HiLo” here so that readers understand the context without backtracking.\n\nFigure 3: The figure would benefit from a clearer explanation, both in the caption and in the main text. Specifically, mapping each part of the diagram to its corresponding loss component would improve interpretability.\n\nLine 333: \"hindering\" -> \"hinders.\"\n\nLine 447: The term \"Theoretical Analysis\" is misleading here; the content largely consists of background explanation on Fourier transforms. Consider renaming this section to Preliminaries for accuracy.\n\nLine 458: The phrase “relative strength between different directional templates” is ambiguous. Additionally, please ensure that all formulas and technical statements are carefully reviewed for accuracy. The supplementary material, particularly in lines 458, 460, 463, and 465, sometimes lacks clarity and displays inconsistent style. If these sections were drafted with the help of AI tools, please carefully review them.\n\n\nLine 472: The paper frequently omits proper citations. For example, DomainNet should be cited.\n\nA pseudocode explaining the method in the appendix can be helpful to understand the steps well.  \n\n**Quality:**\nWhile the motivation and core insights of the method are strong, the paper would benefit from further revision and refinement, especially in the appendix.\n\n**Clarity:**\nSome explanations lack clarity, and the use of notation is inconsistent, sometimes underexplained, other times overly detailed, which can make the paper challenging to follow.\n\n**Significance:**\nThe method enhances domain adaptability through augmentation. Given that HiLo has already addressed domain shift within generalized category discovery, this work primarily positions itself at the intersection of domain adaptation and generalized category discovery, and more as a solution to an already established problem. \n\n**Originality:**\nAlthough Fourier amplitude swapping has been explored in domain generalization and adaptation, its application to generalized category discovery is novel. Additionally, the introduction of difficulty-aware sampling is an interesting contribution.", "was_revised": true, "final_justification": "While I would ideally like to reproduce the results using the authors’ provided source code (in the rebuttal), the limited time window may make this difficult. Nevertheless, the authors have provided a detailed rebuttal, and I am in favor of accepting this paper.", "rebuttal": "### **Q1:contribution of each component:**\nWe thank the reviewer for the insightful comment. As shown in Table 1, directly applying frequency transformations without domain separation often leads to negative transfer, especially in the unseen domain where pseudo-labels are noisy. This is because the model relies entirely on pseudo-labels to supervise clustering in these unfamiliar domains, which may result in noisy guidance and degraded performance. This motivated us to first perform domain separation and leverage the more familiar source domain to learn domain-invariant feature representations. Building on this, we design two specialized frequency-domain perturbation strategies to improve domain generalization and reinforce semantic structure. As shown in Table 2, the class-aware cross-domain frequency perturbation enhances generalization by promoting domain-invariant representation learning. Additionally, the intra-domain frequency perturbation consistently boosts performance across all, old, and new classes in the target domain, reflecting improved intra-class compactness and inter-class separability. Finally, our CDAS module adaptively emphasizes harder categories based on clustering difficulty, leading to better representation learning and overall clustering quality.\n\n#### Table 1: Ablation study on different transformation strategies\n| Method     | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|\n| SimGCD     | 61.3 | 77.8 | 52.9 | 34.5 | 35.6 | 33.5   |\n| Random     | 62.7 | 76.5 | 54.3     | 33.2  | 34.5 | 32.5 |\n| FREE       | 67.7 | 78.1 | 61.2     | 45.6 | 46.1  | 44.8  |\n\n#### Table 2: Ablation study of different components\n| FDS | IDFP | CDFP | CDAS | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|-|-|-|\n| ✗   | ✗    | ✗    | ✗    | 61.3 | 77.8 | 52.9| 34.5| 35.6 | 33.5 |\n| ✓   | ✓    | ✗    | ✗    | 62.0 | 77.8  | 53.3| 36.6| 37.8 | 35.5  |\n| ✓   | ✗    | ✓    | ✗    | 65.6 | 77.9  | 58.2  | 41.6 | 41.9  | 40.7 |\n| ✓   | ✗    | ✗    | ✓    | 63.1 | 77.9  | 54.8  | 37.6| 38.0| 36.9  |\n| ✓   | ✓    | ✓    | ✗    | 66.1| 78.0 | 59.5  | 42.8  | 43.1  | 42.0   |\n| ✓   | ✓    | ✓    | ✓    | 67.7| 78.1  | 61.2 | 45.6  | 46.1  | 44.8 |\n\nSemi-supervised K-means was also conducted in the frequency domain. Additionally, we applied it to the original image space for comparison. The advantage of working in the frequency domain lies in the ability to isolate the amplitude component, which predominantly captures image style—something not feasible in the raw image space. As shown in Table 3, our method consistently outperforms Semi-supervised K-means in both domains. Frequency-based features yield stronger separation than raw image space representations under both clustering schemes.\n\n#### Table 3: Clustering performance of other separation strategies\n| Method     | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|\n| Semi-supervised K-means(image space) | 65.3 | 77.4 | 57.8 | 42.6 | 45.5 | 41.6 |\n| FREE | 67.7 | 78.1 | 61.2 | 45.6 | 46.1 | 44.8 |\n\nWhile IDFP alone has been explored in prior work as a general augmentation strategy, we observed that applying IDFP without the proposed FDS module leads to negative transfer and limited performance gains. Therefore, identifying a task-specific and well-integrated solution is crucial. Without the introduction of the FDS module, IDFP cannot effectively contribute to the generalized category discovery task.\n\n### **Q2:lacking in important citations**\n\nWe thank the reviewer for the valuable suggestion. We will add the following citation to clarify the statement in Line 112:\n> Yang, Yanchao, and Stefano Soatto. *FDA: Fourier Domain Adaptation for Semantic Segmentation*. CVPR 2020.\n\nThis work serves as a key reference for frequency-based domain adaptation strategies. Additionally, we acknowledge the omission of prior methods such as ORCA in the related work section. We will include a more comprehensive discussion of these methods in the final version to ensure completeness.\n\n### **Q3:ablation studies of each component**\nWe appreciate the reviewer’s concern regarding the complexity of our framework and the need for clearer justification of each component. To address this, we have conducted comprehensive ablation studies on the DomainNet dataset, as summarized in Table 1 and Table 2. Starting from SimGCD as the baseline, we incrementally integrate each module and evaluate its individual impact. As shown in Table 1, applying frequency perturbation without domain separation often causes performance degradation, especially on the unknown domain. This is because performing perturbations indiscriminately in the frequency domain may lead to negative transfer. To mitigate this, we introduce domain separation, which leverages amplitude discrepancies across sample groups to isolate known and unknown domains. We then apply Cross-Domain Frequency Perturbation (CDFP) to guide domain-invariant representation learning using the more familiar source domain. Furthermore, we employ In-Domain Frequency Perturbation (IDFP) within the target domain to capture intra-domain variation while avoiding semantic collapse. As shown in Table 2, IDFP consistently improves clustering accuracy across all/known/unknown subsets. Finally, the Clustering Difficulty-Aware Sampling strategy further enhances performance by dynamically balancing training on easy and hard samples.\nThese ablation results clearly demonstrate the necessity and complementary nature of each module. We will also revise the appendix to include more detailed explanations of the experimental setup and the design rationale for each component.\n\n### **Q4:Writing clarity needs improvement**\n\nThank you for the helpful suggestion. We will revise the manuscript to improve the clarity of figure captions and explanations. All terminology and symbols will be properly defined, and we will ensure consistency throughout the paper.\n\n### **Q5:Ambiguity of the method name \"Free\"**\n\nWe have changed Free to FREE and will apply consistent formatting throughout the final version.\n\n### **Q6:Unclear difference between SimGCD and standard GCD losses**\n\nThe contrastive loss is inherited from the original GCD framework, while the clustering loss is novel and specific to SimGCD. We will clarify this distinction in the revised version.\n\n### **Q7:\"Low frequency\" not clearly defined**\n\nFollowing FDA, we define low-frequency components using a centered square of side length $2L*min(H,W)$ in the frequency domain. We will clarify this in the main text and refer readers to the corresponding analysis in the appendix.\n\n### **Q8:Undeclared or rarely used symbols.For example, symbol $E$ is used without prior definition.**\nThank you. The symbol $E$ denotes the feature extractor, which is introduced in the “Revisiting SimGCD” section. We will define it clearly when first used and simplify any unnecessarily complex notations.\n\n### **Q9:Clarify references to \"HiLo\" in lines 261 and 264**\n\nThanks. We will explicitly mention HiLo in those lines to improve clarity and minimize backtracking for readers.\n\n### **Q10:Insufficient explanation of Figure 3**\n\nWe appreciate the suggestion. We will revise both the caption and the main text to map each visual element to its corresponding loss component and enhance interpretability.\n\n### **Q11:Grammatical error at line 333 (\"hindering\")**\n\nThanks for pointing this out. We will correct the grammar in the final version.\n\n### **Q12:Misleading section title \"Theoretical Analysis\"**\n\nWe agree and will rename the section to Preliminaries for clarity and accuracy.\n\n### **Q13:Ambiguity in line 458 and inconsistent supplementary content**\n\nThank you. We will revise the supplementary material (especially lines 458, 460, 463, and 465) for clarity and consistency, and ensure the accuracy of all formulas and statements.\n\n### **Q14:Missing citations (e.g., DomainNet at line 472)**\n\nThank you. We will add all missing citations, including DomainNet, in the final version.\n\n### **Q15:Suggestion to include pseudocode in the appendix**\n\nThank you. We will include clear pseudocode in the appendix to improve method transparency and reproducibility.\n\n### **Q16:GMM validity in multi-domain setting (Table 6). Does using a 2-mode GMM remain valid when multiple domains are present?**\nEven in multi-domain settings, a two-component GMM remains effective because all unknown domains are stylistically dissimilar to the known domain. As shown in Table 6, our method still performs well with multiple domains, validating the approach.\n\n### **Q17:Applicability of components to standard GCD without domain shift**\n\nThank you for the insightful question. When domain shift is absent, our modules can still enhance baseline methods. As shown in Table 4, both clustering difficulty-aware sampling and Fourier perturbation improve SimGCD’s performance even without domain shift.\n\n#### Table 4: performance comparison between SimGCD and our method on CUB (no domain shift)\n|  | CUB All | CUB Old | CUB New | \n|-|-|-|-|\n| SimGCD | 60.3    |  65.6   | 57.7 | \n| FREE | 64.5    | 68.3     | 60.8    | \n\n### **Q18:computational overhead**\n\nRegarding the computational overhead introduced by FFT, we mitigate this concern by leveraging efficient implementations such as `torch.fft`, which is highly optimized for GPU computation. Additionally, we adopt the FAISS library to significantly accelerate KNN retrieval during training, keeping the extra cost minimal. As for the GMM component, although it relies on effective separation between known and unknown domains, our experiments demonstrate its robustness even in multi-domain scenarios, as shown in Table 6 (Appendix)."}, {"review_id": "ixdp1q72wn", "reviewer": "Reviewer_xWh6", "summary": "This paper focuses on generalized category discovery under domain shift, which is more practical compared to traditional UDA and GCD. To handle this scenario, this paper proposes a divide and conquer strategy based on the frequency domain, namely Free, which includes five objective functions.", "questions": ">1. Eq.(11) seems a probability, not an objective function, how to utilize it?\n>2. What is the setting in Fig. 2?", "limitations": "The limitations can be found in the weaknesses and questions.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "## Strengths\n\nThis paper tackles a more realistic scenario, and the reported results show noticeable improvements on the chosen benchmarks.\n\n\n## Weaknesses\n\n\n>1. Limited novelty in motivation and methodology.\n>> The proposed framework is a divide-and-conquer integration of UDA and GCD techniques. From the perspective of motivation, this paper only states that “GCD fails under domain shift” without offering deeper insight. From the perspective of methodology, frequency-domain manipulation has been widely used in UDA [1, 2], and the corresponding components in the proposed Free also handle domain shift merely. As a result, the method may appear more like an extension of UDA rather than a principled solution to the core challenges of GCD.\n>2. **Missing key related work.**\n>> CDAD-Net [3] tackles essentially the same setting but is neither cited nor compared. The manuscript must clarify conceptual differences and provide empirical comparisons.\n>3. Complex method without hyper-parameter analysis.\n>> The proposed pipeline contains five components, yet no parameter-sensitivity study is provided. Are all hyper-parameters fixed to the values listed in the paper?\n>4. Writing issues.\n>>* *Unknown domains* is confusing, since these unlabeled domains are visible during training. Target domains would be clearer.\n>>* The methodological description in the abstract and introduction is vague, where the rationale for each component is not evident.\n\n[1] Kumar, Vikash, et al. \"Improving domain adaptation through class-aware frequency transformation.\" International Journal of Computer Vision 131.11 (2023): 2888-2907.  \n[2] Kumar, Vikash, et al. \"Caft: Class aware frequency transform for reducing domain gap.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2021.  \n[3] Rongali, Sai Bhargav, et al. \"CDAD-Net: Bridging Domain Gaps in Generalized Category Discovery.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding the lack of motivation and missing related work, which were my main reasons for giving a borderline reject. I therefore raise my score to borderline accept.", "rebuttal": "### **Q1:Limited novelty in motivation and methodology**\nThank you for your thoughtful feedback. We respectfully argue that, while frequency-based techniques have been explored in the UDA community, their direct application to GCD is non-trivial and potentially harmful. GCD presents unique challenges: unlike UDA, it must discover novel categories in unlabeled target domains without access to any ground truth. This reliance on pseudo-labels makes the task particularly sensitive to semantic noise. As shown in Table 1, naïvely applying frequency perturbations without distinguishing between known and unknown domains leads to negative transfer, especially in the novel class space.\nTo address this, our FDS module explicitly distinguishes known and unknown samples before perturbation, avoiding cross-domain contamination and enabling stable representation learning. This is essential in GCD, where noisy pseudo-supervision is the only guidance available for novel categories.\nFurthermore, our method introduces three novel components specifically tailored for GCD: Class-aware Cross-Domain Frequency Perturbation: It leverages the more familiar source-domain data in a class-aware manner to guide cross-domain feature learning while preserving semantic structures. Intra-Domain Frequency Perturbation: This improve generalization within the unknown domain. Clustering Difficulty-Aware Sampling: To our knowledge, this is the first method to incorporate difficulty-awareness into GCD. It adaptively rebalances training based on estimated category-level clustering difficulty, addressing the issue of uneven class separability that is critical in discovering novel categories.\nWhile our approach draws inspiration from UDA literature, it is designed to principally address the underexplored GCD problem under domain shift, with components carefully constructed to handle the semantic noise, lack of supervision, and class discovery difficulties that define GCD. We hope this clarification better communicates the principled design and GCD-specific motivation behind our work.\n\n### Table 1: Ablation study on different transformation strategies\n| Method     | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|\n| SimGCD     | 61.3  | 77.8 | 52.9 | 34.5| 35.6  | 33.5   |\n| Random     | 62.7 | 76.5  | 54.3 | 33.2 | 34.5  | 32.5 |\n| FREE | 67.7  | 78.1 | 61.2 | 45.6 | 46.1 | 44.8 |\n\n### Table 2: Ablation study of different components.\n| FDS | IDFP | CDFP | CDAS | Real All | Real Old | Real New | Painting All | Painting Old | Painting New |\n|-|-|-|-|-|-|-|-|-|-|\n| ✗   | ✗    | ✗    | ✗    | 61.3     | 77.8     | 52.9     | 34.5  | 35.6  | 33.5  |\n| ✓   | ✓    | ✗    | ✗    | 62.0     | 77.8     | 53.3     | 36.6 | 37.8| 35.5|\n| ✓   | ✗    | ✓    | ✗    | 65.6     | 77.9     | 58.2     | 41.6 | 41.9 | 40.7 |\n| ✓   | ✗    | ✗    | ✓    | 63.1     | 77.9     | 54.8     | 37.6 | 38.0| 36.9  |\n| ✓   | ✓    | ✓    | ✗    | 66.1     | 78.0     | 59.5     | 42.8  | 43.1 | 42.0  |\n| ✓   | ✓    | ✓    | ✓    | 67.7     | 78.1     | 61.2     | 45.6  | 46.1 | 44.8 |\n\n### **Q2:Missing key related work.**\nThank you for the suggestion. While CDAD-Net tackles a related problem, it assumes that all unlabeled data come from unknown domains—a more restrictive setting. In contrast, our method addresses a more practical scenario where unlabeled data include both known and unknown domains. As shown in Tables 3 and 4, our approach consistently outperforms CDAD-Net across all metrics, highlighting its effectiveness in this more challenging setting. We will clarify the conceptual differences and emphasize the empirical results in the final version.\n\n### Table 3: Performance on the SSB-C Dataset\n| Method     | CUB-O All | CUB-O Old | CUB-O New | CUB-C All | CUB-C Old | CUB-C New | Scars-O All | Scars-O Old | Scars-O New | Scars-C All | Scars-C Old | Scars-C New | FGVC-O All | FGVC-O Old | FGVC-O New | FGVC-C All | FGVC-C Old | FGVC-C New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| CDAD-Net     | 40.4±1.8   | 38.9±1.3   | 39.3±2.2   | 37.7±1.9   | 39.1±1.5   | 34.2±2.3   | 32.1±1.4   | 42.9±2.0   | 32.2±1.6   | 28.8±2.1   | 35.6±1.7   | 21.4±1.9   | 33.8±2.0   | 35.5±1.1   | 31.2±2.2   | 27.8±1.6   | 29.6±2.4   | 25.6±1.5   |\n| FREE  | 60.4±1.1  | 58.5±1.4  | 63.2±1.3  | 55.7±1.6  | 57.1±1.7  | 53.7±1.5  | 43.6±1.1     | 48.1±1.5     | 40.8±1.2     | 38.9±1.7     | 46.1±1.6     | 32.6±1.5     | 48.5±1.3    | 54.9±1.4    | 51.2±1.1    | 35.0±1.5    | 32.4±1.3    | 38.9±1.2    |\n\n### Table 4a: Real+Painting Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Painting All   | Painting Old   | Painting New   |\n|-|-|-|-|-|-|-|\n| CDAD-Net  | 63.6 ± 1.5   | 77.8 ± 1.4   | 56.3 ± 2.2   | 38.4 ± 1.5   | 38.4 ± 1.4   | 37.5 ± 1.8   |\n| FREE | 67.7±1.4       | 78.1±1.7       | 61.2±1.2       | 45.6±1.1       | 46.1±1.3       | 44.8±1.6       |\n\n### Table 4b: Real+Sketch Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Sketch All   | Sketch Old   | Sketch New   |\n|-|-|-|-|-|-|-|\n| CDAD-Net  | 61.9 ± 1.2   | 76.3 ± 2.1   | 52.1 ± 1.1   | 17.3 ± 1.5   | 20.9 ± 1.1   | 15.9 ± 1.3   |\n| FREE | 67.8±1.5        | 78.2±1.4        | 61.6±1.3        | 22.5±1.4        | 25.8±1.3        | 20.9±1.1        |\n\n### Table 4c: Real+Quickdraw Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       |Quickdraw All   | Quickdraw Old   | Quickdraw New   |\n|-|-|-|-|-|-|-|\n| CDAD-Net | 48.5 ± 1.0   | 66.5 ± 2.1   | 36.7 ± 2.0   | 6.4 ± 1.0    | 5.6 ± 1.1    | 7.3 ± 1.1    |\n| FREE | 61.4±0.9        | 78.1±1.6        | 55.1±1.8        | 8.9±0.7         | 7.8±0.5        | 9.0±0.9         | \n\n### Table 4d: Real+Clipart Performance on DomainNet\n| Method     | Real All       | Real Old       | Real New       | Clipart All   | Clipart Old   | Clipart New   |\n|-|-|-|-|-|-|-|\n| CDAD-Net | 61.3 ± 1.5   | 77.0 ± 1.3   | 53.1 ± 1.8   | 25.2 ± 1.6   | 31.9 ± 1.4   | 19.0 ± 2.2   |\n| FREE | 66.4±1.0   | 78.1±0.9  | 60.1±0.9  | 29.3±1.5 | 37.2±1.6 | 26.3±1.6 |\n\n### Table 4e: Real+Infograph Performance on DomainNet\n| Method | Real All  | Real Old | Real New | Infograph All   | Infograph Old   |Infograph New   |\n|-|-|-|-|-|-|-|\n| CDAD-Net  | 56.5 ± 2.0   | 68.0 ± 1.4   | 47.1 ± 1.3   | 11.8 ± 1.2   | 15.6 ± 1.7   | 9.4 ± 1.3    |\n| FREE  | 68.1±1.4 | 78.9±1.3 | 60.2±1.6 | 16.1±1.6 | 18.6±1.2   | 13.4±0.9        |\n\n### **Q3:hyper-parameter analysis**\nThank you for your comment. We would like to clarify that the sensitivity analysis of the hyperparameters designed in our framework is included in the appendix. As shown in the results, our method demonstrates stable performance across a wide range of settings, indicating its robustness to hyperparameter choices.\nIn addition, we now include a new ablation study on the loss balancing coefficient \\\\(\\beta\\\\), and rewrite the overall loss function as: \\\\(L_{total} = \\beta L_{kd} + (1 - \\beta)L_{ud}+ \\epsilon\\\\bigtriangleup\\\\). As shown in Table 5, setting $\\beta$ to 0 or 1 leads to suboptimal performance. In contrast, our method consistently achieves stable results across different values of \\\\(\\beta\\\\), further demonstrating the robustness of the proposed training strategy. We will ensure all parameter values used in experiments are clearly listed in the final version.\n\n### Table 5: Sensitivity analysis of the loss weight $\\beta$\n| \\\\(\\beta\\\\) | Real All       | Real Old       | Real New       | Painting All   | Painting Old   | Painting New   |\n|-|-|-|-|-|-|-|\n| 0.0  |64.0 | 77.9 | 55.7 |39.3 | 40.2| 38.9|\n| 0.3 | 67.4 | 77.8 | 60.9 |45.3 | 45.8| 44.3|\n| 0.5| 67.7 | 78.1 | 61.2 |45.6 | 46.1| 44.8|\n| 0.7| 67.5 | 77.7 | 61.1 | 45.4 | 46.0| 44.4|\n| 1.0 | 66.5 | 77.9 | 59.8|42.8 | 44.0 | 42.1 |\n\n### **Q4:Writing Clarity Concern**\nThank you for pointing this out. We agree that the term unknown domain may be confusing since the unlabeled target domain is visible during training. In the final version, we will revise the terminology to use target domain consistently for clarity.\nWe also acknowledge that the methodological descriptions in the abstract and introduction could be more precise. We will revise these sections to better articulate the intuition and motivation behind each component of our framework. These changes will improve the overall readability and clarity of the paper.\n\n### **Q5:Eq.(11) seems a probability, not an objective function, how to utilize it?**\nWe first sample categories from the categorical distribution \\\\(c \\sim p_{\\text{difficulty}}\\\\), where the probability \\\\(p_{\\text{difficulty}}^c\\\\) reflects the clustering difficulty of class \\\\(c\\\\). We then retrieve real feature embeddings from the current pool of samples predicted as class \\\\(c\\\\) by the model. These features are used for classification or contrastive learning to refine the model's representation. We appreciate the feedback and will incorporate further details in the final version of the paper.\n\n### **Q6:What is the setting in Fig. 2**\nFigure 2 presents the results of directly applying FDA to SimGCD, where we report the clustering accuracy across all categories. As shown, our method outperforms SimGCD+FDA both in terms of final clustering accuracy and convergence speed. In contrast, the random transformations introduced by SimGCD+FDA can sometimes hinder learning in the unknown domain, potentially leading to negative transfer effects. This observation further motivates the need for a more tailored perturbation strategy."}]

Author rebuttal:

Meta-review: This paper introduces a novel frequency-based framework for Domain-Shifted Generalized Category Discovery (DS-GCD) that leverages the Fourier spectrum to separate domain-specific style (amplitude) from semantic content (phase). The method employs class-aware frequency perturbations and a difficulty-aware sampling mechanism, achieving state-of-the-art performance on the DomainNet and SSB-C benchmarks.

The reviewers acknowledged its strengths including its novelty in the GCD problem setting, strong empirical performance across challenging benchmarks, and well-structured presentation.  However, several major concerns were raised: 1) limited novelty in some components, which adapt existing techniques from domain adaptation literature without significant innovation; 2) high complexity with many hyperparameters, lacking thorough parameter sensitivity analysis; 3) missing comparisons with important recent work like CDAD-Net and lacking proper citations for relevant prior art; and 4) insufficient analysis of mechanisms: The paper doesn't adequately explain how frequency manipulation specifically aids unknown class discovery or justify design choices like using GMM for domain separation.

In their rebuttal, the authors provided a detailed response, including clarification on differentiation from domain adaptation techniques, computational complexity results, additional ablation studies, comparisons with recent methods and hyperparameter analysis. All four reviewers positively responded to the rebuttal, with Reviewer xWh6 raising their ratings to borderline accept and the other reviewers maintaining their borderline accept ratings. The AC concurs with the reviewers' assessment, noting that while the added experiments and clarifications from the rebuttal stage are substantial, they have addressed most concerns and can be incorporated in revision. Overall, the main merits of the work outweigh its weaknesses and therefore the AC recommends acceptance. The authors should revise the manuscript to incorporate the reviewers' feedback and address the points discussed in the rebuttal.
Decision: Accept (poster)