Generalized Category Discovery Utilizing Reciprocal Learning and Class-wise Distribution Regularization

Q3: Experiments with DINOv2 are needed to better demonstrate the advantages of your methods.

A3: Thank you for your valuable comment. Below, we present the GCD performance using the DINOv2 backbone on three representative datasets: CUB200, ImageNet-100, and Stanford Cars. As shown in the table below, our method consistently achieves the best overall performance. Particularly, our method obtains an 8.2% improvement to SimGCD [1] on Stanford Cars dataset. Additional results on other datasets are provided in the revised submission, and our method consistently reaches the best performance.

[1] Wen X, Zhao B, Qi X. Parametric classification for generalized category discovery: A baseline study. ICCV2023.
[2] Wang H, Vaze S, Han K. SPTNet: An efficient alternative framework for generalized category discovery with spatial prompt tuning. ICLR2024.
[3] Hao S, Han K, Wong K Y K. Cipr: An efficient framework with cross-instance positive relations for generalized category discovery. TMLR2024.

Q1: Could you provide an intuitive understanding of $m_k$?

A1: Thanks for your comment. By definition, $m_k$ represents the weighted average of mini-batch distributions, where the weight for each sample is its probability belonging to category $k$. Moreover, the $k$-th probability of $m_k$, denoted as $m(k, k)$, intuitively reflects the confidence that "the mini-batch contains at least one sample belonging to category $k$." The other probability of $m_k$ , $m(k,i),i \neq k$, reflects the affinity between category $i$ and category $k$.

For instance, if the mini-batch does not contain any samples from class $k$, $m_k$ behaves like the average distribution of all samples. Conversely, if the mini-batch includes samples from class $k$, $m_k$ should be close to a one-hot distribution.

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Q2: It seems that the KL loss is similar to the approach by [1], which distills knowledge from a supervised model. Could you offer a more detailed analysis of the differences?

A2: Thank you for highlighting this point. Although both our approach and CRNCD [1] adopt knowledge distillation, our method is fundamentally different from CRNCD. We first provide a detailed analysis of the key differences:

• Different tasks. CRNCD [1] deals with novel class discovery (NCD) problems, where all unlabeled data belong to novel classes. In contrast, our focus is on GCD, where unlabeled data comprises both novel and base class samples. Applying CRNCD to GCD demonstrates unsatisfactory performance in GCD due to the intrinsic task difference, as shown in the following table.

• Different motivations for using distillation. The distillation in CRNCD aims to improve novel class performance, whereas our distillation is intended to promote base class discrimination.

• Different training paradigms. CRNCD adopts a two-stage training procedure that first trains a supervised model and then freezes it in the second stage. Contrarily, our framework is more efficient, which adopts one-stage training in which the main and auxiliary branches help each other simultaneously.

• Different distilled data. While CRNCD employs distillation on all unlabeled data, our approach focuses on the selective data (i.e., pseudo-base data in our submission), which are predicted to the base classes in the main branch. The following additional experiments compare these two approaches and demonstrate that our method is more effective.

• Different distillation weight assignments. CRNCD adopts a learnable weight function to control the distillation strength. Instead, we utilize the maximum auxiliary probability as a determined uncertainty-based weight, which provides a simpler and more effective mechanism for regulating the distillation. This can be seen in the following experiments.

[1] Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.

Thank you for your valuable comments. We are glad to have addressed most of your concerns and would like to provide further discussion on CRNCD.

Q1: Can you provide more details on how you implement crNCD?
A1: CRNCD [1] builds upon the UNO [2] framework, which employs optimal transport to assign labels. However, as pointed out by SimGCD [3], this framework may not generate reliable pseudo-labels in the GCD task. To ensure a fair comparison, we incorporate the distillation function [4] from CRNCD into our parametric baseline. Specifically, we follow a two-step procedure:

1. We first train a supervised model using the supervised loss function $L_{sup}$, where the training data consists solely of labeled samples.
2. We then freeze the supervised model and proceed to train the parametric-based model with a combination of supervised loss, self-supervised loss, and distillation loss:
   $L$ = $\lambda$ $L_{sup}$ + ( 1- $\lambda$)($L_{self}$ - $\epsilon H$） + $\alpha$ $L_{rkd}$,
   where $L_{rkd}$ represents the distillation loss from CRNCD, $\lambda,\epsilon$ are common hyper-parameters in the parametric-based methods, and $\alpha$ controls the strength of the distillation. The distillation is performed on all unlabeled data, and we follow the default distillation hyper-parameters used in CRNCD for consistency.

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Q2: Can you apply the naive distillation loss (w/o reweighting) of crNCD to the SimGCD?
A2: We have applied the naive distillation loss (without reweighting) from CRNCD to SimGCD. To further investigate the effect of distillation, we experiment with two different values for the distillation strength: $\alpha = 0.1$(the default value in CRNCD), and $\alpha = 0.5$. Additionally, we provide results of our distillation method without the CDR loss for comparison. The performance on fine-grained datasets is summarized in the table below, where KD refers to the naive distillation approach.

The results indicate that naive distillation can improve SimGCD performance on the CUB200 and Stanford Cars datasets, with similar performance on Aircraft. Notably, the improvement from KD primarily comes from the base class, with stronger distillation ($\alpha$) leading to higher base class accuracy. However, KD shows limited impact on novel class performance, resulting in degradation on CUB200 and Aircraft. The unbalanced performance suggests a learning bias in the naive distillation. In contrast, our distillation method achieves the best results, with consistent improvements across both base and novel classes.

[1] Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.
[2] Fini E, Sangineto E, Lathuilière S, et al. A unified objective for novel class discovery. ICCV2021.
[3] Wen X, Zhao B, Qi X. Parametric classification for generalized category discovery: A baseline study. ICCV2023.
[4] https://github.com/kleinzcy/Cr-KD-NCD/blob/main/model/losses.py#L38

Q3： I noticed that the contrastive learning loss is applied only to labeled data (Eq. 3). Could you explain the reason for excluding it from unlabeled data?

A3： Thanks for your insightful comment. We apply contrastive learning on only labeled samples for two reasons.

• We found the official implementation of SimGCD applies InfoNCE to all samples in the mini-batch. However, InfoNCE would also push apart same-class features which contradicts the objective of SupCon loss and impairs discrimination.
• By removing self-CL, we observed an improvement in oracle base accuracy, increasing from 83.6% to 84.4% on CIFAR-100.

To make this point clearer, we have included the explanation above in the revised submission.

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Q4: In Eq. 5, is the item $\max \left(\mathbf{p}_{b, i}^{a u x}\right)$ detached during the computation?

A4: Yes. Specifically, our ${L}\_{KL}$ would first freeze the auxiliary probability distribution, ensuring that the gradients do not flow back to the AUX branch. $\max \left(\mathbf{p}_{b, i}^{a u x}\right)$ is naturally detached in the operation. To ensure clarity, we have included this implementation detail in the revision.

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Q5: The method as a whole lacks a distinctive name. It would be beneficial for clarity and reference if the authors could provide a name for their approach.

A5: Thanks for your advice, we prefer to name our method as "RLCD", derived from "Reciprocal Learning and Class-wise Distribution regularization".

Q2:* The reciprocal learning framework bears a resemblance to the approach presented in [1]. In that work, an additional base classifier head is trained with labeled base class data, and the distribution between this base-class classifier and the main classifier is distilled with a weight function (Eq. 8 in [1]) to reduce the impact of noisy unlabeled data learning. While there are differences in details, such as the design of the weight function (specifically, Eq. 5 of this paper versus Eq. 8 in [1]) and the training method of the base classifier, the framework and the final loss function (Eq. 5 in this paper versus Eq. 9 in [1]) are quite similar. A thorough analysis of the necessity of these modifications and a discussion of the novelty claim would strengthen the contribution.

A2: Thanks for your thoughtful comment. We would clarify the fundamental difference between CRNCD [1] and our approach. Besides, Comparative experiments validate the necessity of our design.

• Different motivations for using distillation. The distillation in CRNCD aims to improve novel class performance, whereas our distillation is intended to promote base class discrimination.

• Different training paradigms. CRNCD adopts a two-stage training procedure that first trains a supervised model and then freezes it in the second stage. Contrarily, our framework utilizes an AUX token to enable one-stage training in which the main and auxiliary branches help each other simultaneously. Without the AUX token, the base classifier and full classifier are forced to share the same feature space. This limits the effectiveness of distillation, resulting in a significant performance drop, as shown in the table below.

• Different distilled data. While CRNCD employs distillation on all unlabeled data, our approach focuses on the selective data (i.e., pseudo-base data in our submission), which are predicted to the base classes in the main branch. The following additional experiments compare these two approaches and demonstrate that our method is more effective.

• Different distillation weight assignments. CRNCD adopts a learnable weight function to control the distillation strength. Instead, we utilize the maximum auxiliary probability as a determined uncertainty-based weight, which provides a simpler and more effective mechanism for regulating the distillation. This can be seen in the following experiments.

[1] Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.

Q1： While class-wise distribution regularization serves as an effective regularization term, its motivation is unclear. The authors claim it primarily addresses the learning bias towards base classes caused by RLF and sharpens model predictions. However, CDR is applied to both branches, including the base classifier branch where it affects only the pseudo base classes. This could potentially reinforce the bias towards base classes and is contradictory to the stated motivation. Further clarification and an ablation study focusing on the impact of CDR in each branch would be beneficial. For instance, it would be useful to compare the effects of applying CDR exclusively to the main branch versus its application across both branches.

A1： Thank you for your insightful comment. According to our Theorem 2, CDR aims to implicitly increase prediction confidence. Since each class is treated equally, through expected class-wise distribution, CDR effectively mitigates the base class learning bias. When applied to the auxiliary branch, CDR also benefits base class learning with minimal impact on the novel class performance of the main branch. To further validate the role of CDR, we conduct an ablation study comparing: w/o CDR, CDR on the main branch, and CDR on both branches.

• From the above table, applying CDR exclusively to the main branch effectively mitigates the learning bias and boosts novel class performance.
• When applied to both branches, CDR maintains novel class accuracy on the main branch while slightly improving base class performance. Since the AUX and CLS features exist in separate spaces, applying CDR additionally to the AUX branch does not exacerbate the learning bias toward base classes.

The clarification and ablation study have been included in our revised submission.

Q3: Lacking Deep Reason Analysis: The authors aim to reduce bias in pseudo-labels but don't analyze the root causes deeply, even though they explain the motivation in Section 3.2-whether it's due to weak representations, class maximum regularization in SimGCD, or something else.

A3: Thanks for your constructive suggestion. To address this concern, we have conducted a step-by-step loss analysis of the parametric baseline on CUB200. The baseline consists of three loss components: supervised learning $L_{\text{sup}}$, self-supervised learning $L_{\text{self}}$, and mean entropy regularization $H$. Moreover, we introduce three metrics:

• OB: oracle base class accuracy to evaluate pseudo-label quality.
• N2N: represents the percentage of novel class samples correctly classified as novel.
• B2B: indicates the percentage of base class samples correctly classified as base.

The results are summarized in the table below:

• Firstly, ${L}_{\text{sup}}$ builds a strong discriminative model for base classes as only the base training data is correctly labeled. Since novel classes are unlabeled initially with prototypes randomly initialized, all unlabeled data will be classified as the base, thus leading to 0% N2N and 100% B2B.

• Additionally, adding ${L}\_{\text{self}}$ still results in all unlabeled novel data being misclassified. Due to the absence of annotations for novel data, the novel class probability is rather low. Moreover, ${L}_{\text{self}}$ adopts a shrink-soft probability distillation mechanism, which essentially increases the incorrect confidence of novel data. Training with noisy labels on novel samples degrades the model’s representation, causing a decline in OB (86.7->85.6) performance.

• Furthermore, incorporating $H$ encourages the model to make more uniform predictions across classes, resulting in a higher proportion of unlabeled data being classified as novel. This leads to an increase in N2N (0->93.1) but a decrease in B2B (100->69.8). Furthermore, the self-distillation of $L_{\text{self}}$ would amplify the impact of these misclassifications, exacerbating noisy label learning and further degrading OB (85.6->83.9) performance.

• To summarize, the above results indicate that both $L_{\text{self}}$ and $H$ contribute to unreliably pseudo-labels. This motivates us to introduce a more robust base-class expert to mitigate the noisy base labels and enhance discrimination.

The above discussion is included in the revised submission.

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Q4: Confusing Sentence: What is the meaning of K in line 234: ‘K is the number of base and novel classes, while K denotes the number of base classes in the auxiliary branch’

A4: Thank you for pointing out this. To clarify, the CDR is applied to both branches. In the main branch, $K$ represents the total number of classes ( base + novel). While in the auxiliary branch, $K$ specifically denotes the number of base classes. To avoid further confusion, we have revised the paper to distinguish between these two meanings by using $K^{main}$ and $K^{aux}$ in the updated version.

Q1: Missing Relevant Works: The paper overlooks key recent works like CMS and InfoSieve.

A1: Thank you for pointing this out. We have now incorporated CMS [1] and InfoSieve [2] into the related works section and included their results in Tables 1 and 2 of the revised manuscript. The results show that our method consistently outperforms both CMS and InfoSieve across all seven datasets.

It's worth noting that InfoSieve achieves close performance to our approach on CUB200. Actually, InfoSieve fine-tunes the last two blocks of the backbone for fine-grained datasets, whereas our approach only fine-tunes the last block. When we adopt the same fine-tuning paradigm as InfoSieve, our method achieves further improvements.

[1] Choi S, Kang D, Cho M. Contrastive mean-shift learning for generalized category discovery. CVPR2024.
[2] Rastegar S, Doughty H, Snoek C. Learn to categorize or categorize to learn? self-coding for generalized category discovery. NeurIPS2023.

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Q2: Missing Self-Contrastive Learning (CL): SimGCD also uses self-CL in representation learning.

A2: Thank you for your detailed observation. While it is true that SimGCD incorporates self-CL in representation learning, we would like to clarify that our method does not utilize self-CL.

This design was made because the InfoNCE loss in SimGCD tends to push same-class features apart, which can harm the discrimination of the base classes. By removing self-CL, we observed an improvement in oracle base accuracy, increasing from 83.6% to 84.4% on CIFAR-100. To make this point clearer, we have included the explanation above in the revised submission.

Thank you once again for your valuable time and effort in reviewing our work and considering our rebuttal. We are glad to address your main concerns and remain open to further discussion regarding $H$.

First, we would like to clarify the relationship between $H$ and $L_{self}$.

• $H$ is dependent on $L_{self}$. While $H$ encourages more predicted novel class samples, its impact is minimal when $L_{self}$ is removed. As shown in the table below, without $L_{self}$, the model suffers a significant N2N drop from 93.1% to 18.8%. $L_{self}$ essentially increases prediction confidence, which facilitates novel class prototype learning and attracts more novel class samples. In this way, our approach refines the pseudo-label quality, which directly enhances $L_{self}$ and indirectly influences $H$.

To further investigate the effect of $H$, we introduce class-wise prediction distribution (CPD) and show the result on CUB200. CPD provides a detailed view of how the model assigns predictions to each class. In particular, we use the Root Mean Squared Error (RMSE) to quantify the deviation between the CPD and the ground truth distribution, with smaller RMSE values indicating better results. The results are summarized in the table below:

• $H$ steers CPD toward the ground truth. When $H$ is removed, all unlabeled data are classified as base classes, resulting in a large RMSE in both base and novel CPDs: 45.87 and 29.97, respectively. Incorporating $H$ encourages more diverse predictions and induces more predicted novel samples. Therefore, $H$ effectively reduces the RMSE: 45.87 -> 3.24 for base classes, and 29.97 -> 12.19 for novel classes.

• Our approach compensates $H$ for better base performance. Actually, $H$ leads to misclassification of some base class samples, and the total predicted number of base samples is lower than the ground truth (1346 vs. 1499). To mitigate this, our method introduces cross-branch distillation during training, which helps reduce the misclassification. As a result, our predicted base number is closer to the ground truth number (1480 vs. 1499). Moreover, our method achieves a lower RMSE than the baseline: 3.24 -> 1.76 for base classes, and 12.19 -> 8.21 for novel classes.

While $H$ may hinder base class discrimination, it provides a simple and efficient way to improve novel class recognition. Therefore, our motivation is to mitigate the negative impact of $H$ and leverage its strengths to enhance novel class recognition. This detailed discussion and the experiments have been included in the revised submission (see Appendix A.11). Once again, thanks for your insightful suggestion.

Thanks for your thoughtful comment. We have corrected the book quotation and reviewed the manuscript to prevent similar issues. Besides, we have revised the loss analysis in Table R1 to include the influence between $\mathcal{L}_{\text{self}}$ and $H$ in Lines 227-232 as follows：

The combination of $\mathcal{L}\_{\text{sup}}$ and $H$ increases novel class prediction, slightly improving N2N but causing a decline in OB. This decline occurs because $H$ encourages a balanced average prediction. When all three losses are applied, the model predicts more novel class samples, leading to 93.1% N2N. This is because $\mathcal{L}\_{\text{self}}$ increases the novel class confidence, facilitating novel class prototype learning. However, $H$ simultaneously drives the misclassification of some base samples, while $\mathcal{L}\_{\text{self}}$ amplifies incorrect novel confidence, further deteriorating the pseudo-label quality. These findings suggest that both $\mathcal{L}\_{\text{self}}$ and $H$ contribute to unreliable pseudo-labels.

Furthermore, we have modified our motivation in Lines 233–235 as follows:

Besides, $\mathcal{L}\_{\text{self}}$ is particularly susceptive to $H$ and exacerbates noisy learning. This motivates us to introduce a more robust base-class expert to assist $\mathcal{L}\_{\text{self}}$. By providing more reliable base labels, this intervention aims to enhance discrimination and mitigate the side effects of $H$.

The revised version has been updated. We sincerely appreciate your valuable feedback, which has helped us improve the clarity and rigor of our work.

Q10: The paper's presentation needs improvement. Some terminologies are used without proper explanation, for example: ln 052: "base prediction of base unlabeled data". ln 072: "pseudo-base samples" ln 199: "concentrating it with CLS ..."? Theorem 2. "converges to zero": should be “equals to".

A10: Thank you for your insightful feedback. We truly appreciate your attention to detail. Based on your comments, we have carefully revised the relevant sections in the updated version of our manuscript to improve clarity and accuracy.

Q8: Is AUX component necessary for the method? It would be interesting to show the ablation results for the full model minus each component.

A8: Thanks for your valuable comments. In fact, AUX is indispensable in our method. Below, we give a detailed statement about AUX and provide additional ablation results:

• AUX Creates a complementary feature space. The AUX component is crucial to our framework as it establishes an independent feature space that complements the main CLS branch. This design enables AUX to enhance base performance through the distillation loss, completing the one-stage reciprocal learning.

• Removing AUX leads to a significant decrease in performance. We also quantitatively validate the necessity of AUX by temporarily removing this component. When AUX is removed, the base and full classifiers are forced to share the same feature space. This shared space results in a significant performance drop, as shown in the table below. The metric OB in the table denotes oracle base class accuracy to evaluate pseudo-label quality.

• Additional ablations of each component. To provide a comprehensive analysis, we have extended the ablation experiment in Table 3 of the submission to include the impact of removing each component from the full model. These results clearly highlight the importance of each component, including AUX, Distill, and CDR. Both AUX and Distill contribute to improved base performance and CDR effectively enhances novel performance.

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Q9: It would be more convincing to include the full results on 7 datasets for the analysis of different regularizations (ln 426) and estimated class numbers (ln 454).

A9: Thanks for your thoughtful suggestion. We have extended the analysis experiment of different regularizations and estimated class numbers on other datasets.

For comparing to different regularizations, we are here to report the main result of "All accuracy", and the detailed performance can be found in the updated submission. Note that, PDR is the modification of CDR, denoting pair-wise class-distribution regularization.

In addition, we also provide extra experiments on the estimated class numbers. Since GCP accurately estimates the category number for CIFAR100 and CIFAR10, we show the comparison result under CMS [5] estimation.

From the above results, our CDR consistently outperforms other regularization methods on various datasets. Additionally, our approach performs better than CMS when dealing with estimated class numbers.

[1] Yves Grandvalet and Yoshua Bengio. Semi-supervised learning by entropy minimization. NeurIPS2004.
[2] Jin Y, Wang X, Long M, et al. Minimum class confusion for versatile domain adaptation. ECCV2020.
[3] Cui S, Wang S, Zhuo J, et al. Towards discriminability and diversity: Batch nuclear-norm maximization under label insufficient situations. CVPR2020.
[4] YZhang Y, Yao Y, Chen S, et al. Rethinking guidance information to utilize unlabeled samples: A label encoding perspective. ICML2024.
[5] Choi S, Kang D, Cho M. Contrastive mean-Shift learning for generalized category discovery. CVPR2024.

Q6: The claim of this work on enhancing base classification is not well supported by the results in Table 1&2, where the base class performances are much lower than previous methods in several cases.

A6: Thanks for your valuable feedback.

First, we would like to clarify that our method achieves superior base accuracy compared to other parametric-based methods, such as SimGCD [1] and LegoGCD [2]. In these cases, the results align with our motivation. Besides, our approach also achieves leading oracle base class performance shown in Figure 1 and Appendix A.5.

Second, while our base class accuracy may lag behind a few methods belonging to other taxonomies, we attribute this to the essential limitation of parametric-based methods, whose losses include entropy mean regularization. Concretely, this regularization encourages diverse prediction, and thus partial base class data would be misclassified as the novel [2]. Methods like GPC [3] and UNO [4], which are not parametric-based methods, avoid such regularization, and naturally exhibit higher base accuracy but often sacrifice novel performance.

Furthermore, the reported base accuracy is adjusted by the Hungarian algorithm [5], and is not directly equivalent to the true base accuracy. For instance, while SPTNet [6] shows a higher reported base accuracy (79.2% vs. 76.6%), the true base accuracy is similar (81.4% vs. 82.1%), based on results reproduced from SPTNet's official checkpoint [7].

The above discussion has been added to our revision to better support the motivation of this work.

[1] Wen X, Zhao B, Qi X. Parametric classification for generalized category discovery: A baseline study. ICCV2023.
[2] Cao X, Zheng X, Wang G, et al. Solving the catastrophic forgetting problem in generalized category discovery. CVPR2024.
[3] Zhao B, Wen X, Han K. Learning semi-supervised gaussian mixture models for generalized category discovery. ICCV2023.
[4] Fini E, Sangineto E, Lathuilière S, et al. A unified objective for novel class discovery. ICCV2021.
[5] Kuhn H W. The Hungarian method for the assignment problem. Naval research logistics quarterly, 1955.
[6] Wang H, Vaze S, Han K. SPTNet: An efficient alternative framework for generalized category discovery with spatial prompt tuning.
[7] https://github.com/Visual-AI/SPTNet

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Q7: The visualization in 4.3 is not very informative as it only includes baseline methods. It should compare with the SOTA methods.

A7: Thanks for your thoughtful comment. To present a more informative visualization, we add the most recent work LegoGCD [1] (CVPR 2024) as a comparison and our approach still performs the best clustering visualization result. Please refer to Figure 4 in the revised submission.

In brief, the t-SNE for pre-trained DINO [2] shows random clustering results, primarily due to the significant domain gap between the ImageNet and Aircraft datasets. Meanwhile, both LegoGCD [1] and SimGCD [3] exhibit unsatisfactory feature clustering. Specifically, some intra-class features of SimGCD are spread out in the feature space, while LegoGCD forms two separate clusters for a single class. In contrast, our model reveals distinct clusters corresponding to different categories. The visualization comparison validates the superior feature representation of our model.

[1] Cao X, Zheng X, Wang G, et al. Solving the catastrophic forgetting problem in generalized category discovery. CVPR2024.
[2] Caron M, Touvron H, Misra I, et al. Emerging properties in self-supervised vision transformers. ICCV2021.
[3] Wen X, Zhao B, Qi X. Parametric classification for generalized category discovery: A baseline study. ICCV2023.

Q4: There are many hyper-parameters in this method and it is unclear how they are tuned.

A4: Thanks for pointing this out. First of all, we would like to clarify that most of the hyper-parameters are simply adopted from previous works, such as $\lambda = 0.35$, $\epsilon = 2.0$, while our method only introduces two additional hyper-parameters: $\alpha$ and $\beta$.

For those hyper-parameters adopted from previous works, we follow the same configuration in their original papers (i.e., SimGCD [1] and LegoGCD [2]) as reasonable default choices. We also validate these hyper-parameters and they indeed achieve the optimal result, which is consistent with existing works.

• Specifically, the balancing weight $\lambda \in [0, 1]$, and the default $\lambda = 0.35$. The ablation study results on CUB200 are as follows:

• Hyper-parameter $\epsilon$ is used for weighting mean-entropy regularization ($H$), and the default value is set to $2$ on CUB200. The ablation results are as follows:

For the two new hyper-parameters $\alpha$ and $\beta$, where $\alpha$ adjusts distillation strength and $\beta$ controls regularization strength, we conduct experiments in our submission to analyze the effect of these two hyper-parameters $\alpha$ and $\beta$.

• The results have been shown in Figure 5 of our submission, indicating that they are not sensitive to the final performance. Based on the above observations, we choose to use the value of $0.5$ for both $\alpha$ and $\beta$.

[1] Wen X, Zhao B, Qi X. Parametric classification for generalized category discovery: A baseline study. ICCV2023.
[2] Cao X, Zheng X, Wang G, et al. Solving the catastrophic forgetting problem in generalized category discovery. CVPR2024.

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Q5： The baselines are insufficient. A baseline derived from NCD (Gu et al., ICCV 2023) should be included to validate the design of the AUX token.

Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.

A5： Thanks for your constructive suggestion. Since CRNCD (Gu et al., ICCV 2023) is tailored for the NCD task, it cannot directly apply to the GCD task considered in our paper. To this end, we have incorporated the core idea of CRNCD into the GCD task and included the reproduced results in Tables 1 and 2 in our revised submission. Below we provide a sketch result (please see full results in our revision):

The table above shows the overall accuracy comparison across seven GCD datasets between CRNCD and our method. The result demonstrates that CRNCD is unsuitable in GCD, consistently underperforming compared to our method across all datasets. Notably, our method outperforms CRNCD by 7.0% on Stanford cars dataset and achieves an average improvement of 4.7% on 7 datasets.

Q2: Moreover, the class-wise distribution regularization technique is similar to Zhang et al. (ICML 2024), which includes several properties, such as Theorem 1 in this work. While this work integrates those ingredients into SimGCD, the overall contribution seems rather limited.

Yulong Zhang, Yuan Yao, Shuhao Chen, Pengrong Jin, Yu Zhang, Jian Jin, and Jiangang Lu. Rethinking guidance information to utilize unlabeled samples: A label encoding perspective. ICML2024.

A2: Thanks for your comments. In fact, we have already made some comparisons with LERM loss (Zhang et al., ICML 2024) in our original submission (see Table 4). To better address your concern and reflect our contributions, we would like to provide some further comparisons with LERM paper as follows:

• Different loss functions. LERM simply computes class-wise expected distribution $m_k$ for class $k$ using one view of mini-batch images and then explicitly enforces a one-hot distribution constraint on $m_k$ i.e. $m_k = e_k$ where $e_k$ is the unit vector. In contrast, our method first computes $m_k$ and $m_k'$ for view 1 and view 2, respectively. Then the proposed CDR drives $m_k$ and $m_k'$ to become similar, implicitly guiding $m_k$ toward a one-hot distribution. Moreover, LERM overlooks the inter-class relationship, and the explicit regularization often leads to overconfidence. To solve this issue, our CDR leverages probability consistency to implicitly increase prediction confidence. Therefore, LERM and our method employ fundamentally different regularization mechanisms.

• Significant improvement. Due to the above advantages of our method, Table 4 confirms that our CDR outperforms LERM significantly. Specifically, our CDR loss achieves an accuracy improvement of 2.3% on CIFAR100, from 80.5% (LERM) to 82.8% (CDR).

• Theorem 1 is not our contribution, but Theorem 2 is. While Theorem 1 holds both for LERM and our CDR, we do not regard Theorem 1 as our contribution (as we have provided its reference in the paragraph above Theorem 1 in our original submission). In fact, it serves as a precondition for our Theorem 2, which represents the fundamental insight of our method. We have added a clear citation beside the Theorem 1 in our revision.

In addition, we would like to emphasize again that our key novelty stems from the efficient one-stage distillation framework and the refined class-specific distribution regularization.

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Q3: The discussion of the related work is insufficient. Section 2 simply lists previous methods without proper comparisons to the proposed strategy.

A3: Thanks for your constructive suggestions. In our latest revised submission, we have added the two related papers mentioned in A1 and A2, along with the corresponding discussions in Section 2 as follows:

• Prevailing semi-supervised learning methods assume that unlabeled data belong to known classes and widely adopt threshold-based pseudo-label learning during training. However, this mechanism faces significant limitations when unlabeled data include unknown class samples.
• Current SOTA NCD methods are primarily built on the UNO [1] framework and they assume all unlabeled data belong to novel classes. Besides, these methods often utilize the Optimal-Transport (OT) algorithm to dynamically cluster unlabeled data. However, OT achieves unsatisfactory novel class performance when unlabeled data involves known class samples. Consequently, current NCD methods are unsuitable for the GCD task. Moreover, CRNCD [2] introduces a two-stage class-relationship distillation approach to improve novel-class performance. However, we observe that this distillation shows inferior performance on GCD. Unlike CRNCD [2], we propose a novel one-stage distillation method tailored for GCD.
• While parametric-based methods achieve great GCD performance, they often suffer degraded base discrimination. To address this issue, we propose a Reciprocal Learning Framework (RLF) that introduces an auxiliary branch specialized in base classification. RLF provides more reliable base pseudo-labels and effectively strengthens base performance with negligible extra computation cost. Combined with class-wise distribution regularization, our method achieves superior performance than SOTA GCD methods.

[1] Fini E, Sangineto E, Lathuilière S, et al. A unified objective for novel class discovery. ICCV2021.
[2] Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.

Q1: The novelty of this work is limited. The idea of distilling known-class knowledge to improve class discovery has been explored in Gu et al (ICCV 2023), which uses a separate branch for base/known classes.

Gu P, Zhang C, Xu R, et al. Class-relation knowledge distillation for novel class discovery. ICCV2023.

A1: Thanks for bringing this paper to our attention. In fact, there are several key differences between our method and CRNCD (Gu et al., ICCV 2023), listed below.

• Different tasks. CRNCD aims to deal with novel class discovery (NCD), where all unlabeled data belong to novel classes. In contrast, our focus is on generalized category discovery (GCD), where unlabeled data comprises both novel and base classes. These two tasks are fundamentally different. Due to the intrinsic difference between these two tasks, CRNCD demonstrates unsatisfactory performance in GCD (see A5).

• Different motivations for using distillation. The distillation in CRNCD aims to improve novel class performance, whereas our distillation is intended to promote base class discrimination.

• Different training paradigms. CRNCD adopts a two-stage training procedure that first trains a supervised model and then freezes it in the second stage. Contrarily, our framework is more efficient, which adopts one-stage training in which the main and auxiliary branches help each other simultaneously.

• Different distilled data. While CRNCD employs distillation on all unlabeled data, our approach focuses on the selective data (i.e., pseudo-base data in our submission), which are predicted to the base classes in the main branch. The following additional experiments compare these two approaches and demonstrate that our method is more effective.

• Different distillation weight assignments. CRNCD adopts a learnable weight function to control the distillation strength. Instead, we utilize the maximum auxiliary probability as a determined uncertainty-based weight, which provides a simpler and more effective mechanism for regulating the distillation. This can be seen in the following experiments.

Besides the above differences, we would also like to highlight our contribution where we innovate an AUX token to facilitate one-stage distillation. The AUX token establishes a new feature space and effectively strengthens base discrimination with negligible extra computation.