Consistent Supervised-Unsupervised Alignment for Generalized Category Discovery
Authors: Jizhou Han
Shaokun Wang
Yuhang He
Chenhao Ding
Qiang Wang
Xinyuan Gao
SongLin Dong
Yihong Gong
Venue: NeurIPS 2025 poster ()
Keywords: Generalized Category Discovery
Neural Collapse
Primary area: applications
TL;DR: We propose NC-GCD, a Neural Collapse–inspired framework for generalized category discovery that leverages ETF prototypes and a semantic consistency matcher for consistent alignment, enabling structured features and SOTA novel category accuracy.

Abstract: Generalized Category Discovery (GCD) focuses on classifying known categories while simultaneously discovering novel categories from unlabeled data. However, previous GCD methods face challenges due to inconsistent optimization objectives and category confusion. This leads to feature overlap and ultimately hinders performance on novel categories. To address these issues, we propose the Neural Collapse-inspired Generalized Category Discovery (NC-GCD) framework. By pre-assigning and fixing Equiangular Tight Frame (ETF) prototypes, our method ensures an optimal geometric structure and a consistent optimization objective for both known and novel categories. We introduce a Consistent ETF Alignment Loss that unifies supervised and unsupervised ETF alignment and enhances category separability. Additionally, a Semantic Consistency Matcher (SCM) is designed to maintain stable and consistent label assignments across clustering iterations. Our method significantly enhancing novel category accuracy and demonstrating its effectiveness.

Consistent Supervised-Unsupervieed Alignment for Generalized Category Discovery
Jizhou Han', Shaokun Wang"; Yuhang He', Chenhao Ding;,
Qiang Wang',
Xinyuan Gao", Songlin Dong', Yihong Gong
National Key Laboratory of Sluman-Maching Hybrid Augmented Intelligence,
National Engineering Research Center for Visual Information and Applications,
Institute of Artificial Intelligence and Robotics, Xi an Jiaotong University
School Computer Science and Technology. Harbin Institute Technology, Shenzhen
Schoool of Software Engineering, Xi'an Jiaotong University *Kuaishou Technology
Faculty of Microelectronics, Shenzhen University of Advanced Technology
(jizhou-han, dch225739, qvang)@stu. xjjtu edu. en, heyuhang@xj tu. edu. en, wangshaokun@hit.. edu. en, dongsl@suat- edu. en, ygonggmail xxj tu. edu. cn,
Abstract
Generalized Category Discovery (GCD) focuses on classifying known categories while simultaneously discovering novel categories from unlabeled data. However, previous GCD methods suffer from inconsistent optimization objectives. This inconsistency leads feature overlap and ultimately hinders performance on novel categories. To address these issues, we propose the Neural Collapse-inspired Generalized Category Discovery (NC-GDD) framework. By pre-assigning and fixing Equiangular Tight Frame (ETF) prototypes, method ensures optimal geometric structure and a consistent optimization objective for both known and novel categories. We introduce Consistent ETF Alignment Loss that unifies supervised and unsupervised ETF alignment while enhancing category separability. Additionally, Semantic Consistency Matcher (SCM) is designed to maintain stable and consistent label assignments across clustering iterations. Our method achieves tate-of-the-aat performance multiple GCD benchmarks, significantly enhancing novel category accuracy and demonstrating its effectiveness.
Introduction
Generalized Category Discovery (GCD) has raised emerging attention in recent years, which aims to simultaneously classify known categories and discover novel ones from unlabeled data. Unlike traditional supisviue learning, which assumes all categories are predefined during training, where only small portion of known- category data is labeled, and all novel-category samples lack both labels and category information. It requires models utilize limited supervision from labeled known categories while autonomously discovering semantically coherent clusters in the unlabeled subset without assuming predefined category structures or a clear distinction between known and novel distributions.
GCD operates more realistic open-world scenario I 2
Recent research in GCD has witnessed substantial progress. Early research [ introduces contrastive learning framework distinguish known and novel categories. On this basis. contrastive learning- based methods 6 refine category boundaries using dynamic contrastive learning and prompt-based affinity learning. Additionally, representation learning- based methods 7 g 9 10 focus on optimizing feature representations to enhance category separability.
Yihong Gong and Shaokun Wang are the corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure 1: Illustration of the differences between prior studies, proposed NC-GCD framework, and Performance Overview. (a) Our method pre-assigns fixed ETF prototypes rather than dynamically learning prototypes, ensuring consistent optimization objectives for known and novel categories. (b) The overview of the NC-GCD. (c) Compared to previous studies, our method exhibits superior overall accuracy, with notable improvement in the accuracy of novel categories.
However, most existing methods dynamically optimize cluster prototypes or classification weights, leading to two key issues. First, Inconsistent Optimization Objective: Existing frameworks lack a consistent optimization objective for known and novel categories. As result, the models tend to prioritize learning from labeled known categories while failing to establish proper decision boundaries for the novel ones. Second, Category Confusion: As shown in Fig. [ existing methods lack geometric constraints on feature distributions. Moreover, novel categories in an unsupervised manner, making it even more difficult to achieve sufficient separation between feature-similar categories, leading category overlap and reduced accuracy. Based the above observations, we wonder:
optimized entirely
Can we pre-assign an optimal geometric structure where both known and novel categories are equally well-separated, enabling consistent learning for all categories by aligning features to this structure?
Neural Collapse (NC) is a phenomenon in well-trained classification networks, where features of each category align with a Simplex Equiangular Tight Frame (ETF) structure [II]. In this structure, within- category features collapse their respective category mean, and the means different categories are at the vertices of simplex. This alignment maximizes inter-category separation while maintaining within-category compactness, creating an optimal geometric arrangement for classification tasks.
Motivated by Neural Collapse theory, we propose the Neural collaase-inspired Generalized Category Discovery (NC-GCD) framework, which leverages NC principles create structured feature space for both known and novel categories. Unlike existing methods that dynamically learn prototypes, shown in Fig. Dp, approach pre-assigns ETF prototypes before training, ensuring an optimal geometric structure and consistent optimization objective. Our framework integrates three key components: 1) Unsupervised ETF Aligument periodically clustering all categories and aligning the top a% most confident samples to their respective ETF prototypes. This process enhances feature separability, particularly for novel categories. 2) Supervised ETF Alignment stabilizes known categories by aligning labeled features with their corresponding ETF prototypes. Afterwards, we unify supervised and unsupervised alignment by designing Consistent ETF alignment loss. However, clustering instability may lead to inconsistent label assignments, where samples of the same category are mapped to different clusters across multiple iterations, thereby disrupting ETF alignment. Even more critically, the direct mapping between ground-truth labels and ETF prototypes in supervised alignment can introduce mismatches, further compromising model stability. 3) To address these issues, we introduce the Semantic Consistency Matcher (SCM), which enforces

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one-to-one aligmment between clusters across iterations, stabilizing pseudo-label assignments and ensuring proper mapping of supervised labels ETF prototypes. By integrating these components, our method establishes a consistent optimization objective, building structured feature space that enhances category separability and effectively mitigates category confusion. Our contributions are summarized as follows:
(I) We propose fixed ETF prototype framework that establishes a consistent optimization objective for both known and novel categories, improving category separability through a consistent supervised- unsupervised alignment.
(2) We introduce the Semantic Consistency Matcher to maintain consistency in cluster labels across multiple iterations, stabilizing the training process and reducing clustering innuueed fluctuations.
(3) Our method, as demonstrated in Fig. Dp. achieves strong performance on six GCD benchmarks, with significant improvements in novel category accuracy.
2 Related Work
2.1 Generalized Category Discovery (GCD)
GCD identifies known and novel categories within partially labeled dataset. Early methods leveraged contrastive learning to distinguish categories. Later, DCCL [5] and PrompiCAL [6] refined category boundaries using dynamic contrastive learning and prompt-based affinity mechanisms.
GPC 12 and SimGCD [13] introduced Gaussian Mixture Models and parametric classification frameworks estimate category distributions. Other methods have focused on self-supervised clustering and feature refinement. PIM 77 and CMS [8] introduced contrastive mean-shift learning and representation alignment strategies to improve novel category separability. Reciprocal learning and class-wise regularization have been introduced in RLCDD [14), while ProtoGCI) [15] unifies prototype optimization and debiasing for category discovery. Meanwhile, approaches like UNO [T6] and ORCA [17] explored semi-supervised representation learning, while RankStats [18] employed ranking- statistics to facilitate unknown category discovery. Meanwhile, there is a growing line of work on continual generalized category discovery [19] 20 21 However, most existing methods rely on dynamically learned prototypes and lack consistent optimization target. This results in category confusion and imbalanced learning.
2.2 Neural Collapse and its Applications
Neural Collapse (NC) describes geometric phenomenon in deep networks where, in the final stage of training, category feature representations converge to form a Simplex Equiangular Tight Frame structure [II] This structure ensures optimal category separation and minimal intra-category variance, making it highly effective for classification. Several works have provided theoretical insights into Neural Collapse under different loss functions, demonstrating that it emerges naturally in both cross-
entropy loss 223 24 25 and mean squared eтror (MSE) loss (26] 27 28 29 Beyond theoretical exploration, NC has been applied various machine-leariing tasks. In imbalanced learning, NC training In few-shot inssemmneeeetlll learning, studies have explored EaF-based classifiers to enhance ceasure-classifier alignment and mitigate forgetting (32). In federated learning, NC has been shown to improve model generalization under non-iid settings [33]. Similar prototype-based mechanisms have also been applied in domain-incen incrementall scenarios, where consistent concept representations are maintained across domains 334 Furthermore, NC-inspired approaches have been developed to address large-scale classification problems, such as optimizing one-vs-rest margins for generalized NC [35]. TRAILER (36) also draws inspiration from NC; however, it employs fixed classifier with a pross-entropp based ETF loss applied to both labeled and pseudo-labeled data, which can cause optimization bias and instability. Our NC-GCD framework extends NC principles by pre-assigning ETF prototypes to known and novel categories. By integrating supervised and unsupervised ETF alignment, our method effectively addresses GCD's misalignment and category confusion.
principles have been leveraged to stabilize classifier prototypes under
30 31.
3

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Preliminaries
3.1 Problem Setting of GCD
Generalized Category Discovery aims to identify novel categories an unlabeled dataset while maintaining classification performance for known categories, Formally, we define dataset 'D D {(x, y.)) where the labeled dataset given by D [( 3/)] C x y", containing samples x with corresponding labels y from the set of known categories y² The unlabeled dataset is defined as D {>X} C X, which consists of samples from both known and novel categories. The overall category set is )rh UU"", where )d n = 0 and ) represents the unknown novel categories. The goal of GCD to train model that can accurately classify samples from y while discovering and organizing samples from )
3.2 Neural Collapse and Definition of Simplex ETF
Neural Collapse, observed during the terminal training phase in well-regularized neural networks on balanced datasets [II], describes a symmetric geometric structure in the last-layer features and classifier weights. Features of the same category collapse their within-category mean, which aligns with the corresponding classifier weights, forming a Simplex ETF.
Definition of Simplex ETF. A Simplex ETF consists of K vectors in Rd that form optimal geometric contiguration. These vectors, denoted as P = [P1, P21.P...... PK] E idd satisfy:
K U 1K - TO-RE k
P P-
(I)
K-
where U E IR is an orthogonal matrix satisfying UTU = TK. I is the K x K identity matrix, and 1 K-dimensionnal all-ones vector. Each prototype pı has unit f--norm (|pall 1) and fixed pairwise cosine similarity, where ōR.j is the Kronecker delta:
K
1 K-1
Ph Pj
8
Vk,j E E [],
K
Neural Collapse Phenomenon. The neural collapse phenomenon can be summarized follows:
(NC1) Feature Collapse: Last-layer features of the same category collapse to their within-category
mean: (>()) 0, (A) Avg((ue, (UR,, μa) ] where μa, is the feature of the i-th sample the category and μæ the within-category mean.
(NC2) Convergence to Simplex ETF: The within-category means of all categories, centered by the global mean PG Avge, converge to the vertices of Simplex ETF: fux #4 -e-pec -a/lllm - mGl: I. Ak [].
(NC3) Self- Duafity Within- Within-category means align with the corresponding classifier weights: fig wx/[[wal], Wa is the weight of the category k.
(NC4) Simplified Prediction: Model prediction simplifies to a nearest-categorryccntee rule: ÿ arg ming || /sell = arg max (μ,, wx), where is the feature of a test sample.
4 Method
4.1
Overview
As shown in Fig our NC-GCD framework comprises four main components: a pre-trained visual encoder f(-), a periodic clustering module g(-), pre-assigned ETF prototype set P, and a Semantic Consistency Matcher (sCM((-)
First, we utilize the pre-trained visual encoder f(-) to extract the image embedding and augmented image embedding e' for each sample. These embeddings are passed to the periodic clustering module g(-), which groups samples into clusters and computes the clustering prototypes {ci, (er,,,....... . the one hand, unsupervised ETF alignment pulls the top % of samples most similar to their cluster centers toward their corresponding pre-assigned ETF prototypes using dot-regression loss.

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Figure 2: Overview of the NC-GCD Framework. The framework uses periodic clustering to group features, aligning them with pre-assigned ETF prototypes. The Semantic Consistency Matcher (SCM) ensures consistent label assignments across clustering iterations. This process stabilizes feature alignment and maintains consistent geometric structure for both known and novel categories.
On the other hand, supervised ETF alignment ensures that labeled samples are aligned with their corresponding ETF prototypes, maintaining geometric consistency.
However, two key challenges arise. First, clustering is inherently unstable, leading to inconsistencies where the same category may assigned to different clusters across iterations, making difficult to maintain alignment with pre-assigned ETF prototypes. Second, in supervised alignment, the direct mapping between true labels and ETF protolypes may not always hold, creating mismatches that affect model stability. To address these issues, we introduce the Semantic Consistency Matcher (SCM), which guarantees one-to-one matching between clusters over time, reducing inconsistencies caused by clustering dynamics. By integrating these components, method effectively mitigates category confusion and label imbalance, ensuring a structured feature space and improved performance.
4.2 ETF Alignment
Pre-assigned ETF Prototype. We construct Simplex ETF pre-assigned classifier prototypes to enforce a structured feature space and maximize category separability. Given or estimated the number of categories K, can get its categories set V,. Then define the optimal ETF prototypes PK] as [q
P
(p), P2,
Each prototype Pt _d maintains unit 2n-morm and follows fixed pairwise similarity:
K K- 9: 1-19
1 Vi.j K].
P. PTP;
Here, qi denotes a centered orthonormal basis of a (K - (oc--1-diinne 1)-dimensional space, with unit vectors satisfying Σx q: = and q, = dzy- By pre-assigning the ETF prototypes, we provide a stable and optimal alignment structure for both known and novel categories.
Unsupervised ETF Alignment. For each sample x; DD we first extract image embedding e; f(x;) and augmented embedding eç. To introduce structural constraints and stabilize feature learning. we perform periodic clustering on the unlabeled dataset D every 7 epochs. Given the extracted image embeddings {ei,... eN ). we apply clustering to obtain K cluster centers (cı,...,cxx (x). Then, each sample embedding e; is assigned to the nearest cluster based on the cosine similarity:
Ck
f = arg max
Va; E D.
(4)
Once pseudo-labels ii are assigned, we compute the similarity between each sample and its respective cluster center, where D4 is the set of samples assigned cluster k:
e, Ck
8; =
Va,
D
(5)
|es
[c]]
5

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To align features with the pre-assee pre-assigned ETF prototype P = of samples with the highest similarity s; within each cluster. These high-confidence samples are pulled toward the corresponding ETF prototype ps using a Dot-Regression Loss 30
I. we select the top a%
1
ETF
Σ
D
E,ED,
where DR = {xx 8; is in the top a% of D represents the selected high-confidence samples assigned to cluster Cb.
Supervised ETF Alignment. For each sample z E D', we extract its feature embedding eç. The SCM establishes one-to-one mapping between predicted clusters and ground-trume labels. transforming the original labels y into ETF-aligned labels y = Φscu (v() (detailed in Section 4.3 Subsequently, each labeled sample is encouraged to align with its assigned ETF prototype:
CET
1
Σ
|ee Pall [1
D
E
where a uf This loss enforces geometric consistency between known category features and their corresponding ETF prototypes, ensuring a structured feature space.
Consistent ETF Alignment Loss. To balance the contributions of supervised and unsupervised ETF alignment, we define the hybrid ETF loss as:
LETF = (1 - -1 7Cins
where y is weighting coefficient determining.
4.3 Semantic Consistency Matcher (SCM)
In periodically clustering- learning, two key challenges arise: 1) Pseudo-label instability across iterations. Clustering fluctuations introduce inconsistencies, disrupting the learning process and degrading feature alignment. 2) Misalignment between the predicted clusters and the true labels in supervised alignment. Supervised ETF alignment may misassign cluster labels, leading to further optimization instability. To mitigate these issues, we propose the SCM, which stabilizes pseudo-label assignments across iterations and ensures consistent alignment between predicted clusters and true labels. By enforcing one-to-one mapping between clustering results from consecutive iterations, SCM reduces clustering induced fluctuations.
Specifically, SCM aligns yseudo-labels between consecutive clustering iterations through optimal assignment strategy. Given prediction sets (ūí.... :. Voξ E 3/ for the current iteration and (oi-1 1 Vūf-1 1 E V/-1 for the previous iteration, where Vt and D represent the corresponding label sets. Then, we seek an optimal permutation a² that maximizes label consistency:
N
arg max OESK
T(A
=k)))
where a bi-jective mapping function ensuring one-to-one correspondence between clusters from consecutive iterations, and SK is the space of all valid permutations over K clusters. The indicator function L(-) returns 1 the condition holds and 0 otherwise. The label set in the current iteration updated as 3/; = o² (V)-1).
SCM also ensures consistency in supervised ETF alignment by optimally mapping predicted clusters to their corresponding ETF-aligned labels. Given the prediction the labeled samples and the set of ground truth labels, SCM applies the optimal assignment strategy obtain the permutation o!. Using this mapping, the ETF-aligned label set is updated as: ):57F o ()r))
4.4 Comparative Representation Learning
Following & we adopt the unsupervised loss encourages similarity between embeddings of the same sample while distinguishing them from other samples:
explei -(/T)
CREP
log Ejjt explei e//T)
(10)
B

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Table 1: Comparison with the state of the arts on GCD, evaluated with or without the GT for clustering, with DINOv1 backbone.
CUB Stanford Cars FGVC Aireraft Herbarium CIFARI00 ImageNet100
Method
All Old New All Old New All Old New All Old New All Old New
All Old New
(a) Clustering with the ground-truth number of categories K given
GCD (CVPR22)
56.6 48.7 39.0 57.6 29.9 41.1 46.9
35.4.51.0 27.0
73.0
76.2
66.5 74.1
89.8 66.3
DCCL (CVPR23)
63.5 60.8 64.9 43.1 55.7 36.2
75.3
76.8
70.2
80.5
90.5 76.2
PromptCAL
62.9 64.4 62.1 50.2 70.1 40.6
52.2
52.3
37.0.2.0 28.9
81.2
84.2 75.3 83.1
92.7 78.3
GPC (ICCV23)
55,4 58.2 53.1 42.8
32.8 46.3
42.5
47.9
77.9
76,9
94.3 71.0
SimGCD (ICCV23)
60.3 60.3 65.6 57.7 71,9 45.0
54.2
$4.2
59.1
51.8
44.0
36.4
80.1
81.2
77.8
83.0
93.1 77.9
PIM (CVPR23)
62.7 75.7 56.2 43.1 66.9 31.6
42.3
34.8
78.3
84.2 66.5
83.1
95.3 77.0
TRAILER (CVPR24)
65.1 71.3 61.9 71.7 47.6
34.5
62.6
50.5
44.5 37.8
SelEx (ECCV24)
73.6 73.6 72.8 58.5 75.6 50.3
57.1
64.7 53.3
82.3
85.3 76.3
83
93.6 77.8
CMS (CVPR24)
68.2 76.5 64.0 56.9 76.1 47.6
56.0
63.4
$2.3
54.
26.4
82.3
85.7
75.5
84.7
95.6 79.2
SPT (ICLR24)
65.8 68 8 65.1 59.0 79.2 49.3 59.3
61.8 58.1
53.4
35.2
81.3
84.3
75.6
85.4
93.2 81.4
Ours (NC-GCD)
74.8 76.8 73.8 59.9 77.8 51.2 60.0 57.6 61.2 46.4
58.4
40.7
82.7
85.5
77.3
88.4
94.1
85.5
(b) Clustering without the ground-trudh number of categories given
GCD (CVPR22)
51.1 56.4 48.4 39.1 58.6 29.7
37.2
29.4
77.6
57.0
77.9
91.1
71.3
GPC (ICCV23)
55.5 47.5 38.2 58.9 27.4 43.3 40.7 44.8
36.5
51.7 27.9
75
84.6
60.1
75.3
93.4 66.7
PIM (CVPR23)
62.0 55.1 42.4 65.3 31.3
52.0
34.7
75.6
81.6
63.6
83.0
95.3
76.9
CMS (CVPR24)
64.4 68.2 62.2
51.7 68.9 43.4
55.2
60.6
$2.4
56.4
27.1
79.6
83.2
12.3
81.3
95.6 74.2
Ours (NC-GCD)
70.3 72.1 69.4 54.0 73.1 44.8
57.3 54.5 42.3
56.2 34.8
80.5
83.7 74.0 85.7 95.9 80.6
where eς is the augmented view of ec, is the temperature parameter, and |B] is the batch size.
For labeled samples, we apply a supervised loss to enforce compact intra-category representations:
exp(e) et/T) Ej exple) ee/T)²
Σ log
(11)
Bi
(E#(i)
where (i) represents the samples sharing the same label The representation learning objective is:
CREP = C) ACCEP>>
(12)
where À balances the contributions of unsupervised and supervised components.
4.5
Final Objective
The final loss function integrates all components to ensure stable feature alignment and category separability:
BETF + CREP,
(13)
where 3 controls the contributions of ETF loss and representation learning loss.
5
Experiments
5.1
Experimental Setup
Datasets. Our evaluation spans six image classification benchmarks, including both generic and fine-grained datasets. For generic datasets, we use CIFAR-I00 fine-grained datasets, we evaluate CUB-200 [39], Stanford Cars [40), FGVC Aireraft [41], and Herbarium 19
[37] and ImageNet-100 [38]. For
42 To separate categories into known and novel categories, we follow the SSB split 43 for the fine-grained datasets. For CIFAR-100 and ImageNet-100, we perform random category split using a fixed seed, consistent with previous studies.
protocol
Implementation Details. Our method utilizes the pre-trained DINO ViT-B/16 45 as the backbone network. We fine-tune the final layer of the image encoder along with a projection head, following prior work [. The projection head consists of an MLP with a 768-dimensional input, a 2048-dimensional hidden layer, and a 768-dimensional output, followed by a GeLU activation function [46). The learning rate is set to O.I. Other hyperparameters, including batch size, temperature
7

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Table Comparison of various methods across multiple metrics, including tineggrained datasets. Classification datasets, and All datasets.
Fine-grained Avg
Classification Avg
All Avg
Method
All
Old
New
Old
New
All
Old
New
(a) Clustering with the ground-truth number of categories K given
SimGCD (ICCV 2023)
53.1
63.7
47.7
81.6
87.2
77.9
62.6
71.5
57.8
CMS (CVPR 2024)
54.4
67.7
47.6
83.5
77.4
64.1
75.4
57.5
SPT (ICLR R 2024)
56.9
51.9
83.4
78.5
65.7
74.3
60.8
Ours (NC-GCD)
60.3
67.6
56.7
85.5
89.8
81.4
68.7
75.0
64.9
Improv. over SPT
+3.4
+0.5
+4.8
+2.1
+1.0
+2,9
+3.0
+0.7
+4.1
(b) Clustering without the ground- Iruth number of categories K given
GPC (ICCV 2023)
46.2
50.8
38.9
75.4
89.0
63.4
53.5
64.1
45.7
CMS (CVPR 2024)
52.2
63.6
46.3
80.5
89.4
73.3
61.6
72.2
55.3
Ours (NC-GCD)
55.5
64.6
50.9
83.1
89.8
77.3
64.7
73.0
59.7
Improv. over CMS
+3.3
+1.0
+4.6
+2.6
+0.4
+4.0
+0.8
+4.4
Ta: weight decay X, and the number of augmentations, are set to 128, 0.07, le=1, and 2, respectively, in accordance with previous studies. All experiments are conducted on an NVIDIA 3090 GPU. Further implementation details can be found in the Appendix.
5.2 Comparison with State of the Art Methods
We evaluate our NC-GCD framework on several fine-grained and generic classification benchmarks to demonstrate its efficacy in GCD. Table presents comparison between our method and the previous methods
10 36], evaluated on both fine-grained and generic datasets with and without access to the ground-truth (GT) number of categories K for clustering. For the case without access to GT K. we estimate the K through clustering, which is then used to align the ETF prototypes. Mcanwhile, to comprchensively evaluate the performance of various methods across Fine-Grained Datasets, Generic Classification Datasets, and All datasets, Table 2 presents the average performance.
12
Fine-Grained Datasets. On fine- -ieeggraied benchmarks such as CUB-200, Stanford Cars, FGVC Aircraft, and Herbarium19, NC-GCD outperforms previous methods, whether or not the ground-truth is provided. As shown Table 2p. when the GT K available, NC-GCD achieves an average all-category accuracy of 60.3%, surpassing SPT by 3.4 % and improving novel category accuracy over SPT by 4.8% Even without GT K, as shown in Table Pb, NC-GCD remains robust, surpassing CMS by 3.3% in all-category accuracy. Notably, CUB-200 200, NC-GCD outperforms CMS by 5.9 in all-category accuracy and 7.2% in novel category accuracy, demonstrating strong generalization without the number of categories. Fine-graines datasets present higher category confusion due to minimal intra-category variation, and our method effectively mitigates this and enhances category separabilityy.
Generic Classification Datasets. NC-GCD achieves strong performance on standard classification datasets such as CIFAR-100 and ImageNet-1000 as shown in Table With known K. NC-GCD attains an all-category accuracy of 82.7% on CIFAR-100 and 88.4% on ImageNet- 100, outperforming CMS and SPT. Notably, novel category accuracy improves by 1.7% on CIFAR-100 and 4.1% % on ImageNet-100. When must be estimated, NC-GCD maintains its competitive edge, achicving 85.7 % all-category accuracy on ImageNet-100, surpassing CMS by 4.4%. %, demonstrating its adaptability in generic classification scenarios.
Across both fine- mme-grained and generic datasets, NC-GCD consistently achieves well performance. As shown Table 2h. with GT K. NC-GCD reaches the highest all all-category accuracy of 68.7% %, surpassing SPT by 3.0% and improving novel category accuracy by 4.1% %. Even without GT K, NC- GCD remains robust, surpassing CMS by 3.1% in all-category accuracy and 4.4% % in novel category accuracy. By pre-assigning ETF prototypes, NC-GCD effectively improves category separability, mitigating category confusion and ensuring balanced learning across old and novel categories. These results highlight the robustness and versatility of NC-GCD for real-worke GCD applications.

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Table 3: Performance comparison with Supervised and Unsupervised ETF Alignment.
Sup ETF
Unsup ETF
CUB
Herbarium 19
ImageNet100
Six Datasets Avg
Alignment
Alignment
All
Old
New
All
Old
New
All
Old
New
All
Old
New
X
X
67.7
75.7
63.9
36.5
55.0
26.5
84,4
94.0
80.8
63.3
73.7
57.5
X
69.6
75.8
66.5
37.6
56.7
28.1
85.0
95.3
79.3
64.6
75.2
58,3
X
V
75.7
71.3
77.8
47.2
60.0
40.3
87.6
94.5
84.1
68.0
73.2
64.9
74.8
76.8
73.8
46.4
58.4
40.7
88.4
94.1
85.5
68.7
74,9
64.9
Improv. over baseline
+7.1
+1.1
+9.9
49.9
+3.4
+14.2
+4.0
+0.1
+4.7
+5.4
+1.2
+7.4
5.3
Ablation Study
The Effectiveness of ETF Alignment. To evaluate the impact of Unsupervised ETF Alignment and Supervised ETF Alignment, conduct ablation studies with four configurations: (1) Baseline (both disabled), (2) Supervised ETF only, (3) Unsupervised ETF only, and (4) Full model (both enabled). Table 3 presents the results, revealing key insights into each component's contribution.
Unsupervised ETF Alignment: This component yields the most significant improvements, especially in fine-grained datasets. As shown in Table enabling unsupervised ETF alignment alone leads to substantial gains novel category accuracy. The model effectively learns robust representations, particularly for novel categories, where differentiation between visually similar categories is crucial.
Supervised ETF Alignment: This component stabilizes and preserves old categories' accuracy. By aligning labeled features with their corresponding ETF prototypes, it ensures the retention of learned knowledge while maintaining high performance on known categories. Though contribution to novel category accuracy is smaller than that of unsupervised alignment, it plays a crucial role in preventing forgetting and maintaining model stability.
Synergistic Combination: The full model, integrating both alignments, achieves the highest overall accuracy, with average all-category accuracy of 68.7 %, significantly surpassing the baseline. This combination enhances novel category discovery while preserving old category performance. Specifically. the average novel category accuracy increases by 7.4%, and the overall accuracy improves by 5.4% %. The results highlight the synergy between supervised and unsupervised alignment, demonstrating the NC-GCD effectiveness in balancing learning across known and novel categories.
The Effectiveness of SCM. To evaluate the impact of the Semantic Consistency Matcher (SCM), we conduct ablation studies on CUB- 200, Ima and Herbarium 19. As shown in Table 4 enabling SCM consistently improves performance on all three datasets. On Herbarium 19, which poses greater challenges due its large number of categories and high intra-category variance, SCM provides more significant improvements, with gains of 4.6% for all categories and 5.7% % for novel categories, demonstrating its effectiveness in complex classification tasks. By mitigating clustering fluctuations, SCM ensures stable pseudo-label assignments. These results highlight its crucial role in stabilizing training, particularly in datasets with large category numbers.
Table 4: Ablation study of SCM module.
CUB
Herbarium 19 ImageNet100
SCM
All Old New All Old New All Old New
70.3 71.0 70.0 42.6 54.3 36.3 84.3 88.9 82.0 75.7 71.3 77.8 47.2 60.0 40.3 87.6 94.5 84.1 Improv. +5.4 +0.3 +7.8 +4.6 +5.7 +4.0 +3.3 +2.6
The Influence of the ETF Scope Coefficient a. The ETF Scope Coefficient a plays cru- cial role in determining the number of sam- ples selected for alignment with the ETF pro-
totype. By controlling the percentage of high- confidence samples, influences the model's 's ability focus on either old or novel cate- gories. As seen in Fig. 3. when is too small, the model may not leverage enough high- confidence samples, leading to suboptimal per- formance. On the other hand, as increases, novel category accuracy improves significantly,
AB
ETP Scape Rute
Figure 3: Ablation study of the a on CUB-200.

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DINO.VI
(6 CMS
(c) Own
(d) Oars
Figure Visualization of Comparison with DINOv1, CMS, and our method on CUB-200.
especially in fine-grained datasets where category distinctions are subtle. However, when a exceeds certain threshold, the model's focus new categories comes at the expense of old category accuracy, highlighting the trade-off between the two. The best balance is achieved at a = 0.8, where both old and novel category accuracy reach optimal values, demonstrating the importance of selecting an appropriate a.
Ablation study of ETF loss coefficient 3, more results of the effectiveness of ETF Alignment and Parameter analysis will be presented in the Appendix.
5.4 Visualization
Comparison with Previous Methods. As shown in Fig. 4 we compare the embeddings extracted by DINOvI (a), CMS (b), and our method (c) for categories. with (d) focusing on subset of three categories from (c). The embeddings from DINO- V1 and CMS show significant overlap between categories, whereas our method clearly separates the categories into distinct clusters. Notably, categories 17, 74, and 104 collapse almost into single point in (c), which aligns with the Neural Collapse hypothesis. This demonstrates that our method enhances feature discriminability. improving category separability across both known and novel categories.
6 Conclusion and Future Work
We propose NC-GCD, framework for Generalized Category Discovery that integrates unsupervised and supervised ETF alignment enhance category separability. Extensive experiments demonstrate that NC-GCD consistently outperforms previous methods in both known and novel category accuracy. Ablation studies validate the complementary effects of the two alignment strategies, while t-SNE visualizations highlight its effectiveness in distinguishing similar categories, aligning with the Neural Collapse hypothesis. promising future research direction is extending our NC-GCD incremental GCD settings.
7 Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant No.U2182048 and No.62302382, the Shenzhen Key Technical Projects Under Grant 111ZD2022051714116 the China Postdoctoral Science Foundation No.2024M752588, and the Joint Fund Project the National Natural Science Foundation China under Grant No. U24A2028.
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NeurIPS Paper Checklist
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Question: Do the main claims made in the abstract and introduction accurately reflect the
paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction clearly summarize the main contributions, including the proposal of NC-GCD, the of ETF prototypes. the introduction of Consistent ETF Alignment Loss, and the Semantic Consistency Matcher (SCM). These claims are thoroughly validated in the experiments and ablation studies.
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Answer: [Yes]
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The paper provides complete assumptions (e.g., well-regularized neural net- works, balanced datasets), strict definition of Simplex ETF, and detailed elaboration of NC1-NC4 properties for the Neural Collapse (NC) theoretical result in Section 3.2 "Neural Collapse and Definition of Simplex ETF
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Appendix Contents
A. More Implementation Details
A.1. Training Parameters and Details
A.2. Dataset Details and Category Splits
A.3. Pseudocode of SCM
26
B. More Experiment Results and Ablation Study
B.1. Effectiveness ETF Alignment
24
B.2. Main Results with Different Backbones
B.3. Influence of ETF Loss Coefficient /
25
B.4. Impact of Incorrect Estimation of Category Number K
26
B.5. Performance under Estimated Category Number K
27
B.6. Clustering Frequency T Analysis
28
C. Parameter and SCM Efficiency Analysis
28
C.I. Parameter Analysis
28
C.2. SCM Efficiency
D. More Visualization
D.I. Comparison with State-of-the-Art Methods
29
D.2. Visualization of Training Process
30
E. Limitations and Future Work
F. Broader Impacts
21

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A More Implementation Details
A.1 Training Parameters and Details
In this study, we evaluate the NC-GCD framework on various datasets using a pre-trained DINO ViT-B/16 model as the backbone. The final layer of the image encoder is fine-tuned alongside projection head for both supervised and unsupervised alignment tasks, as per previous works 4 8) The projection head is Multi-Layer Perceptron (MLP) consisting of 768 dimensional input layer, a 2048- -48-dimensional hidden layer, and 768-dimensional output layer, followed by a GeLU activation function [46]. We empirically set periodic clustering epoch T=5 as a trade-off between stability and computational efficiency. Larger 'T may reduce adaptation speed, while smaller T increases computational cost.
The learning rate is set to 0.1, and other key hyperparameters such as batch size (128), temperature (T. 0.07), weight decay (le=4), and the number of augmentations (2) follow the settings used in prior works 4). All experiments are conducted using an NVIDIA 3090 GPU, which provides sufficient power for the fine-grained operations required our method.
For training, we use the SGD optimizer with a momentum of 0.9 and weight decay of le We apply cosine annealing learning rate scheduler to adapt the learning rate during the course of training. The method is trained for a total of 200 epochs. Additionally, data augmentation and random cropping are applied to enhance the model's ability generalize across different transformations.
In our model, we combine supervised and unsupervised contrastive losses and the ETF alignment loss. The unsupervised ETF alignment uses clustering method for periodic feature grouping, while the supervised ETF alignment ensures that labeled data is aligned with their corresponding ETF prototypes. During training, we use a weighted random sampler to balance labeled and unlabeled data in each batch, allowing the model to learn from both known and novel categories effectively.
A.2 Dataset Details and Category Splits
We evaluate our proposed framework on six diverse datasets covering general and fine-grained image classification tasks. Table provides overview of the category distributions for each dataset, categorizing them as known and unknown categories for assessing Generalized Category Discovery (GCD) performance. Below, summarize the details and category split protocols for each dataset.
consists of 60,000 images across 100 categories. For the GCD evaluation, we used 80 categories as known categories for training and the remain- ing 20 as unknown categorics for testing.
CIFAR-100. CIFAR-100
Table 5: Distribution of labeled (known) and unla- beled (novel) categories across datasets. Labeled categories have annotated training samples and serve known categories for supervision, while unlabeled categories represent novel categories that the model must discover without labels.
ImageNet100. ImageNet100 [38] is a subset of ImageNet with 100 categories. Following standard protocols, we randomly assign 50 cat- egories as known categories and the other 50 as unknown categories.
Labeled Categories
Unlabeled Categories
Dataset
CIFARI00
37
80
20
CUB-200-2011. CUB-200-2011
39 fine-
ImageNet
38
50
50
grained bird dataset with 200 categories. We split the dataset into 100 known and 100 un- known categories following the standard fine- grained GCD protocol 43
CUB-200-201
[39
100
100
Stanford Cars
40
98
98
FGVC-Aircrafi
[4
50
50
Herbarium 19 42
341
342
Stanford Cars. Stanford Cars 40
is a fine- grained dataset with 196 car categories. We use 98 categories for training (known categories) and 98 for testing (unknown categories), consistent with previous fine-grained GCD work.
FGVC Aircraft. FGVC Aireraft [4]] includes 100 aircraft categories. The dataset is split into 50
known and 50 unknown categories, adhering to the SSB protocol.
22

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Algorithm Semantic Consistency Matcher (SCM)
1:
Input:
Prediction sets from the current iteration: {ūi,.... Viv Vit E 3/ Vo, V
Prediction sets from the previous iteration: {8/ "..
Prediction sets of labeled samples from the current iteration: (0f ..., 1
Vot yo
Ground-truth labels sets: (v1, s.rk, Vol )
Number of clusters: K
2:
Output:
Updated label set: Vi + ()((-11)
Updated supervised ETF ETF-aligned label set: D.T t o'4)))
3: Define permutation set:
SK = fo a: (1,2, K] (1,2,..., K}, is bi-jective mapping function]
4: Step 1: Optimal Alignment for Prediction (Unsupervised)
5: Find optimal one-to-one mapping o* between clusters at iteration t and t:
K
ΣΣ
- o(k))
arg max OESK
6: Here, Sx denotes the set of all possible permutations (bi-jective mappings) K clusters Update pseudo-labels for the current iteration:
7:
V - o (V:-1)
8:
Step 2: Optimal Aligmment for Supervised ETF Labels
9:
Find an optimal one-to-one mapping of between predicted labels and ground-truth labels:
M
16T j)[(() =(())
arg max
Here, Sy denotes the set of all possible permutations (bi-jective mappings) over J clusters Update ElF-aligned labels for supervised samples:
11:
yFTF <- o'())
12: Return: Updated label set 3/. and alT-aligned supervised label set YETF
Herbarium19. Herbarium19 19 42 is a large-scale its high intra-category variance, we split the dataset into 341 known and 342 unknown categories to evaluate GCD on more challenging fine-grained datasets.
dataset with 683 plant species. Due to
Category Split Protocol. For general datasets (CIFAR-100 and ImageNer100), apply random category split using a fixed seed to ensure reproducibility. For fine-graines datasets (CUB-200-201) I, Stanford Cars, and FGVC Aircraft), we use the SSB split protocol [43), which ensures balanced category distributions while preserving intra-category variance. For Herbarium 19, the dataset is split into nearly equal known and unknown categories, testing the model's robustness handling datasets with significant intra-category variation.
A.3 Pseudocode of SCM
Semantic Consistency Matcher (SCM) addresses two key issues in generalized category discovery tasks: the instability of pseudo-label assignments caused by periodic clustering and the misalignment between predicted labels and ground -oound-truth labels in supervised ETF alignment. Specifically, SCM operates in two steps, detailed in Algorithm
(1) Unsupervised Scenario (Pseudo-label Alignment): Given a prediction set from the current iteration with N samples, let (.i..... where of E Dr. Similarly, prediction sets from the
23

---

Table 6: Performance comparison on CUB, Stanford Cars, FGVC Aircraft, and Herbarium 19.
Sup ETF
Unsup ETF
CUB
Stanford Cars
PGVC Aircraft
Herbarium 19
Alignment
Alignment
All
Old
New
All
Old
New
All
Old
New
All
Old
New
X
X
67.7
75.7
63.9
55.1
74.3
45.8
54.3
57.4
52.8
36.5
55.0
26.5
X
69.6
75.8
66.5
57.0
75.1
46.7
56.1
62.9
53.2
37.6
56.7
28.1
X
75.7
71.3
77.8
56.0
74.7
46.9
59.8
54.7
62.3
47.2
60.0
40.3
74.8
73.8
59.9
77.8
51.2
60.0
57.6
61.2
46.4
58.4
40.7
Improv. over baseline
47.1
+1.1
49.9
+4.8
+3.5
+5.4
+5.7
+0.2
+8.4
+9.9
+3.4
+14.2
Table 7: Performance comparison on CIFAR100, ImageNet100, and Six Datasets Average results.
Sup ETF Alignment
Unsup ETF
CIFARI00
ImageNet100
Six Datasets Avg
Alignment
All
Old
New
All
Old
New
All
Old
New
X
82.0
85,4
75.2
84.4
94.0
80.8
63.3
73.7
57.5
82.3
85.7
75.7
85.0
95.3
79.3
64.6
75.2
58.3
82.0
84.1
77.8
94.5
84.1
68.0
73.2
82.7
85.5
77.3
88.4
94.1
85.5
68.7
74.9
64.9
Improv. over baseline
+0.7
+0.1
+2,1
+4.0
+0.1
+4.7
+5,4
+1,2
+7.4
previous iteration denote as: {0) ..... VN }. where 0/- 1 E Vi-1- Both Vi and D/-1 contain K cluster labels. SCM finds an optimal bijective mapping o² between clusters of consecutive iterations by maximizing their agreement. S5 denotes all possible permutations (one-to-one mappings) over K clusters. The indicator function I(.) returns the condition is satisfied and O otherwise. The
pseudo-label set iteration is then updated as: Y4+ o² ())-1).
(2) Supervised Scenario: In the supervised setting, given M labeled samples, ..... TM denote the predicted sets of labels samples from the current iteration Let [y',..., VMr denote the ground- truth labels, each belonging to the true label set y with cardinality J. SCM identifies an optimal one-to-one mapping o' between predicted and ground-truth labels by maximizing their consistency.5, denotes all possible permutations over the known categories. The supervised ETF-aligned label set then updated D ()*)..
B
More Experiment Results and Ablation Study
B.1 Detailed Experiment Results of the Effectiveness of ETF Alignment
In the main manuscript, we have demonstrated the effectiveness of the proposed ETF Alignment strategy on CUB, Herbarium 19, and ImageNet100 datasets. To further validate its generalization capability, we conduct additional experiments on Stanford Cars, FGVC Aircraft, and CIFAR100, and report the comprehensive results in Tables and
From Table we observe that applying either supervised or unsupervised ETF Alignment leads to noticeable performance improvements across different datasets. Specifically, the combination of both supervised and unsupervised ETF Alignment consistently achieves the best results, especially on the novel categories, which demonstrates the effectiveness of our method in handling categories under generalized category discovery scenario.
Table further reports the results CIFAR100 and ImageNet100, as well the average performance over all six datasets. Our method achieves significant improvements both overall accuracy and novel category accuracy, confirming its strong generalization ability and robustness across various datasets and domains.
B.2
Main Results with Different Backbones
To evaluate the generalization ability of NC-GCD across different pretrained representations, conduct experiments using three representative backbones: DINOvI, DINOv2, and CLIP. The results on the CUB-200 datasct are summarized in Table g

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Table 8: Comparison across different backbones (DINOvI, DINOV2, CLIP) and average CUB200. The best results are in bold, the second best are underlined.
Method
DINOv1
DINOv2
CLIP
AVG
ALL
Old
New
ALL
Old
New
ALL
Old
New
ALL
Old
New
GCD (CVPR 22)
51.3
56.6
48.7
71.9
71.2
72.3
51.1
56.2
48.6
58.1
61.3
56.5
SimGCD (ICCV 23)
60.3
57.7
74.9
78.5
73.1
69.6
25.8
66.5
68.3
73.3
ProtoGCD (TPAMI-25)
63.5
68.5
60.5
75.7
81.5
72.9
RLCD (ICML 25)
70.0
79.1
65.4
78.7
79.5
78.3
SelEx (ECCV 24)
73.6
75.3
72.8
87.4
85_1
88.5
74.2
69.5
76.5
78.4
76.6
79.3
Ours (NC-GCD)
74.8
76.8
73.8
87.9
85.3
89.2
78.5
79.3
78.0
80.4
80.5
80.3
Improvement over SelEx
+1.2
+1.5
+1.0
+0.5
+0.2
+0.7
+4.3
+9.8
+1.5
+2.0
+3.9
+1.0
Table Performance on CUB-200 with different ETF loss rates.
CUB-20
ETF loss
rate |
Best ACC
Final ACC
ALI.
Old
Novel
ALI.
Old
Novel
0.5
71.57
75.85
69.44
71.44
75.85
69.24
76.67
73.72
77.31
76.33
74.18
77.41
77.45
74.85
78.75
71.42
66.
74.07
0h1--1
00,0-1
Figure 5: Visualization of the influence of the ETF loss coefficient on CUB-200.
Our method consistently achieves the best performance across all backbones. With DINOvI and DINOv2 as backbones, NC-GCD slightly outperforms SelEx by up to +1.5% Old accuracy and +1.0% in New accuracy, demonstrating stable and balanced gains. It should be noted that SclEx, GCD, and SimGCD did not originally adopt CLIP as their backbone-we thus reproduced these methods with CLIP as the backbone. When using the CLIP backbone. method's improvements become more significant, achieving +4.3% in All accuracy and +9.8% Old accuracy. This result indicates that consistent supervised unsupervised alignment effectively leverage semantic priors from large-scale lasion-language pretraining.
Averaged over all backbones, NC-GCD reaches 80.4%, 80.5% and 80.3% All, Old, and New categories, respectively, outperforming all existing methods. These results verify that the proposed framework maintains strong backhone-agnostic consistency: by fixing Equiangular Tight Frame (ETF) prototypes, NC-GCD enforces a unified geometric structure regardless of the feature distribution of the encoder. Moreover, the large gain under CLIP shows that our geometric alignment is complementary to semantic alignment, resulting in a more structured and discriminative representation space for both known and novel categories. NC-GCD exhibits robust generalization across diverse backbones, demonstrating its universality and adaptability for generalized category discovery tasks.
B.3 Analysis of ETF Loss Coefficient 3
The ETF loss coefficient 3 plays crucial role in balancing the contributions of the ETF alignment loss and the representation learning loss in our model. As shown in Table 9 and Fig. varying significantly influences both the "Best Accuracy" (Best ACC) and "Final Accuracy" (Final ACC)
25

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Table 10: Impact of estimation bias in category number K on CUB-200 and CIFAR-100.
CUB-200
CIFAR-100
Bias in K
All (%)
Old (%)
Novel (%)
All (%)
Old (%)
Novel (%)
-20%
70.3
72.1
69.4
79.8
83.7
72.5
-10%
72.5
73.5
72.0
81.2
84.3
75.2
0%
74.8
76.8
73.8
82.7
85.5
77.3
+10%
74.2
75.2
73.7
82.6
85.7
76.8
+20%
73.5
74.5
73.0
81.4
84.9
74.8
during training. "Best Accuracy" (Best ACC) refers to the highest accuracy achieved by the model at any point during the training process, typically before the model converges. It represents the model's peak performance in classifying both known and novel categories during training. "Final Accuracy" (Final ACC) refers to the accuracy achieved the last epoch, which indicates the model's final performance after all epochs. This measure is typically considered the most reliable indicator of how well the model generalizes to unseen data.
In Fig. [] we observe the accuracy curves across various values of B. When 3 = 1 (Fig. 5b). the model demonstrates the best overall performance with the highest Best ACC of 76.67% and solid Final ACC of 76.33% indicating an optimal balance between ETF alignment and representation learning. The model shows excellent performance in both known and novel categories, with consistent improvements across all category types. The curves in Fig. 6b stabilize, reflecting the model's ability to learn stable features across both known and new categories without overfitting.
When 3 is reduced to 0.5 (Fig. 54), we see a noticeable decrease both Best ACC (71.57%) and Final ACC (71.44%), especially for novel categories, where the accuracy drops to 69.44%. The model's performance on novel categories is notably weaker compared to the scenario when 3 = 1. as reflected in the flatter curves for new categories in Fig. 6a. The lower / value reduces the contribution of ETF alignment, impairing the model's ability to effectively separate categories geometrically, which results in poorer category discovery and less effective feature alignment.
On the other hand, increasing to 2 (Fig. 5p) leads to a higher Best ACC for novel categories (78.75%) but a significant drop in Final ACC for old categories, which falls to 66. 16%. While the model achieves better performance on novel categories during early training, it eventually overfits to the new categories, as seen in the accuracy curves for new categories. This causes performance imbalance, with the model neglecting the stability of learned representations for known categories. As result, the Final ACC for old categories is significantly lower, leading to an overall drop in model performance.
In conclusion, the results show that 3 = 1 strikes the optimal balance, achieving the highest and most stable performance across both known and novel categories. The Best ACC indicates the model's peak performance, while the Final ACC reflects its robustness in the final phase of learning. As our evaluation focuses on Final ACC, the results indicate that 1 is the best choice for stable and high performance in generalized category discovery tasks, ensuring effective feature alignment and balanced learning across categories.
B.4 Impact of Incorrect Estimation of Category Number K
In the NC-GCD framework, the pre-assigned ETF prototypes rely on the estimated number of cate- gories to construct the Simplex ETF structure. However, accurately determining the true number of novel categories is often difficult in real-world scenarios. To investigate the model's robustness to estimation errors, we systematically evaluate NC-GCD under different levels of estimation bias, specifically with deviations of +10% and +20% from the ground-truth value, using the CUB-200 and CIFAR- 100 datasets.
As shown in Table TO underestimating K leads to significant decline in performance, particularly for novel categories. When K is underestimated by 20%, the novel category accuracy on CUB-200 drops to 69.4%, and All category Accuracy (All ACC) decreases to 70.3%. In contrast, overestimating K by 20% results a much smaller drop, with All ACC still maintaining 73.5%. A similar trend observed on CIFAR- 100, where underestimating K by 20% causes the novel category accuracy to
26

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Table 11: Comparison of category number estimation (K) and all category accuracy (All ACC) across
different methods.
CIFARI00
ImageNet100
CUB
Stanford Cars
FGVC Aircraft Herbarium19
Method
K All ACC
All ACC
K
All ACC
K
All ACC
K All ACC
K
ACC
Ground Truth
100
100
200
196
100
683
GCD
4
100
70.8
77.9
230
51.1
230
39.1
520
37.2
GPC
12
100
75.4
103
75.3
201
52.0
201
38.6
PIM
7
95
75.6
102
83.0
227
62.0
169
55.1
563
42.0
CMS
8
97
79.6
116
81.3
170
64.4
156
51.7
98
55.2
666
37.4
Ours (NC-GCD)
96
80.5
109
85.7
182
70.3
169
54.0
105
55.4
568
42.3
fall 72.5% and All ACC to 79.8%, while overestimating K by 20% still preserves relatively high novel accuracy of 74.8% and All ACC of 81.4%
These results confirm that underestimating K has more detrimental impact novel category discovery due to insufficient prototype diversity, whereas the model is more tolerant to overestimation. This observation supports conservative K estimation strategy, where slightly overestimating the number categories is preferred to mitigate the negative effects prototype under--eprresentaion.
Overall, these findings demonstrate that accurate estimation of K is crucial for optimal performance, particularly in novel category discovery. Underestimating K significantly hampers the model's 's ability to generalize to novel categories, while overestimating K introduces redundancy without severe performance degradation. This conclusion further validates our conservative estimation strategy adopted in Section B.5 where slightly larger K' is preferred to ensure sufficient prototype capacity. In future work, we will explore adaptive prototype adjustment techniques to dynamically refine K during training and further enhance model robustness in open- opendworld settings.
B.5 Performance under Estimated Category Number K
In real-world scenarios, the exact number of novel categories is often unknown. Instead of assuming access to the ground-truth K, our NC-GCD framework is capable of estimating the number of categories directly from data through clustering-based methods. This section evaluates how well the model performs under such automatic estimation compared to other state-of-the sofftth-art approaches.
We conduct an initial CMS etylstyle S representation learning phase for 30 epochs and estimate the number of categories every 5 epochs based the current feature space. Following our earlier analysis on the impact of ETF prototype number deviations, we adopt a conservative estimation strategy by selecting the maximum estimated K across all estimation points. This approach effectively reduces the negative impact of underestimating K, which, as previously shown, leads to significant performance degradation on novel categories, while the model remains more tolerant to overestimation.
As shown in Table II our NC-GCD achieves the highest All category Accuracy (All ACC) across all evaluated datasets, despite moderate estimation biases in K. On challenging fine-grained datasets such as CUB and Stanford Cars, our method significantly outperforms other baselines. Specifically, NC-GCD achieves 70.3% All ACC CUB, surpassing CMS by +5.9%, and 54.0% Stanford Cars, improving over CMS by +2.3%. On Herbarium 19, even with a slight underestimation of K, method still leads by considerable margin, achieving 42.3% All ACC compared the next best 37.4% by CMS.
For more generic datasets like CIFARI00 and ImageNet100, where the estimated K values are closer to the ground truth, NC-GCD continues to deliver the best performance, reaching 80.5% and 85.79 75.7% All ACC, respectively. These results demonstrate that our method is not only effective in fine-grained scenarios but also robust across diverse apen-world classification tasks.
Although the estimated K may deviate from the true value, especially in complex fine- ineigrained settings, NC-GCD maintains superior accuracy and shows strong resilience to estimation errors. In future work, we plan to explore advanced model selection and adaptive prototype adjustment techniques to further improve the estimation accuracy of K and enhance the overall performance of generalized category discovery.
27

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Table 13: Comparison of parameters and accuracy.
Method
Total parameter
Trainable parameter
Avg Acc
SimGCD (ICCV 2023)
92.89M
20.74M
62.57
CMS (CVPR 2024)
92.49M
20.34M
64.08
NC-GCD (Ours)
92.89M
20.34M
68.70
B.6 Analysis of Clustering Frequency T
We further analyze the sensitivity of our NC-GCD framework to the clustering frequency, controlled by the parameter T, which determines how often clustering and prototype updates occur. shown in Table [2. setting 7' = 5 achieves the best overall performance, with the highest All accuracy of 74.80 and the highest Novel accuracy of 73.8 %. This indicates that performing clustering every five epochs strikes an effective balance between feature stability and timely prototype updates, leading to improved novel category discovery.
Interestingly, when T = 10, the accuracy for Old categories peaks at 77.5%, suggesting that less frequent clustering better preserves the learned representations of known categories. However, this comes at the cost of reduced Novel accuracy, highlighting trade-off be- tween stability for known categories and adapt- ability for novel categories.
Table 12: Impact of T on CUB-200.
Accuracy
Clustering Period T
All
Old
Novel
73.7
75.2
72.9
74.8
76.8
73.8
When the clustering frequency is too high (T' 1). the model suffers from unstable proto- type updates, negatively affecting both Old and Novel accuracies. Conversely, setting T significantly reduces the model's ' ability to adapt to novel categories due to infrequent updates, leading the lowest overall performance.
10
74.2
77.5
72.6
20
72.9
74.5
71.9
C Parameter and SCM Efficiency Analysis
We analyze the computational efficiency of method from perspectives: (1) model parameter efficiency and (2) the computational cost introduced by the Semantic Consistency Matcher (SCM).
C.1 Parameter Analysis
We analyze the computational efficiency of our method by comparing the total number of parameters, the trainable parameters, and the average accuracy (Avg ACC) achieved by our approach, SimGCD, and CMS.
As shown in Table 13 our method achieves competitive performance with an average accuracy of 68.7%, significantly outperforming SimGCD and CMS, which achieve accuracies of 62.57% and 64.08%, respectively. Our method has a similar total parameter count (92.89M) compared to SimGCD (92.89M), but unlike SimGCD, where the classifier is trained alongside the rest of the model, we pre-assign ETF prototypes and do not require training a classifier. This results in the same number of trainable parameters (20.34M) as CMS, which does not use classifier either.
This comparison demonstrates that our approach does not introduce additional trainable parameters compared to methods like CMS, which do not rely on classifiers but still achieve significantly higher accuracy. The efficiency of our model is evident the fact that it improves performance without requiring extra learnable parameters for the classifier, seen in the results. In conclusion, our method achieves high performance with highly efficient parameterization, making it an attractive solution for generalized category discovery tasks, it strikes a balance between computational cost and accuracy.
28

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Table 14: Computation time comparison (per iteration) on CUB-200 (3090 GPU).
Feature Extraction (s)
SCM
Class Center
Method
Clustering (s)
Matching (ms)
Computation (s)
CMS (CVPR 2024)
17.2846
4.2050
NC-GCD (Ours)
17.2846
4.2050
0.138
0.2828
DINO-VI
(00 CMS
<c) Ours
Figure 6: Visualization of all categories of CUB-200.
(a) DINO-VI
(b) CMS
Figure 7: Visualization of 10 random categories of CUB-200.
C.2 SCM Efficiency
The Semantic Consistency Matcher (SCM) effectively improves the stability of clustering assignments while introducing minimal computational overhead. As reported in Table I4] SCM Matching takes only 0.138 ms per execution, and the additional time for category center computation is just 0.2828 Moreover, SCM is executed only once every 5 epochs, which further reduces its impact on the overall training time.
All experiments are conducted on single NVIDIA 3090 GPU, and even under this setting, the additional overhead introduced by SCM remains negligible.
Despite this minimal overhead, SCM plays critical role in improving label consistency and enhancing model performance. Notably, our NC-GCD framework achieves significant performance gains with almost no additional computational cost, demonstrating excellent trade-off between accuracy and efficiency. These results highlight the practical scalability and real-world applicability of NC-GCD for generalized category discovery tasks.
D More Visualization Results
D.1 Comparison with State of the Art Methods
To further demonstrate the effectiveness of our NC-GCD framework, we present additional visualiza- tions of the feature space learned by our method. The t-SNE visualizations all categories and 10 random categories from the CUB-200 200 dataset are shown in Figures o and respectively.
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Figure 8: Visualization of our training process on CUB-200 (All categories).
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Glrpak-4 48
Obopech
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Figure Visualization of our training process on CUB-200 (3 random categories).
In Fig. we visualize the embeddings of all categories in the CUB-200 dataset. Fig. (a) shows the t-SNE visualization of the embeddings extracted using DINOv1, 1, where significant overlap between categories is observed. This overlap indicates that model struggles to distinguish between many of the categories. Fig. (b) presents the embeddings extracted by CMS, which also show notable clusters but still suffer from some confusion and overlap. In contrast, Fig. (c) shows the embeddings from our NC-GCD method, where the categories more clearly separated. This demonstrates our model's ability to learn more distinct and structured feature representations for all categories, confirming the efficacy of our pre-assigned ETF prototypes and alignment strategy in improving class separability.
Fig. provides zoomed-in view with t-SNE visualizations of 10 randomly selected categories from the CUB-200 dataset. Fig. (a) again shows the embeddings from DINOv1, where the categories are still widely scattered and not well separated. Fig. (b) shows CMS embeddings, where the clustering has improved still lacks fine-grained separation seen in (c). In Fig. 7 (c), our method successfully groups the categories with minimal overlap, and the embeddings show compact, well-separated clusters. This highlights our method's ''s ability to preserve class separability even with limited subset of categories, further demonstrating the robustness of NC-GCD in handling both known and novel categories.
These visualizations underscore the power of our NC-GCD framework in ensuring clear category separation and reducing category confusion. The effectiveness the ETF alignment strategy is evident in both the overall category separability and the detailed random category embeddings, where our method significantly outperforms both DINOv] and CMS in organizing the feature space.
D.2 Training Process
To better understand how our NC-GCD framework organizes feature representations over time, provide t-SNE visualizations of the training process on the CUB-200 dataset. These visualizations demonstrate how method progressively refines feature distributions, ultimately achieving well-structured and highly separable feature space.
Fig. g illustrates the evolution of feature representations for all categories across different training epochs. At epoch O, the features are highly entangled, with significant category confusion due the lack of geometric constraints. As training progresses, the feature clusters gradually become more
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distinct, aligning with their respective ETF prototypes. By epoch 40, the initial separation between categories emerges, and by epoch 100, the majority categories are well-structured. By epoch 200, the features exhibit a near-complete collapse to simplex ETF structure, aligning closely with the Neural Collapse (NC) theory [1,, where features within each class concentrate around their mean while inter-class distances remain maximized.
Fig. 9 further highlights this phenomenon by showing three randomly selected categories. Initially, these categories exhibit substantial overlap, but as training progresses, their feature distributions become increasingly compact while maintaining distinct separation. Eventually, each category collapses onto single point, which is consistent with the expected NC behavior. This confirms that our method successfully enforces geometric structure that maximizes category separability while maintaining within-categon compactness.
These visualizations validate the effectiveness of approach. By leveraging Neural Collapse principles and ETF alignment, NC-GCD ensures a consistent and optimal feature arrangement throughout training. The final collapse of features well-defined simplex ETF structure highlights the theoretical soundness of our method and its strong alignment with NC theory, making it highly effective for Generalized Category Discovery.
E Limitations and Future Work
While our NC-GCD framework demonstrates strong performance across various benchmarks, there remain opportunities for further improvement.
First, the scalability of the fixed ETF prototype structure has not been thoroughly explored. Although the current design works well on the evaluated datasets, its effectiveness in large-scale or highly complex scenarios remains be validated. Future work will investigate how extend the ETF framework to better handle diverse and large-scale category distributions.
Second, the estimation of the category number K relies clustering -based heuristics, which generally perform well but may be sensitive to feature quality some challenging scenarios. Incorporating more robust estimation techniques could help improve performance stability, especially in cases with highly ambiguous data distributions.
F Broader Impacts
This work explores a novel framework for Generalized Category Discovery (GCD), enhancing the ability of Al systems to autonomously recognize and differentiate new concepts in open-worid environments. By reducing the dependence on large-scale labeled datasets, our method lowers the barriers to applying Al technologies in domains where data annotation is expensive difficult to obtain
The proposed framework encourages more efficient use of unlabeled data, offering practical solutions for knowledge discovery fields such as environmental monitoring, healthcare diagnostics, and industrial quality control. Furthermore, it has the potential to accelerate the development of adaptive intelligent systems capable of continuously learning from new, unseen data without extensive human supervision. We hope this research will contribute to broader advancements in learning with limited supervision and inspire further innovations building more flexible and scalable Al systems [49]
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Reviews:
[{"review_id": "kmeSwxoTHw", "reviewer": "Reviewer_38Tx", "summary": "This paper presents NC-GCD, a Neural Collapse-inspired framework for Generalized Category Discovery. The key idea is to pre-assign Equiangular Tight Frame prototypes for both known and novel categories, aiming to achieve consistent optimization objectives and improve class separability. The framework introduces (1) supervised and unsupervised ETF alignment with a consistent loss function and (2) a Semantic Consistency Matcher to stabilize cluster assignments across iterations. Extensive experiments on multiple benchmarks demonstrate improvements over prior state-of-the-art methods.", "questions": "1. All experiments use DINO ViT-B/16. Could the authors show results with other backbone architectures (e.g., ResNet variants) to validate generalization?\n\n2. The paper does not compare with several recent works. Please add the recent SoTA works and compare those with the proposed method.\n\n3. Please update references to use NeurIPS [number] format consistently throughout the paper.", "limitations": "The authors discussed potential limitations.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n+ The proposed method looks novel. They leverage Neural Collapse insights to enforce consistent category separation.\n+ Experimental results across six benchmarks are thorough, including comparisons to strong baselines and ablation studies demonstrating the contributions of individual components.\n+ The motivation and presentation of the proposed method are clear with good illustrations and visualizations of feature separability.\n\nWeaknesses\n- All experiments rely exclusively on DINO ViT-B/16 as the backbone. This raises concerns about whether improvements generalize to different architectures.\n- Several recent strong baselines for GCD are missing in the comparison below. Including these would strengthen claims of state-of-the-art performance.\n- Although the method is well motivated, the reliance on ETF prototypes is not entirely novel (prior works have leveraged Neural Collapse in other contexts), which somewhat limits originality.\n- A minor thing. Citation formatting does not follow NeurIPS style (should be [1] instead of (1)).\n\n\n[1] Kim, Hyungmin, Sungho Suh, Daehwan Kim, Daun Jeong, Hansang Cho, and Junmo Kim. \"Proxy anchor-based unsupervised learning for continuous generalized category discovery.\" In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 16688-16697. 2023.\n[2] Cendra, Fernando Julio, Bingchen Zhao, and Kai Han. \"Promptccd: Learning gaussian mixture prompt pool for continual category discovery.\" In European Conference on Computer Vision, pp. 188-205. Cham: Springer Nature Switzerland, 2024.\n[3] Park, Keon-Hee, Hakyung Lee, Kyungwoo Song, and Gyeong-Moon Park. \"Online Continuous Generalized Category Discovery.\" In European Conference on Computer Vision, pp. 53-69. Cham: Springer Nature Switzerland, 2024.\n[4] Rypeść, Grzegorz, Daniel Marczak, Sebastian Cygert, Tomasz Trzciński, and Bartłomiej Twardowski. \"Category adaptation meets projected distillation in generalized continual category discovery.\" In European Conference on Computer Vision, pp. 320-337. Cham: Springer Nature Switzerland, 2024.", "was_revised": true, "final_justification": "The authors provided the detailed response with the additional experimental results. I keep my initial positive rating.", "rebuttal": "## Response to Reviewer 38Tx  \n\nWe sincerely thank the reviewer for the detailed and insightful comments. We appreciate the recognition of our contributions, including the principled theoretical motivation from Neural Collapse, the consistent and well-structured optimization design, and the thorough experimental validation across six benchmarks. We address the concerns point-by-point below.\n\n---\n\n### 🔹Q1: *All experiments use DINO ViT-B/16. Could the authors show results with other backbone architectures?*\n\n**A1**: We thank the reviewer for raising this important point.  Most recent GCD methods — including CMS (CVPR 2024), PromptCAL (CVPR 2023), and SelEx (ECCV 2024) — are built on ViT-based backbones, reflecting the community’s focus on transformer architectures.  To evaluate the generalization ability of our method under this mainstream setting, we conducted additional experiments using stronger backbones: **DINOv2 ViT-B/14** and **CLIP-ViT/B16**\n\n- **Results on DINOv2 :**\n\n  As shown in Table R1, our method achieves an average accuracy of **84.0%**, **consistently outperforming SelEx (ECCV 2024) and RLCD (ICML25) [1] across all three datasets** (*CUB, Stanford Cars, FGVC Aircraft*). This confirms that NC-GCD maintains its advantage even under stronger ViT architectures.\n\n#### **Table R1: Results with DINOv2**\n| Method             | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n| - | -       | -       | -       | -        | -        | -        | -             | -             | -             | -       | -       | -       |\n| GCD (CVPR-22) | 71.9    | 71.2    | 72.3    | 55.4     | 47.9     | 59.7     | 49.7  | 47.9   | 50.5   | 59.0  | 55.7    | 60.8    |\n| μGCD (NIPS-23)  | 74.6    | 75.0    | 74.4  | 60.6  | 64.7  | 58.6  | 60.0  | 62.0  | 59.0 | 65.1 | 67.2|64.0 |\n| SelEx (ECCV-24)  | 87.4  | 85.1 | 88.5  | 79.8 | 82.3 | 78.6|82.2      | **93.7**      | 76.7      | 83.1  | 87.0  | 81.3  |\n| ProtoGCD (TPAMI-25)  | 75.7    | 81.5    | 72.9    | 77.6 | 90.5   | 71.5  | 71.1  | 76.3  | 68.5     | 74.8  | 82.8  | 71.0  |\n| RLCD (ICML-25)  | 78.7    | 79.5    | 78.3    | 79.5 | **91.8**   | 73.5  | 72.6  | 73.3  | 70.3     | 76.9  | 82.9  | 74.0  |\n| **NC-GCD**         | **87.9**| **85.3**| **89.2**| **81.1** | 90.9  | **79.3** | **83.1**      | 88.3          | **82.5**      | **84.0**| **88.2**| **83.7**|\n> GCD and μGCD results are collected from the SelEx (ECCV 2024), and will be properly cited in the revised version.\n---\n\n- **Results on CLIP:**\n\n  As shown in Table R2, our method achieves **73.8%** average accuracy, surpassing CMS (CVPR 2024) by: **+9.1%** in overall accuracy ; **+3.8%** on old classes ; **+12.0%** on novel classes  \n\n#### **Table R2: Results with CLIP**\n| Method             | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n| -                  | -       | -       | -       | -        | -        | -        | -             | -             | -             | -       | -       | -       |\n| GCD (CVPR-22)       | 51.1    | 56.2    | 48.6    | 62.5     | 73.9     | 57.0     | 41.2          | 43.0          | 40.2          | 51.6    | 57.7    | 48.6    |\n| PromptCAL (CVPR-23) | 53.7    | 61.4    | 49.9    | 60.1     | 77.9     | 51.5     | 42.2          | 48.4          | 39.0          | 52.0    | 62.6    | 46.8    |\n| CMS (CVPR-24)       | _65.8_  | _75.3_  | _61.4_  | _77.9_   | _89.0_   | _72.6_   | _50.3_        | _59.1_        | _45.9_        | _64.7_  | _74.5_  | _59.9_  |\n| **NC-GCD**         | **78.5**| **79.3**| **78.0**| **79.0** | **90.6** | **73.4** | **63.8**      | **62.8**      | **64.3**      | **73.8**| **77.6**| **71.9**|\n> All baseline results are collected from the CMS (CVPR 2024) appendix, and will be properly cited in the revised version.\n\nThese results demonstrate the architecture-agnostic nature of our design and its **robustness across DINOv1, DINOv2 and CLIP backbones**. And these results will be included in the revised version to provide a more comprehensive evaluation of our framework across mainstream transformer architectures.\n\n---\n\n### 🔹Q2: *The paper does not compare with several recent works. Please add the recent SoTA works and compare those with the proposed method.*\n\n**A2**: We appreciate the reviewer’s valuable suggestions. The mentioned works [3]–[6] represent strong advances in the **Continuous Generalized Category Discovery (C-GCD)** setting, where novel categories emerge over time. In contrast, our work focuses on the **static GCD** scenario, where all unlabeled data is provided at once without temporal structure. \n\n  To strengthen our comparison in the static setting, we have added the most recent method **RLCD (ICML-25) [1]  and ProtoGCD (TPAMI-25) [2]** to **Table R1**. As RLCD and ProtoGCD are also designed for static GCD, this provides a more **direct and fair comparison**. Our method consistently outperforms [1,2] across datasets, particularly on novel class accuracy, further validating the effectiveness of our unified alignment strategy.\n\n   Additionally, to better compare with C-GCD works, we performed a **migrated experiment of DEAN [5] in the static GCD setting** by removing its session-wise update loop while preserving *energy-guided discovery* and *feature augmentation*. As shown in Table R3, the migrated DEAN achieves strong old-class performance but lower novel-class accuracy, illustrating the different focus of these methods, which are optimized for incremental protocols. We are also actively extending NC-GCD to the C-GCD protocol, exploring how ETF-based geometric alignment can benefit continual discovery. Preliminary results are promising, and we will include more comprehensive comparisons and discussions of these works in future research. \n\n  In this paper, we will also expand the Related Work section to discuss these C-GCD approaches and include the corresponding experimental results to provide a more comprehensive comparison. Further in-depth analysis and comparisons will be presented in future research.\n\n\n\n#### **Table R3: Comparison of NC-GCD and migrated DEAN [5] (Static GCD) on CUB**  \n| Method| All | Old| New|\n|-|-|-|-|\n| DEAN (migrated)   |68.2  | 72.6 | 65.9   |\n| **NC-GCD (ours)** | **74.8** | **76.8**   | **73.8** |\n\n---\n\n### 🔹Q3: *Please update references to use NeurIPS [number] format consistently.*\n\n**A3**: We thank the reviewer for catching this formatting issue. We will carefully revise the manuscript to ensure that all in-text citations and the bibliography strictly follow the NeurIPS [number] style throughout the revised submission.\n\n---\n\n### **Reference:**\n- #### [1] Liu, Duo, et al. \"Generalized Category Discovery via Reciprocal Learning and Class-Wise Distribution Regularization.\" In *ICML*. 2025.\n- ####  [2] Ma, Shijie, et al. \"Protogcd: Unified and unbiased prototype learning for generalized category discovery.\" IEEE *Transactions on Pattern Analysis and Machine Intelligence* .2025.\n- #### [3] Kim, Hyungmin, Sungho Suh, Daehwan Kim, Daun Jeong, Hansang Cho, and Junmo Kim. \"Proxy anchor-based unsupervised learning for continuous generalized category discovery.\" In CVPR. 2023.\n- ####  [4] Cendra, Fernando Julio, Bingchen Zhao, and Kai Han. \"Promptccd: Learning gaussian mixture prompt pool for continual category discovery.\" In ECCV, 2024. \n- #### [5] Park, Keon-Hee, Hakyung Lee, Kyungwoo Song, and Gyeong-Moon Park. \"Online Continuous Generalized Category Discovery.\" In ECCV, 2024. \n- #### [6] Rypeść, Grzegorz, Daniel Marczak, Sebastian Cygert, Tomasz Trzciński, and Bartłomiej Twardowski. \"Category adaptation meets projected distillation in generalized continual category discovery.\" In ECCV, 2024."}, {"review_id": "dZM0zLWut3", "reviewer": "Reviewer_ryPc", "summary": "This paper addresses generalised category discovery (GCD). As its main contribution, it proposes to use fixed prototypes determined by maximally seperated simplex point s along an equiangular tight frame, instead of learned ones. To this end a new loss is proposed that combines supervised and self-supervised data. The paper evaluates the method on a range of GCD benchmarks and finds favorable performances.", "questions": "* How does the method perform with other non-DINOv1 backbones and other sizes?\n* the method has a trade-off between old and new classes performance with the hyperparameter alpha. Is there a way to determine this per dataset in an unsupervised way?\n* In what way does the SCM address clustering instability?\n* What if you use random fixed points instead of equiangular ones? Similar to \"Unsupervised Learning by Predicting Noise\" paper \n* How does the method perform on more realistic unbalanced GCD datasets?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "+ strong results on classic GCD benchmarks\n+ relatively simple method\n+ clear writing\t\n\n- results shown only for a single backbone\n- no results for unbalanced datasets, potentially overfitting to equal-class distribution nature of the evaluated datasets\n- no analysis whether the points actually do follow the NC hypothesis and end up near the simplex points\n- (minor) figures have too small fontsizes", "was_revised": true, "final_justification": "I've read the author rebuttal and my concerns have been all well addressed. I've raised my score.", "rebuttal": "## Response to Reviewer ryPc\n\nWe thank the reviewer for the constructive feedback and appreciate the positive recognition of our method’s clarity and performance. Below we respond to the reviewer’s questions and concerns.\n\n---\n\n### 🔹Q1: *How does the method perform with other non-DINOv1 backbones and other sizes?*\n\n**A1**: We thank the reviewer for raising this important point.  To evaluate the **generalization ability** of our method under this mainstream setting, we conducted additional experiments using stronger backbones: **DINOv2 ViT-B/14** and **CLIP-ViT/B16**\n\n- **Results on DINOv2 :**\n\n  As shown in Table R1, our method achieves an average accuracy of **84.0%**, **consistently outperforming SelEx (ECCV 2024) and RLCD (ICML25) [1]  across all three datasets** (*CUB, Stanford Cars, FGVC Aircraft*).  This confirms that NC-GCD maintains its advantage even under stronger ViT architectures.\n\n#### **Table R1: Results with DINOv2**\n| Method | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| GCD (CVPR22)| 71.9|71.2| 72.3| 55.4|47.9| 59.7|49.7|47.9|50.5|59.0|55.| 60.8    |\n| μGCD (NIPS23)| 74.6 | 75.0| 74.4 | _60.6_ | _64.7_ | _58.6_   | _60.0_  | _62.0_| _59.0_ | _65.1_  | _67.2_  | _64.0_  |\n| SelEx (ECCV24)| _87.4_  | _85.1_  | _88.5_ | 79.8 | 82.3 | 78.6|82.2      | **93.7**  | 76.7 | _83.1_  | _87.0_  | _81.3_  |\n| RLCD (ICML25)  | 78.7 | 79.5| 78.3 | 79.5 | **91.8**  | 73.5  | 72.6  | 73.3  | 70.3  | 76.9  | 82.9  | 74.0 |\n| **NC-GCD**| **87.9**| **85.3**| **89.2**| **81.1** | 90.9 | **79.3** | **83.1** | 88.3  | **82.5** | **84.0**| **88.2**| **83.7**|\n> All baseline results are collected from the SelEx (ECCV 2024) and RLCD (ICML25) [1], and will be properly cited in the revised version.\n\n- **Results on CLIP:**\n\n  As shown in Table R2, our method achieves **73.8%** average accuracy, **surpassing CMS (CVPR 2024)** by:**+9.1%** in overall accuracy  ; **+3.8%** on old classes ;  **+12.0%** on novel classes  \n\n#### **Table R2: Results with CLIP**\n| Method  | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| GCD (CVPR22) | 51.1| 56.2 | 48.6| 62.5| 73.9 | 57.0  | 41.2  | 43.0 | 40.2 | 51.6 | 57.7| 48.6|\n| PromptCAL (CVPR23) | 53.7    | 61.4 | 49.9 | 60.1 | 77.9 | 51.5 | 42.2   | 48.4 | 39.0| 52.0| 62.6    | 46.8    |\n| CMS (CVPR24) | 65.8  | 75.3  | 61.4 | 77.9 | 89.0| 72.6 | 50.3| 59.1| 45.9| 64.7| 74.5 |59.9 |\n| **NC-GCD**| **78.5**| **79.3**| **78.0**| **79.0** | **90.6** | **73.4** | **63.8** | **62.8** | **64.3**| **73.8**| **77.6**| **71.9**|\n> All baseline results are collected from the CMS (CVPR 2024) appendix, and will be properly cited in the revised version.\n\nThese results demonstrate the architecture-agnostic nature of our design and its **robustness across DINOv1, DINOv2 and CLIP backbones**. And these results will be included in the revised version to provide a more comprehensive evaluation of our framework across mainstream transformer architectures.\n\n---\n\n### 🔹Q2: *The method has a trade-off between old and new classes performance with the hyperparameter alpha. Is there a way to determine this per dataset in an unsupervised way?*\n\n**A2** :We thank the reviewer for this insightful suggestion. The scope coefficient α controls the proportion of confident samples used for alignment, which affects the balance between old and novel class performance. Our original implementation simply uses a **fixed α across all datasets**, already demonstrating strong generalization.\n\nInspired by your comment, we explored an **adaptive α strategy** inspired by the adaptive thresholding ideas in semi-supervised learning [2]. Specifically, we update α every 5 epochs based on the accuracy of labeled (known) samples, without using any extra validation data. This data-driven adaptation dynamically adjusts α, providing greater flexibility across different datasets.\n\nAs shown in **Table R3**, adaptive α brings only **marginal changes** (CUB +0.3% novel, Cars +0.2% novel), indicating that our fixed-α setup is already robust and well-balanced across datasets. The experiment confirms the **flexibility and stability** of NC-GCD, which performs consistently **without dataset-specific hyperparameter tuning**, highlighting its practical generalization ability.\n\n\n#### **Table R3: Comparison of Fixed α and Adaptive α on CUB and Stanford Cars**\n| Method| CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New |\n|-|-|-|-|-|-|-|\n| Fixed α|**74.8**|**76.8**|73.8|**59.9**|**77.8**| 51.2 |\n| Adaptive α | 73.4|72.6|**74.1**| 58.3| 76.3| **51.4** |\n\n---\n\n### 🔹Q3: *In what way does the SCM address clustering instability?*\n\n**A3**: Thank you for the insightful question. The Semantic Consistency Matcher (SCM) mitigates clustering instability by enforcing temporal label consistency across iterations. Specifically, it performs optimal one-to-one label matching between clustering results from consecutive iterations using the Hungarian algorithm (see Algorithm 1 and Appendix A.3). This ensures that semantically similar clusters are assigned consistent labels over time, preventing label drift and improving pseudo-label stability. In the supervised case, SCM also aligns predicted cluster labels with ground-truth categories for known classes, which further stabilizes ETF-based supervised alignment. \n\nOur ablation in Table R4 shows that disabling SCM leads to a significant drop in novel class accuracy, confirming its effectiveness in reducing label inconsistency.\n\n\n#### **Table R4: Ablation study of SCM on Herbarium19 (683 classes, long-tailed) and ImageNet-100 (100 classes).**\n| SCM | Herbarium-All | Herbarium-Old | Herbarium-New | ImageNet-All | ImageNet-Old | ImageNet-New |\n|-|-|-|-|-|-|-|\n| ✗ (w/o SCM) | 42.6 | 54.3| 36.3  | 84.3| 88.9| 82.0 |\n| √  (with SCM) | **47.2** | **60.0**| **40.3** | **87.6**| **94.5** | **84.1**|\n| *Improvement*| **+4.5** | **+5.6**| **+3.9**| **+3.3**| **+5.6**| **+2.1**|\n>The original Table 4 in Section 5.3 Ablation Study.\n---\n\n### 🔹Q4: *What if you use random fixed points instead of equiangular ones?*\n\n**A4**: We appreciate the reviewer’s insightful question. To investigate the role of the ETF structure in our method, we conducted ablation studies by replacing our equiangular tight frame (ETF) prototypes with randomly sampled fixed unit vectors, following the strategy of Noise As Targets [3]. This corresponds to removing the angular constraints that enforce equidistant separation between class prototypes.\n\nAs shown in Table R5, using random fixed points leads to a noticeable drop in performance across all benchmarks. Specifically, we observe an average decrease of 5.5% in all-class accuracy and up to 7.6% in novel-class accuracy compared to our NC-GCD framework. These results suggest that the ETF structure plays a critical role in promoting both inter-class separability and intra-class compactness—two key properties that are especially important in the Generalized Category Discovery (GCD) setting. The benefit is even more pronounced for novel classes, which lack labels and thus rely more heavily on geometric regularization.\n\nOverall, the results validate that ETF prototypes not only provide a theoretically grounded structure based on Neural Collapse, but also deliver concrete performance benefits over random alternatives. We will include this reference [3] and the corresponding results in the revised version.\n\n#### **Table R5: Comparison of NC-GCD and random fixed points on CUB and Stanford Cars**\n| Method | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New |\n|-|-|-|-|-|-|-|\n| Random fixed points | 68.5| 75.9 | 64.7| 55.1| 76.2 | 45.1|\n| **Ours (NC-GCD)**   | **74.8**| **76.8**| **73.8**| **59.9** | **77.8** | **51.2** |\n\n---\n\n### 🔹Q5: *How does the method perform on more realistic unbalanced GCD datasets?*\n\n**A5**: **Herbarium19** is a highly imbalanced and fine-grained dataset consisting of 683 plant species. It exhibits a **long-tailed distribution**, where some species are represented by hundreds of images while others have very limited samples. \n\nFor example, the class *Miconia prasina (Sw.) DC.* **contains 647 images**, whereas *Miconia approximata Gamba & Almeda* has **only 19 samples**. This distribution closely reflects **real-world taxonomic imbalances** in herbaria collections and poses a significant challenge for generalized category discovery.\n\nAs shown in Table R6 , our method achieves **SOTA performance on Herbarium19**. Specifically, it attains 46.4% all-class accuracy and 40.7% novel-class accuracy, outperforming SimGCD by **+2.4% (All)** and **+4.3% (New)**, and CMS by **+10.0% (All)** and **+14.3% (New)**. These results confirm that our consistent ETF alignment framework remains robust and effective under imbalance dataset.\n\nWe will supplement the description of the long-tail characteristics and imbalance of the Herbarium19 dataset in the revised version to further highlight the robustness of our method.\n\n#### **Table R6: Performance on Herbarium19 (683 classes, long-tailed).**\n| Method| Herbarium-All | Herbarium-Old | Herbarium-New |\n|-|-|-|-|\n| SimGCD(ICCV23)|44.0 | 58.0 | 36.4|\n| CMS(CVPR24)| 36.4 | 54.9 | 26.4|\n| **Ours (NC-GCD)** | **46.4**  | **58.4**  | **40.7** |\n> The original Table 1 in Section 5.2  Comparison with State-of-the-Art Methods.\n\n---\n\n### **Reference:**\n- #### [1] Liu, Duo, et al. \"Generalized Category Discovery via Reciprocal Learning and Class-Wise Distribution Regularization.\" In ICML. 2025.\n- #### [2] Guo, Lan-Zhe, and Yu-Feng Li. \"Class-imbalanced semi-supervised learning with adaptive thresholding.\" In ICML. 2022.\n- #### [3] Bojanowski, Piotr, and Armand Joulin. \"Unsupervised learning by predicting noise.\" In ICML, 2017."}, {"review_id": "DYMVwSmMf9", "reviewer": "Reviewer_zv7T", "summary": "The paper proposes NC-GCD, a Neural Collapse-inspired framework for Generalized Category Discovery, integrating supervised and unsupervised ETF alignment and a Semantic Consistency Matcher to enhance class separability and achieve state-of-the-art performance on multiple GCD benchmarks.", "questions": "Please see the weaknesses.", "limitations": "This paper needs to clarify its differences from the paper[1] and articulate its own contributions to better influence the community.\n\n[1] Targeted Representation Alignment for Open-World Semi-Supervised Learning, CVPR 2024.", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. This paper is well-written and easy to follow.\n\n2. The problem investigated is realistic and complex.\n\n3. The proposed approach outperforms other competitors on various datasets.\n\nWeaknesses:\n\n1. The idea of this paper is not novel, as there is ETF-based method prposed in the GCD / Open-World SSL field[1]. The paper should discuss in detail the differences from this uncited paper, and the key losses appear to be the same in my view.\n\n2. The framework of this paper is designed based on the SOTA method CMS. Given that CMS is already strong in terms of predicting class numbers, accuracy, etc., how would the performance improve if this framework incorporates more other GCD methods or weaker GCD methods?\n\n[1] Targeted Representation Alignment for Open-World Semi-Supervised Learning, CVPR 2024.", "was_revised": true, "final_justification": "The author's response addressed my questions well. The method proposed in the paper can be combined with many other approaches and demonstrates good generalization ability.", "rebuttal": "## Response to Reviewer zv7T  \n\nWe sincerely thank the reviewer for the positive evaluation and thoughtful comments. We appreciate your recognition that the paper is clearly written, addresses a realistic and challenging problem, and delivers strong performance across multiple benchmarks. Your encouraging feedback affirms the relevance and impact of our work. Below, we carefully address your concerns point by point and will incorporate your suggestions into the revised version.\n\n---\n\n### 🔹Q1: *Clarify differences from Targeted Representation Alignment (CVPR24).*\n\n**A1:**  We appreciate the reviewer’s attention to related work and are happy to clarify the methodological and empirical differences between our approach and TRAILER [1] . TRAILER is a solid and effective method, providing a well-designed framework for open-world semi-supervised learning. While both methods draw inspiration from Neural Collapse theory, our framework introduces several key innovations:\n\n- **Consistent ETF Alignment Across Classes and Supervision Types**\n  \n  Our core distinction lies in achieving **consistency across supervision types (labeled and unlabeled)** and **class partitions (old and novel)** — a property that TRAILER does not explicitly enforce. \n\n  - TRAILER uses a **fixed classifier** trained with all classes and applies the same Cross-Entropy-based ETF loss to both labeled and unlabeled samples. This setup **requires prior knowledge of the total number of categories**, including novel ones, limiting its use in open-world scenarios.  And this shared loss implicitly encourages the model to treat both types of samples as if they were supervised—potentially introducing **optimization bias** when pseudo-labels are noisy or novel class distributions are underrepresented.\n\n  - In contrast, our method **does not rely on a fixed classifier**. We align features to a predefined set of ETF directions and can **dynamically estimate and update the number of classes (K)** during training. Labeled samples are aligned to their known ETF targets, while unlabeled data are clustered and softly matched to unused ETF directions. This **decoupled, confidence-guided alignment** improves stability and ensures balanced learning across old and novel classes.\n\n  As shown in Tables R1, our method achieves significantly higher novel class accuracy, with an average **+7.28%** gain on fine-grained datasets and **+5.91%** overall improvement.\n\n- **Loss Design – Dot Regression vs. Cross-Entropy ETF Loss:**  \n  - TRAILER employs a **Cross-Entropy-based ETF Loss**, which involves softmax normalization over dot products between features and fixed ETF prototypes. This design requires careful tuning of a temperature parameter and introduces push gradients from non-target classes, which can hinder optimization stability—particularly under imperfect class separability or in the presence of emerging novel categories. \n\n  - In contrast, our NC-GCD adopts the **Dot Regression (DR) ETF Loss**, which directly minimizes the angular discrepancy between features and their target ETF directions. This design avoids log-softmax normalization and push terms, enabling a simpler, more stable, and interpretable optimization process. Importantly, as supported by Yang et al. (2022) [2], the DR Loss aligns closely with Neural Collapse conditions, producing geometrically consistent and compact representations—a critical advantage for novel class discovery under limited supervision.\n\n\n  - Empirically, as shown in Table R1, TRAILER exhibits a clear bias toward old classes. For example, on fine-grained datasets, it achieves 65.65% on old classes but only 49.45% on novel ones—a gap of over 16%, indicating poor balance. In contrast, our method consistently maintains smaller old-new accuracy gaps while also achieving higher all-class accuracy. Specifically, we improve fine-grained average accuracy by **+5.40%** and boost the overall average across all datasets by **+4.32%**, demonstrating both **superior generalization and alignment consistency across class types**.\n\n- **Semantic Consistency Matcher (SCM):**  \n  - **TRAILER** uses PU learning and optimal transport for pseudo-labeling, which can **introduce label inconsistencies across iterations and propagate noise throughout the training process**.  Moreover, TRAILER relies on an externally estimated class number K to initialize a **fixed classifier** with ETF weights. Once this classifier is set, the framework becomes **rigid**, as it cannot adapt to evolving cluster structures or re-estimate K during training, making it less flexible in open-world scenarios.\n\n  - In contrast, our **SCM module** lays the foundation for **consistent alignment and flexible clustering**.  It establishes one-to-one cluster correspondences to **stabilize pseudo-labels across iterations** and **mitigate semantic drift**.  Meanwhile, our framework can **dynamically re-evaluate and update \\(K\\)** during training, enabling it to adapt to the evolving feature space and achieve more balanced performance across old and novel classes.\n\n- **Global Clustering and Confident Sample Alignment:**  \nUnlike TRAILER’s batch-level optimal transport refinement, our method performs global clustering across the full dataset at regular intervals. We then select top α% high-confidence samples and align them to pre-defined ETF prototypes. This global strategy ensures more stable pseudo-labels and reduces error propagation, particularly beneficial in fine-grained or ambiguous domains where local batch-level matching may be unreliable.\n\n\n---\n\n#### **Table R1: Comparison of average performance across different dataset types.  Evaluation is performed with the ground-truth number of classes \\(K\\) provided.**\n\n| Method         | F-All | F-Old | F-New | C-All | C-Old | C-New | A-All | A-Old | A-New |\n|-|-|-----|-----|---------------------|-----|-----|--------------|-----|-----|\n| TRAILER (CVPR24) | 54.88           | 65.65 | 49.45 | 83.40             | 89.10 | 78.20 | 64.38      | 73.47 | 59.03 |\n| **NC-GCD**       | **60.28**       | **67.63** | **56.73** | **85.55**         | **89.78** | **81.37** | **68.70**  | **75.01** | **64.95**|\n| **Improvement**  | **_+5.40_**    |**_+1.98_**| **_+7.28_** | **_+2.15_**  | **_+0.68_** | **_+3.17_** | **_+4.32_**    | **_+1.54_** | **_+5.91_** |\n>F- indicates the average over fine-grained datasets (CUB, Cars, Aircraft and Herbarium19), C- refers to classification datasets (ImageNet-100, CIFAR-100), and A- denotes the average across all datasets. The suffixes All, Old, and New represent overall accuracy, known-class accuracy, and novel-class accuracy, respectively.\n\n\nIn summary, our NC-GCD framework is explicitly tailored for Generalized Category Discovery, emphasizing **consistent alignment across supervision types**, **robust support for unknown class discovery**, and **balanced performance across old and novel categories**. The clear and consistent improvements across diverse datasets, particularly on novel classes, underscore the effectiveness of our unified alignment strategy. We will incorporate the above discussion and references [1] in the revised version to clarify these distinctions.\n\n---\n\n### 🔹Q2: *How would the performance improve if the framework incorporates more other GCD methods or weaker GCD methods?*\n\n**A2:**  We thank the reviewer for this valuable suggestion. To evaluate the general applicability of our proposed framework, we integrated NC-GCD into both a weaker baseline (GCD [CVPR22]) and a stronger one (CMS [CVPR24]). As shown in **Table R2**, our method consistently improves performance across all datasets and evaluation splits.\n\nWhen combined with the weaker GCD backbone, our framework achieves clear gains over the original baseline, with up to **+6.6%** improvement on all-class accuracy on CUB and Stanford Cars (e.g., CUB: from 51.3% to 69.8%). More importantly, even when built upon the stronger CMS backbone, our method achieves SOTA performance.\n\nThese results validate that our alignment strategy is orthogonal and complementary to existing GCD frameworks—it enhances both weak and strong baselines by enforcing consistent representation geometry and improving novel class discoverability.\n\n#### **Table R2: Comparison with the state-of-the-art on GCD with different baselines.  Evaluation is performed with the ground-truth number of classes \\(K\\) provided.**\n\n| Method               | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New  |\n|--|-|-|-|-|-|-|\n| TRAILER (CVPR24)   | 65.1    | 71.3    | 65.1    | 55.4     | 71.7     | 47.6   |\n| GCD (CVPR22)            | 51.3    | 56.6    | 48.7    | 39.0     | 57.6     | 29.9        |\n| CMS (CVPR24)            | 68.2    | **_76.5_**  | 64.0    | 56.9     | **_76.1_**   | 47.6 |\n| **NC-GCD (+GCD)**    | **_69.8_**| 76.0| **_66.6_**| **_57.2_** | 75.8   | **_48.3_**    |\n| **NC-GCD (+CMS)**    | **74.8**| **76.8**| **73.8**| **59.9** | **77.8**   | **51.2**   |\n\n---\n\n### **Reference**:\n- #### [1] Xiao, Ruixuan, et al. Targeted representation alignment for open-world semi-supervised learning. CVPR 2024.\n- #### [2]  Yibo Yang and Timothy M. Hospedales. Do We Really Need a Learnable Classifier at the End of Deep Neural Network?  NeurIPS, 2022."}, {"review_id": "rmNTjMqNr1", "reviewer": "Reviewer_5vtH", "summary": "The paper aims to improve GCD accuracies by providing an optimal geometric structure that maximizes inter-class separation and maintains intra-class compactness. These fixed prototypes ensure consistent optimization goals for both known and novel categories, reducing category confusion coupled with semantic consistency matcher. The paper further adopts comparative representation learning to ensure consistent training objective for both known and unknown classes. Extensive experiments demonstrate the effcacy of their method.", "questions": "I like this paper due to its abundant experiments and solid improvements over several GCD benchmarks. My main concern lies in  \"weaknesses\"-(1).", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n(1) The proposed method follows a simple but effective GCD pipeline by improving GCD accuracies via representation learning.\n\n(2) The improvement over previous methods are significant, demonstrating their method's efficacy.\n\n(3) The overall writing is good and easy to understand.\n\n(4) Moreover, authors conduct extensive experiments and theoretical proof to verify their method.\n\nWeaknesses:\n\n(1) Based on the paper's analysis, initial estimation of K may have significant affect on final GCD accuracies. That is because the initial K determines how SCM matches pseudo labels across different epochs. However, the estimation of K may be more accurate after several epochs of training. Therefore, is it possible to further polish your method by adjusting K after several epochs of training ? E.g., after several epochs of training, we re-estimate K and start a new NC-GCD training pipeline.  \n\n(2) The authors did a great job in verifying the proposed method. Extensive experiments have been conducted and all implementation details are introduced. However, I think some important implementation details and conclusions should be moved to the main paper. e.g., the setting of periodic clustering should be demonstrated in the main paper and the results in appendix Sec. B.4 \n\n(3) Minor: Text fonts in Fig.1 and 2 are too small.", "was_revised": true, "final_justification": "I will keep my initial score.", "rebuttal": "## Response to Reviewer 5vtH  \n\nWe sincerely thank the reviewer for the encouraging feedback and high rating. We are delighted to hear that you enjoyed reading our paper. We especially appreciate your recognition of the method’s simplicity, its solid gains over prior baselines, the clarity of our writing, and the completeness of both the theoretical analysis and experimental validation. Below, we respond to each of your thoughtful comments in detail.\n\n---\n\n### 🔹Q1: *Re-estimating K after several epochs – is it beneficial?*\n\n**A1:**  We appreciate the reviewer’s insightful suggestion. As detailed in Appendix B.5 (line 952), our default strategy performs cluster number estimation every 5 epochs during the first 30 epochs, and selects the maximum value as the final estimate of *K* to initialize the ETF prototypes. This early-stage aggregation helps capture a reliable cluster structure before alignment begins.\n\nTo further investigate the benefits of dynamic class number estimation, we conducted additional experiments on the **CUB** dataset by **re-estimating *K* at different training stages**. \nOur strategy for handling changes in *K* is straightforward: \nif the newly estimated *K* is **smaller** than the previous estimate, we **keep the existing ETF structure unchanged** to avoid disruptive prototype reassignments; \nif the new *K* is **larger**, we **reset the ETF structure** to accommodate additional prototypes for the emerging clusters. \n\nThis design is guided by our findings in Appendix B.4, where we analyze the effect of class number estimation errors. \nWe observe that **underestimating *K*** severely harms the model’s ability to generalize to novel classes, while **overestimating *K*** only introduces redundant prototypes without significantly degrading performance. \nThus, our dynamic re-estimation strategy emphasizes **stability under *K* reduction** and **flexible expansion** when *K* increases.\n\nAs shown in **Table R1**, periodic re-estimation leads to consistent performance gains over fixed strategies. In particular, re-estimating every 50 epochs yields the best result of **74.9%** all-class accuracy, outperforming the fixed-\\(K\\) baseline (epoch 30) by **+4.6%**. While overly frequent re-estimation (e.g., every 20 epochs) introduces instability—especially for novel class alignment—moderate intervals (40–50 epochs) enable the model to adapt to evolving feature structures and improve novel discovery without harming old class retention.\n\nOnce again, we sincerely thank the reviewer for the valuable suggestion, which not only inspired new experiments but also helped **demonstrate the flexibility and robustness of our NC-GCD framework**. Dynamic adaptation to the evolving feature space improves alignment quality and better captures emerging structures, particularly under uncertain or shifting class distributions. We will include these findings in the revised version.\n\n#### **Table R1: Performance with different re-estimation frequencies of \\(K\\). Accuracy (\\%) on the CUB dataset.**\n\n| Re-estimate *K* every| All | Old | New |\n|-|-|-|-|\n| No Re-estimation (20 epochs)    | 68.7 | 70.5 | 67.9 |\n| No Re-estimation (30 epochs)    | 70.3 | 72.1 | 69.4 |\n| No Re-estimation (50 epochs)    | 70.1 | 70.7 | 69.7 |\n| Every 20 epochs     | 65.7 | 72.0 | 61.5 |\n| Every 40 epochs      | 70.7 | **76.5** | 68.4 |\n| Every 50 epochs           | **72.9** | 70.6 | **73.0** |\n\n---\n\n### 🔹Q2: *Some important details (e.g., clustering period \\(T\\)) should be in the main paper.*\n\n**A2:**  Thank you for pointing this out. We agree that certain hyperparameters such as the clustering interval \\(T\\) (set to every 10 epochs by default) are crucial for reproducibility. We will move this detail from the appendix to the main paper in the revised version.\n\n---\n\n### 🔹Q3: *Figures 1 and 2 font size is too small.*\n\n**A3:**  We appreciate the reviewer’s feedback. We will revise Figures 1 and 2 with enlarged fonts and improved resolution to ensure clarity and readability in the camera-ready version."}, {"review_id": "GB8ZgaJPNU", "reviewer": "Reviewer_npmJ", "summary": "This paper tackles inconsistent objectives in Generalized Category Discovery by pre-assigning a fixed Simplex Equiangular Tight Frame (ETF) of prototypes for all classes and aligning both labeled and unlabeled samples to that frame via a unified “ETF alignment” loss. It augments periodic clustering of unlabeled data (unsupervised ETF) with supervised alignment of known-class embeddings and introduces a Semantic Consistency Matcher (SCM) that enforces one-to-one cluster mappings across iterations to stabilize pseudo-labels. Extensive theory (Neural Collapse proofs), hyperparameter studies, ablations, error bars over five seeds, and runtime/parameter efficiency analyses on six benchmarks demonstrate substantial gains, especially in novel-class accuracy, over previous GCD methods.", "questions": "### *Questions*\n- #### Q1 **Adaptive Prototypes.** Could small learnable offsets to ETF prototypes improve fit to non-ideal manifolds?\n\n- #### Q2 What are the advantages of applying ETF over non-Euclidean geometry representation such as hyperbolic representation?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### *Strenghts*\n- #### S1 **Principled Geometry via Neural Collapse.** Pre-assigned ETF prototypes enforce optimal inter-class angles and intra-class compactness. Theoretical grounding justifies the fixed simplex structure for both known and novel classes.\n\n- #### S2 **Unified Supervised / Unsupervised Loss.** A single “Consistent ETF” loss seamlessly blends labeled alignment and high-confidence unlabeled alignment, leading to promising results.\n\n- #### S3 **Thorough Evaluation.** Benchmarks on generic and fine-grained datasets, with GT-K and estimated-K settings, error bars over five seeds. Full pseudocode, hyperparameters, runtime/parameter tables, and feature visualizations provided in the appendix.\n\n### *Weaknesses*\n- #### W1 **Rigid Prototype Structure.** Fixed ETF assumes ideal simplex geometry; real data may require prototype flexibility. No mechanism to adjust or refine prototypes when feature distributions deviate.\n\n- #### W2 **Scalability of SCM's Permutation Search.** SCM’s exact permutation over K clusters might scales poorly as K grows. Approximate or hierarchical matching strategies are not explored for large-scale or streaming discovery.\n\n- #### W3 **Experiment on Other Vision Foundation Model.** All experiments use DINO ViT-B/16. It’s unclear if gains hold with stronger DINO v2, other stronger backbones.\n\n- #### W4 **Typo.** Notation inconsistencies (e.g., undefined qᵢ in Eq. 3), typos in figure 8 & 9 captions (“processs”).", "was_revised": true, "final_justification": "Thank you for the authors' detailed response, the additional experiments, and the clarifications. Based on all of the comments and responses, I find the overall contribution and completeness of the work to be solid (despite a few minor issues). Thus, I'll raise my score.", "rebuttal": "## Response to Reviewer npmJ\n\nWe sincerely thank the reviewer for the thoughtful summary and constructive feedback. We are especially encouraged by your recognition of our theoretical motivation, unified loss design, and extensive empirical evaluation. Below, we address each concern in detail.\n\n---\n\n### 🔹Q1: *Could small learnable offsets to ETF prototypes improve fit to non-ideal manifolds?*\n\n**A1:**  This is an interesting and valuable suggestion. In this work, we adopt fixed ETF prototypes to enforce a consistent and interpretable geometric structure across all classes, aligned with the Neural Collapse theory. While learnable offsets may help better fit data with non-ideal manifolds, they can also break the equiangularity and compromise the interpretability of the prototype space. To explore this, we conducted a pilot experiment where we introduced a learnable offset vector to each prototype while keeping the ETF directions fixed.\n\nAs shown in **Table R1**, this variant slightly underperforms the original NC-GCD method, with an average drop of 1.4% in novel-class accuracy across datasets. We hypothesize that while learnable offsets increase adaptability, they reduce inter-class separability and undermine the benefits of the ETF geometry. We believe this trade-off between adaptability and structural regularity is an important direction for future research. We will include this discussion and findings in our revised version.\n\n#### **Table R1: Comparison of NC-GCD and its variant with learnable prototype offsets. Accuracy (%) on the CUB and Stanford Cars datasets.**\n\n| Method               | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New |\n|----------------------|---------|---------|---------|----------|----------|----------|\n| Learnable Offsets    | 71.2    | 76.0    | 70.9    | 57.1     | 76.2     | 46.3     |\n| **Ours (NC-GCD)**    | **74.8**| **76.8**| **73.8**| **59.9** | **77.8** | **51.2** |\n\n---\n\n### 🔹Q2: *SCM’s exact permutation may scale poorly; consider approximate/hierarchical matching?*\n\n**A2:**  We appreciate the reviewer’s concern regarding scalability. In our current setup, the number of clusters K is fixed per dataset, and all benchmarks involve moderate-to-large class counts—e.g., 683 classes in Herbarium19 and 100 classes in ImageNet-100—where our SCM module runs efficiently without observable latency. As shown in **Table R2**(The original Table 4 in Section 5.3 Ablation Study), SCM consistently improves performance across datasets, validating its practicality for realistic GCD settings.\n\nImportantly, Herbarium19 presents a highly **imbalanced long-tailed distribution**, where many rare categories contain fewer than 10 images while others have hundreds. This makes stable cluster matching particularly challenging. Yet, our SCM yields a notable **+4.5%** all-class accuracy gain on Herbarium19, demonstrating strong robustness under class imbalance and larger-scale taxonomies.\n\nWe fully agree that in streaming GCD scenarios, where *K* evolves over time, exact permutation search may become a computational bottleneck. For such settings, we are actively exploring approximate bipartite matching and hierarchical alignment strategies. Overall, our results indicate that SCM remains both scalable and effective in large-scale and imbalanced offline GCD tasks, while also providing a solid foundation for future streaming extensions.\n\n#### **Table R2: Ablation study of SCM on Herbarium19 (683 classes, long-tailed) and ImageNet-100 (100 classes).**\n| SCM            | Herbarium-All | Herbarium-Old | Herbarium-New | ImageNet-All | ImageNet-Old | ImageNet-New |\n|----------------|----------------|----------------|----------------|----------------|----------------|----------------|\n| ✗ (w/o SCM)    | 42.6           | 54.3           | 36.3           | 84.3           | 88.9           | 82.0           |\n| √  (with SCM)   | **47.2**        | **60.0**        | **40.3**        | **87.6**        | **94.5**        | **84.1**        |\n| *Improvement*  | **+4.5**        | **+5.6**        | **+3.9**        | **+3.3**        | **+5.6**        | **+2.1**        |\n>The original Table 4 in Section 5.3 Ablation Study.\n\n---\n\n### 🔹Q3: *No results with DINOv2 or other vision backbones.*\n\n**A3:**  Thank you for highlighting this point. We have conducted new experiments on the CUB, Stanford Cars, and FGVC Aircraft datasets using both DINOv2 ViT-B/14 and CLIP-ViT/B16 backbones. \n\n- As shown in **Table R3, under DINOv2**, our NC-GCD achieves an average accuracy of **84.0%**, outperforming  RLCD (ICML25) [1] by **+7.1%**.\n\n- As shown in **Table R4, under CLIP-ViT/B16**, our method reaches **73.8%** average accuracy, surpassing CMS (CVPR 2024) by **+9.1%** overall and **+12.0%** on novel classes. \n\nThese results demonstrate the architecture-agnostic nature of our design and its robustness across **DINOv1, DINOv2 and CLIP backbones**. And these results will be included in the revised version to provide a more comprehensive evaluation of our framework across mainstream transformer architectures.\n\n#### **Table R3: Results with DINOv2**\n| Method | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| GCD (CVPR22)| 71.9|71.2| 72.3| 55.4|47.9| 59.7|49.7|47.9|50.5|59.0|55.| 60.8    |\n| μGCD (NIPS23)| 74.6 | 75.0| 74.4 | _60.6_ | _64.7_ | _58.6_   | _60.0_  | _62.0_| _59.0_ | _65.1_  | _67.2_  | _64.0_  |\n| SelEx (ECCV24)| _87.4_  | _85.1_  | _88.5_ | 79.8 | 82.3 | 78.6|82.2      | **93.7**  | 76.7 | _83.1_  | _87.0_  | _81.3_  |\n| RLCD (ICML25)  | 78.7 | 79.5| 78.3 | 79.5 | **91.8**  | 73.5  | 72.6  | 73.3  | 70.3  | 76.9  | 82.9  | 74.0 |\n| **NC-GCD**| **87.9**| **85.3**| **89.2**| **81.1** | 90.9 | **79.3** | **83.1** | 88.3  | **82.5** | **84.0**| **88.2**| **83.7**|\n> All baseline results are collected from the SelEx (ECCV 2024) and RLCD (ICML25) [1], and will be properly cited in the revised version.\n\n#### **Table R4: Results with CLIP**\n| Method  | CUB-All | CUB-Old | CUB-New | Cars-All | Cars-Old | Cars-New | Aircraft-All | Aircraft-Old | Aircraft-New | Avg-All | Avg-Old | Avg-New |\n|-|-|-|-|-|-|-|-|-|-|-|-|-|\n| GCD (CVPR22) | 51.1| 56.2 | 48.6| 62.5     | 73.9     | 57.0     | 41.2          | 43.0          | 40.2          | 51.6    | 57.7    | 48.6    |\n| PromptCAL (CVPR23) | 53.7    | 61.4    | 49.9    | 60.1     | 77.9     | 51.5     | 42.2          | 48.4          | 39.0          | 52.0    | 62.6    | 46.8    |\n| CMS (CVPR24)  | _65.8_  | _75.3_  | _61.4_  | _77.9_   | _89.0_   | _72.6_   | _50.3_        | _59.1_        | _45.9_        | _64.7_  | _74.5_  | _59.9_  |\n| **NC-GCD**  | **78.5**| **79.3**| **78.0**| **79.0** | **90.6** | **73.4** | **63.8**      | **62.8**      | **64.3**      | **73.8**| **77.6**| **71.9**|\n> All baseline results are collected from the CMS (CVPR 2024) appendix, and will be properly cited in the revised version.\n\n---\n\n### 🔹Q4: *Notation inconsistencies (e.g., \\(q_i\\) in Eq. 3), typos in figure captions (e.g., “processs”).*\n\n**A4:**  We thank the reviewer for identifying these issues. We will revise the manuscript to define all symbols (e.g., \\(q_i\\)), correct typos in Figures 8 and 9, and thoroughly proofread the final version for clarity and consistency.\n\n---\n\n### 🔹Q5: *What are the advantages of ETF versus non-Euclidean geometry such as hyperbolic space?*\n\n**A5:** We appreciate the reviewer’s insightful question regarding the choice of geometric representation. Hyperbolic spaces, such as the Poincaré ball model proposed in [2], have been shown to be highly effective for learning **hierarchical or tree-like structures** due to their exponential capacity and ability to preserve hierarchy in low dimensions.\n\nHowever, Generalized Category Discovery (GCD) emphasizes **class separation, compactness, and balanced performance across old and novel classes**, rather than hierarchical organization. In this context, Euclidean-based Equiangular Tight Frame (ETF) prototypes provide several advantages:\n\n- **Analytical Simplicity and Theoretical Alignment**:\nETF structures naturally emerge under **Neural Collapse** conditions and offer a **closed-form, interpretable target geometry** in Euclidean space that promotes maximal inter-class separation and minimal intra-class variance [3]. This structure provides a stable optimization target.\n\n- **Compatibility with Alignment Objectives**:\n  Our Dot Regression Loss aligns directly with ETF directions in Euclidean space, providing consistent and geometry-preserving updates. Since both ETF and DR Loss are naturally defined in Euclidean space, they can be seamlessly integrated into existing GCD neural network architectures without requiring specialized optimization.\n\n  In contrast, hyperbolic representations usually demand Riemannian SGD or Möbius transformations, which complicate training and increase engineering overhead, and they may not align naturally with feature alignment goals in GCD.\n\n- **Empirical Performance and Simplicity**:\n  For classification problems like GCD, ETF-based alignment achieves stable and high performance with a simpler training pipeline, while hyperbolic spaces are more suited to taxonomic or hierarchical tasks.\n\nIn summary, ETF-based geometric alignment offers a theoretically grounded, computationally simple, and empirically validated solution for GCD, providing balanced discovery of both known and novel categories in Euclidean space.\n\n---\n\n### **Reference:**\n- #### [1] Liu, Duo, et al. \"Generalized Category Discovery via Reciprocal Learning and Class-Wise Distribution Regularization.\" In ICML. 2025.\n- #### [2] Nickel, Maximillian, and Douwe Kiela. \"Poincaré embeddings for learning hierarchical representations.\" in NeurIPS,2017.\n- #### [3] Yibo Yang and Timothy M. Hospedales. Do We Really Need a Learnable Classifier at the End of Deep Neural Network? NeurIPS, 2022."}]

Author rebuttal:

Meta-review: This paper initially got mixed scores: two accept, one borderline rejects and two borderline accept. The authors have submitted a rebuttal, and after considering it, all reviewers expressed satisfaction with the responses and updated their scores to acceptance (score 4/5). The AC concurs with the reviewers that this is a solid submission with advantages of strong performance, novel ideas, well-written and unified loss design. Therefore, the AC would like to recommend acceptance to this paper and encourages the authors to incorporate the clarifications and experiments provided in the rebuttal into the final version.
Decision: Accept (poster)