In this paper, we make a bold attempt toward an ambitious task: given a pre-trained classifier, we aim to reconstruct an image generator, without relying on any data samples. From a black-box perspective, this challenge seems intractable, since it inevitably involves identifying the inverse function for a classifier, which is, by nature, an information extraction process. As such, we resort to leveraging the knowledge encapsulated within the parameters of the neural network. Grounded on the theory of Maximum-Margin Bias of gradient descent, we propose a novel learning paradigm, in which the generator is trained to ensure that the convergence conditions of the network parameters are satisfied over the generated distribution of the samples. Empirical validation from various image generation tasks substantiates the efficacy of our strategy.
Paper
Similar papers
Peer review
Summary
This paper tackles the problem of reconstructing an image generator, without relying on any data. The authors propose a learning paradigm in which the generator is trained to ensure that the convergence conditions of the network parameters are satisfied over the generated distribution of the samples.
Strengths
1. The paper addresses an important and challenging problem. 2. The method appears to be novel.
Weaknesses
1. The evaluation seems to be weak. the authors have performed the qualitative evaluation alone. The experimental section seems to be incomplete without quantitative evaluation using metrics such as precision, recall, and FID. 2. Related works on Data free knowledge distillation are missing.
Questions
1. Why does the generator generate realistic-looking samples even though it could cheat by learning to generate adversarial examples? 2. Are there any experimental validations/theoretical justifications to confirm if the model is not just reconstructing the training data examples? 3. Can the generator capture all the modes of the training data distribution sufficiently well?
Rating
7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
Confidence
2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness
2 fair
Presentation
2 fair
Contribution
3 good
Limitations
The authors haven't discussed the potential negative social impact of their work, in particular, these methods could be used to recover the training data which may cause privacy concerns.
Summary
This paper addresses a novel and intriguing issue, namely, training a generator reliant on a pre-trained classifier, rather than extensive training data. The authors propose an innovative solution, fundamentally aimed at enabling the generator's training process to continuously extract and leverage information about the dataset distribution from the classifier's parameters. Based on the theory of Maximum-Margin Bias of gradient descent, the authors design stationarity loss and duality loss to ensure that the distribution of data generated by the trained generator guarantee the optimality of the pre-trained classifier. As an expansion, the paper also proposes an algorithm to collectively train a generator using information from multiple pre-trained classifiers. The proposed learning paradigm is empirically validated through experiments in various image generation tasks.
Strengths
This paper investigates an intriguing and innovative task: training a generator using information from the parameters of pre-trained classifiers, rather than relying on training data. Given the vast number of pre-trained models our community has accumulated, I view this as a task of substantial value with potential impact. The paper clearly outlines its motivation and problem definition, and offers a technically sound and concrete method, underpinned by the theory of Maximum-Margin Bias of gradient descent. The paper processes a clear logical structure and reasonable organization. The proposed method and the technical details is validated through several convincing proof-of-concept experiments, as shown in Fig. 3, 4 and 5. The experiments across multiple image generation tasks exhibit promising results.
Weaknesses
Considering that this is a new attempt in this task, the experimental setup is understandably simple. Both the generator and classifier architecture utilized are elementary compared to the practice today. Besides this, I have some minor comments, which I have listed as questions below.
Questions
1. Ln 226 mentions that the construction of the system of equations depends on certain random samples. Are these random samples drawn from the original training dataset? If the solution for \Lambda relies on samples from the training dataset, does it imply that the method proposed in the paper intrinsically presumes \Lambda to be known? 2. The dataset used for training the classifier in the paper is relatively small, consisting of only 500 samples. What is the reasoning behind this setup? How would increasing the size of the training dataset impact the results? 3. Typo a. Ln. 241, the set of classifiers is missing {}
Rating
8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness
4 excellent
Presentation
3 good
Contribution
3 good
Limitations
Owing to the theory of Maximum-Margin Bias, the proposed method has limitations regarding the architecture of the pre-trained classifier and the pre-computation of \Lambda. However, the authors have adequately addressed these challenges. The paper also points out potential privacy risks that may arise from the application of the proposed method, as well as outlining some potential applications.
Summary
The paper propose a method to generate image samples from a trained neural classifier. It proposes a loss to train an image generator where the loss is based on recent results from the realm of the implicit bias of gradient descent of quasi-homogenous functions. It shows empirical results on 2D data and on models trained on MNIST and CELEBA datasets.
Strengths
- Extension of reconstruction to quasi-homogenous neural networks - Trying to create a generator by using a fixed prior on top of the reconstruction scheme
Weaknesses
I think that the main weakness is the novelty in the paper. The proposed paper seems like an extension of Haim et al. 2022 to multiclass quasi-homogenous network, using a "generative" prior. However: - Note that a multiclass extension to Haim et al was done in Buzaglo et al. 2023 ICLR workshops (https://openreview.net/forum?id=SBstNm4OajH), which is somewhat concurrent). - the extension of the reconstructoin loss to quasi-homogenous networks is very slim - technically speaking, the only difference is the introduction of $\Lambda$ in the loss. If this is truly necessary it should be supported by some comparisons to Haim et al. which also showed results on non-homogenous networks. Such comparisons are not provided in the paper. - The generative prior is interesting, but there is no evaluation in the paper for a generative model. All in all, the results are quite similar to those of Haim et al. only it seems that they were not fully converged (what is the difference between a "bad" reconstruction and a "generated sample"?) The paper is poorly written - terminology is cumbersome and hard to follow, which makes it difficult to understand key components of the paper. Many important technical details are missing from the paper. Some comments in introduction and related section are unclear or irrelevant.
Questions
Evaluation is lacking: - the main claim of the paper is the proposed generator that is being born from a classifier. But there are no evaluation whatsoever of generative models. Many common metrics for evaluating generative models exists like FID or IS (for GM that models a classified datasets), but non of these are provided. - There are only very few visual examples in the paper, and no further analysis - The method proposes creating a generative model - what is the point in comparing the outputs of the model to their nearest neighbors (Fig. 6,7,8)? (there are established methods for evaluating generative models, see above) - No comparison to baselines: basically, the results look like a lesser version of the Haim et al. results. What happens if the paper uses Haim et al. reconstruction loss on their trained models? The only concern may be of the multiclass models - such an extension is shown in Buzaglo et al. 2023, which is somewhat concurrent to this submission. However, the current submission can show a comparison of their proposed method to that of Haim et al. only on binary classifiers. - Some other baselines could be other works that try to "turn" a classifier to generator: 1) Use Classifier as Generator, Li 2022 2) Traditional Classification Neural Networks are Good Generators: They are Competitive with DDPMs and GANs, Wang and Torr, 2022 Paper is poorly written. Main parts of the paper are difficult to follow and understand: - The main contribution in the paper is the training of a generator (as assumed from the title). However, the discussion of the generator itself is somewhat hidden in lines 185-186. It took me a while to figure out that this is the so called generator that the paper discusses. I suggest emphasising this element much more. - the discussion of determininig $\Lambda$ (in lines 209-229) - I can't say that I understood the derivation. why is $\Lambda' = \frac{1}{1-\Lambda_{ii}}\Lambda$? I could not understand the two properties. I also did not understand the plot showni in Fig. 3 - discussion in lines 201-205 - why is this network h and ReLU is necessary? this part is very cryptic and not clear (not the mechanism itself, nor the motivation or intuition behind this design choice). - What is the difference between Eq. (7) and Eq. (12) - it seems like the exact same equation - Why is the extension to multiple classifiers (lines 239seqq.) necessary? what is the motivation for that? I also could not understand the mechanism in this paragraph. Many important technical details are missing from the paper: - what is the architectures of the trained models? said to be quasi-homogenous - what is the architecture of the generator g? - what is the architecture of the network h? (in line 202) Some comments in introduction and related section are unclear or irrelevant: - "training process does not rely on any training data" (line 44 and 56) is a bit misleading - it relies on the data on which the classifier was trained. (also it seems from eq.4 that the number of training samples N is assumed to be known). - "GAN require an additional classifier" (line 71) - what is the meaning here? unconditional GANs do not require additional classifiers - "the classifier is trained concurrently with the generator" (line 73) - is this referring to the discriminator? because this is not the classifiers in the sense that are used in the paper. The current paper submission discuss "usual" classifiers (that solve the classification problem of a supervised classification dataset) and discriminators are classifying between true and fake samples. - References in line 85 - "model inversion... given the output and the trained model" - Yin et al. 2020 do not assume the outputs but rather infer training samples from the trained batchnorm statistics. Gal et al. 2022 is really irrelevant here (textual "inversion" tries to find a token in the input of the text encoder that corresponds to a given set of images. It has nothing to do with training samples reconstruction). Minor: - line 207 and supplementary 68 - L_{lagrange} should be L_{stationarity}?
Rating
3: Reject: For instance, a paper with technical flaws, weak evaluation, inadequate reproducibility and incompletely addressed ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness
2 fair
Presentation
1 poor
Contribution
1 poor
Limitations
n/a
Summary
The work extends the dataset reconstruction (DR) method [1] of reconstructing the dataset from a classifier to the generative scenario. It provides several extensions to it: - Instead of reconstructing particular data points, it aims to build a generator for the original dataset. - Extends to the multi-class setting (from a binary classifier). - Moves from homogeneous to $\Lambda$-quasi-homogenous assumptions for the NN classifier. The method is tested on MNIST and CelebA and is able to generate samples which resemble the real ones. [1] Haim et al. "Reconstructing Training Data from Trained Neural Networks"
Strengths
- The overall idea of obtaining a generator from a classifier is very interesting and potentially very influential. - The work is genuine and open about its strengths and limitations. It feels like one of the rare works which is "what you see is what you get". - The method is quite novel and shows some promise to be working. I guess, the current ideas might be extendable to GAN training (or at least Auxilliary Classifier GAN training). - The source code was provided, which should improve the reproducibility. - Table 1 with the notations in the appendix was quite helpful.
Weaknesses
- The paper is not self-sufficient and not possible to understand without reading the DR paper [1] first (at least, I failed to). It lacks intuitive exposition for the general audience who do not have vast background on the related work. Also, there are some confusing formulations on their own — e.g., Eq 5 and 6 define the loss term over $\theta$ and $\eta$, but they do not explicitly appear in the equation itself (only implicitly through $x_i$). And at the same, $x_i$ is not uniquely defined — it denotes both real and fake data. Also, sometimes it appears in bold (L123), and sometimes in normal font (e.g., Eq 1b). Also, Equation 12 is more or less a tautological repetition of Equation 7. - The experimental results do not seem to be strong. E.g., checking the images in Figure 1b, they are hardly recognizable. While for [1], some restored images look quite reasonable, even considering it's CIFAR10 (a more difficult dataset than CelebA). - There should be a comparison with standard approaches of generating samples from a classifier (e.g., DeepDream or DeepDream from an adversarially robust classifier [3]). After checking some random DeepDream implementation on github [2] (probably untuned), it's hard to tell which samples are really better. - Limitations are not discussed Typos: - L181: "objective, We" => "objective, we" - L234: "during the training" => "during training" [2] https://github.com/ianscottknight/deep-dream-implementation-on-mnist-using-pytorch-hooks/blob/main/1.0-deep-dream.ipynb [3] https://arxiv.org/abs/1906.09453
Questions
My two biggest concerns are the writing quality and the scalability of the method, but I'm unsure how they could be addressed during the short rebuttal period. Another interesting direction would be exploring adversarially robust classifiers [3] (I guess, adversarially robust training should prevent the landscape from covering spurious minima and hence help the generation quality).
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness
3 good
Presentation
1 poor
Contribution
3 good
Limitations
Limitations are not discussed at all.
Response to the rebuttal
I am thankful to the reviewers for providing the rebuttal, clarifications and additional results. I decided to increase my rating to "Weak accept", because I find this submission to be quite novel and non-mainstream, and believe that NeurIPS should be welcoming to the works with unusual ideas even they are not tuned well. My two remaining concerns are: - The quality is not good enough and for some people might look like negative results. You can consider applying the technique on top of existing image generators pre-trained for a different objective to show nicer images (note: please, do not treat it a request for additional experiments, I'm just thinking out load). - In its current form, the paper will be a tough read for the image generation community. Since the results are not striking, people will not invest effort into trying to understand such a difficult work. I increased the rating hoping that this will be improved in the revised version.
Response to Reviewer gUqt
We truly appreciate the reviewer for the recognition of our paper and for the valuable feedback. We will incorporate the suggestions and comments the reviewer provided in the “official review” and “response to the rebuttal” to enhance our manuscript, improve its readability, offer a more intuitive background introduction, elucidate our methodology further, and enrich our experimental results.
Thanks for the detailed response. [Are there any experimental validations/theoretical justifications to confirm if the model is not just reconstructing the training data examples?] The attribute editing experiment seems to be quite insightful. A quantitative evaluation would also be quite helpful in this aspect. Regarding performance From the table 1, it seems that quality of the generated images is inferior to that of Li, 2022. I assume the advantage would be then only be then with respect to complexity. Am I correct? Apart from these, the authors have clarified all my concerns. Feedback on these additional points would be appreciated.
Response to Reviewer LZcP
### **Are there any experimental validations/theoretical justifications to confirm if the model is not just reconstructing the training data examples?** #### **Quantitative Evaluation** We appreciate the reviewer's question. To quantitatively assess whether our method can generate images distinct from the training data, we measured the mean-max Structural Similarity Index (mean-max-SSIM). The computation for this metric is as follows: (1) For one generated image, we measure its SSIM against every image in the classifier's training dataset and select the maximum SSIM. This step measures the similarity between the generated image and the most similar image from the training set. (2) For a set of generated images, we perform step (1) for each generated image and then average the resulting max-SSIM values to obtain the mean-max-SSIM. A lower mean-max-SSIM indicates that the generated images, even when compared to their closest counterparts in the training set, are relatively distinct, suggesting the generation of novel data outside the original dataset. We compared our method with Haim et al., 2022, which is designed for reconstructing the training dataset. The FID scores of our method and Haim et al., 2022 are comparable, which are shown in Tab. 1 in the attached PDF file. However, our method exhibits a lower mean-max-SSIM, indicating its capability to produce novel images distinct from the original dataset. | | **Ours** | **Haim et al.,2022** | | :-: | :-: | :-: | | mmSSIM | 0.012±3e-4 | 0.020±1e-4 | ### **Comparison with Li, 2022** We thank the reviewer for the question. To clarify further, our approach differs from Li, 2022 mainly in two aspects. Besides the complexity aspect the reviewer mentioned, the other distinction is that Li, 2022 necessitates prior information from the original dataset to guide image generation. By contrast, our method operates without this information. Specifically, Li, 2022 requires the knowledge of the mean of training images and incorporates the norm between the generated images and the mean of training images as a regularization term in the loss function. We experimentally observe that the method in Li, 2022 heavily relies on this prior knowledge, without which, the method tends to produce adversarial samples.
Response to Reviewer LZcP
We greatly appreciate the reviewer's questions and kindly mention that we have a prior response addressing the questions. In this follow-up response, we present additional new experimental results as an enrichment of our previous answers We are also more than willing to engage in a detailed discussion and address any remaining questions the reviewer might have. ### **Are there any experimental validations/theoretical justifications to confirm if the model is not just reconstructing the training data examples?** #### **Quantitative Evaluation Cont.** In our previous response, we employed the SSIM metric in the **pixel space** to quantitatively demonstrate that our method can indeed generate images not present in the original dataset. We further validated this in the **feature space**. Specifically, we computed the mean-min $l_2$ distance (mean-min-$l_2$) for the features. The calculation for this metric is as follows: (1) We utilized a backbone neural network to compute the latent features of all images in the classifier's training dataset. (2) For a generated image, we first computed its feature using the backbone network, then measured the distance between this feature and the features of each image in the training set, selecting the minimal value as the min-$l_2$. Consistent with our previous idea, this step measures the distance between the generated image and its most similar counterpart in the training set. (3) For a set of generated images, we perform step (2) for each generated image and then average the resulting min-$l_2$ values to obtain the mean-min-$l_2$. A higher mean-min-$l_2$ also shows that the generated images are different, even compared to the closest examples from the training set. This hints at the generation of data that are not in the original set. We use Inception-v3 as the backbone network, which is commonly used for computing metrics such as FID and ISC. We compare our method with the method presented in Haim et al., 2022 as in the previous experiment. The experimental results in the table below are consistent with our previous findings, with our method exhibiting a higher mean-min-$l_2$. This further substantiates our claim that our approach can generate images that do not exist in the training set. Moreover, we replicated the experiment using the feature from different neural network layers, and the results consistently supported our findings. | | Layer Name | Layer Depth | Ours | Haim et al.,2022 | |:------------------:|:----------:|:-----------:|:---------:|:----------------:| | Feature mm-$l_2$ of | MaxPool_2 | Shallow | 1.12±3e-2 | 0.98±3e-2 | | Feature mm-$l_2$ of | Mixed_6e | ↓ | 0.91±2e-2 | 0.82±9e-3 | | Feature mm-$l_2$ of | AvgPool | Deep | 13.0±9e-2 | 12.5±9e-2 |
Response to Reviewer LZcP
We appreciate Reviewer LZcP for the comprehensive review and insightful feedback. If possible, please let us know whether we have addressed all the concerns. Should the reviewer have other comments, we are more than happy to address them.
Thank you for the effort put into the rebuttal. My concerns have been addressed and I would like to increase my score.
I sincerely thank the authors for their elaborated rebuttal. As it seems by looking at the FID/ISC scores, the results are not very different from Haim et al. 2022, and both are pretty "bad" for a generator (very high FID). The way I see it, the main reasons are: - I'm not convinced that the proposed method in the current submission really result in different outputs than simply using Haim et al. 2022 (without the estimation of the lambda etc.). - If the "definition" of a generative model is to model a certain distribution, then using the implicit bias results of Lyu&LI 2019, Kunin et al. 2023 just doesn't make sense. Why would inverting the classifier result in a generative model in the first place? Sample reconstruction is different than modeling a distribution. Simply showing that some reconstruction methods actually work, is not equivalent to saying that they constitute a generative model. This is evident from the FID results, and is the reason why they are so "bad" for a generative model. I assume that many outputs from the proposed "generator" in the work are outputs that doesn't look at all like images from the dataset, because these outputs are in a way solution to the KKT conditions (of the quasi-homogenous case) - which has nothing to do "in general" with modeling the true distribution of the training set. These "bad" outputs are probably also the reason for the very high FID score. On the good side, I wasn't aware to the difference in the number of parameters that are being optimized. This is pretty interesting, and should be emphasized. I also think that the results on attribute editing are impressive - but the details on how they were produced could be clearer. On the bottom line, I find it hard recommending acceptance for the paper in its current form. It would be much easier if the paper was more clearly presenting the novelty w.r.t to previous works and more carefully comparing to them. If the paper was more clearly written, especially the technical parts, and implementing the rest of the remarks in the reviews (which some of the were answered in the rebuttal). Thanks.
Response to Reviewer KxBC
### **Further Comparison with [1] Haim et al., 2022** #### **To address:** ***"by looking at the FID/ISC scores, the results are not very different from Haim et al. 2022 .."*** **and** ***"I'm not convinced that the proposed method in the current submission really results in different outputs than simply using Haim et al. 2022 .."*** We appreciate the reviewer's concern. Our global response and Tab. 1 in the PDF compare our method to [1] regarding perspectives, such as complexity and assumptions. Here, we also compare our outputs with [1]'s. 1. The objective of [1] is to recover images, and the recovered images are their output. However, our goal is to train a generator. The output of our method should be the trained generator, not the images produced by the generator. This generator can produce perceptually satisfying images not present in the original training data, supporting conditional sampling and attribution editing. These capabilities are indeed beyond the reach of [1]. 2. While our method and [1] might not show significant differences in terms of FID/ISC, our parameter space is smaller, and the image generation process is less complex. This indicates that we achieved comparable FID/ISC with a reduced cost, highlighting an advantage of our method over [1]. 3. The fact that our method and [1]'s approach exhibit no significant difference in FID/ISC, does not imply that the generated images of our method and [1] are largely similar. As shown in Fig.4 and 7 of the attached PDF, it's evident that our method produces images with clearer outlines and more complete shapes. Admittedly, given the ambitious nature of our proposed task and being a pioneering effort in this direction, the qualitative result of our approach is not that impressive. This is to be expected, given the inherent challenges of training a generative model, especially as our training was conducted without accessing any data. #### **To address** ***"Why would inverting the classifier result in a generative model ...?"*** We thank the reviewer's question and address it from the following three perspectives. 1. Feasibility: A generative model is essentially an approximation of the conditional probability $P(x|\epsilon, y)$, and its training relies on knowledge about the data distribution $P_x$. When data is available, information regarding $P_x$ can be acquired by accessing the training data directly. However, in our task, training data is absent and only a pre-trained classifier is available. To tackle this task, we adopt the Maximum-Margin Bias (MMB) theory, which the reviewer kindly referred to as the implicit bias theory, to extract information related to training data embedded within the classifier parameters and then train the generator. The crux of this approach's feasibility lies in the sufficiency of the information extracted by the MMB theory. This sufficiency is supported by the findings in [1], as it's conceivable to train a generator using data reconstructed according to [1]. Such an idea demonstrates the sufficiency of the information the MMB theory can extract, affirming the feasibility of our approach. 2. Parameterization: The distinct parameterization ensures that our approach trains a generator, rather than merely reconstructing data as in [1]. To reconstruct training images, the learnable parameters in [1] are the image pixels themselves. By contrast, we designed a neural network where the network inputs are random noise and label index, and the network output is the image. The weights and biases of this neural network are our learning targets. While both our work and [1] design the loss function based on the MMB theory, this difference in parameterization directly leads to a functional divergence: [1] yields images, while our method produces a generative model. 3. Experimental Evidence. As demonstrated by our experimental results, we indeed obtained a generator with the capabilities of conditional sampling and attribution editing, though it currently underperforms in metrics like FID. We are also grateful for the question regarding the KKT conditions. As elaborated in both our manuscript and [1], it's acknowledged that the KKT conditions primarily ensure the extraction of information from data points on the classification margin, which represents only a subset of the training dataset. Consequently, during training, our generator predominantly receives supervision signals from these data points on the margin. For the generation of points outside this margin, the generator depends on its learned generalization ability, which might be a reason for the varied quality of certain generated samples. Nonetheless, it's important to recognize that our model indeed operates as a generator. It transforms from the noise distribution to the real data distribution (or more precisely, to the distribution over a subset of training samples), and it also possesses various functionalities typical of generators, as highlighted above.
Response to Reviewer KxBC
### **Attribution Editing** We thank the reviewer for the suggestions. The experiment of Attribution Editing mainly demonstrates that our method can indeed generate data not present in the original dataset, and it underscores that the generator we trained possesses a semantically structured latent noise space. The specific procedure is delineated in the following four steps: 1. Initially, we sample an image from the training dataset and produce two new images $x_{0}$ and $x_{N}$ not in the original dataset by rotating the sample image clockwise and counterclockwise, respectively. 2. Through inversion, we find the corresponding noise vectors $\epsilon_{0}$ and $\epsilon_{N}$ for $x_{0}$ and $x_{N}$, respectively. 3. We perform linear interpolation between $\epsilon_{0}$ and $\epsilon_{N}$, yielding a sequence of noise vectors $\{\epsilon_{0}, \epsilon_{1}, \cdots, \epsilon_{N}\}$. 4. Finally, we use $\{\epsilon_{0}, \epsilon_{1}, \cdots, \epsilon_{N}\}$ and the class label as the input of the generator, to generate a series of images. ### **Comparison with Other Works** We thank the reviewer for the comments. The comparison of our work with the works mentioned by the reviewers is presented in the global response and Tab. 1 of the attached PDF. We are more than willing to make further comparisons if the reviewer suggests other works or if there's a specific perspective from which the reviewer would like us to compare our work with others. ### **Writing** We thank the reviewer for the comments. In the revised version, we will refine and enhance our writing to make the paper clearer and more comprehensible. Particularly for the technical part, we will provide more detailed explanations and clarifications. ### **Implementing the Rest of the Remarks in the Review** We thank the reviewer for the valuable feedback during the review and discussion phases. In the revised version, we will incorporate all these suggestions and enhance our manuscript based on the reviewer's comments. ### **More Remarks** We are more than willing to engage with the reviewer regarding any remaining concerns. We would appreciate it if the reviewer specify the concerns they feel are still unresolved, and we will promptly address them.
Decision
Accept (poster)