PONE-D-25-38700MViT�Dynamic Positional Encoding Vision Transformer Guided by Recursive Moore CurvesPLOS ONE

Dear Dr. Zhu,

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Reviewer #1: No

Reviewer #2: Partly

Reviewer #3: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: N/A

Reviewer #3: No

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: In this manuscript, the authors proposed an MViT framework to enhance the spatial dependency modeling of traditional vision transformers. Moore curves are used to order the patches for better global continuity, and periodic positional encoding is designed accordingly to adapt to the Moore paths and partition. The proposed framework outperforms a few traditional ViT architectures on multiple image classification tasks, and the ablation study is performed to prove the effectiveness of periodic positional encoding. Despite the strengths mentioned above, I have the following major concerns.

1. The nature of the proposed method. The authors focused on improving patch ordering and encoding in the ViT architecture, without changing the downstream attention layers. Therefore, the proposed method can be used as an “add-on” module to a wide range of existing ViT architectures using traditional ordering and absolute encoding, rather than “replace” them. The authors should consider emphasizing that the proposed method can flexibly equip other ViTs with fancy attention block designs, which can bring additional predicting power. As a result, to present the experimental effectiveness, the authors should consider adding comparisons like “ViT vs. ViT+proposed Moore+PE”, “Swin vs. Swin+proposed Moore+PE”, etc. This could significantly extend the application.

2. Computer vision tasks. Related to (1), as general ViTs can be combined with the proposed method, the enhanced models can still be used as the backbone of different types of CV tasks. Nevertheless, the authors focused on image classification tasks in this manuscript. While Section 4.3 is related to image reconstruction, the data set and settings in Table 3 are not clear. The authors should consider adding data sets and experiments for more common CV tasks such as object detection and instance segmentation (e.g., on COCO data set) to show the general advantages of the proposed module.

3. Baseline models. In Table 2, all the 3 baseline models use traditional absolute positional encoding which is known to be weak in cases like image rotation. As the periodic encoding usage is a novelty in this paper, the author should consider adding a baseline model using stronger encoding methods as well (e.g., relative/rotary encoding [1]).

In addition, while the Swin-T selection for Swin transformer is clear, what is the specific size of vanilla ViT (e.g., L/16) used in Table 2 and 3? If the parameter numbers are not comparable between different models, the results won’t make sense.

[1] Heo, Byeongho, et al. "Rotary Position Embedding for Vision Transformer." European Conference on Computer Vision. 2024.

4. Error bar. In the result tables, most of the accuracy enhancement brought by the proposed method are within 1%. The authors should consider reporting the standard deviation of the performance metrics, to show the stability and reproducibility of the performance.

5. Writing. Please check the writing and fix the typos (e.g., excel -> excels in the abstract).

Reviewer #2: Title - MViT�Dynamic Positional Encoding Vision Transformer Guided by Recursive Moore Curves

In this paper, the authors proposed is a recursive Moore curve based ViT framework (MViT).

Queries and Suggestions (Issues observed)

1. The title of this manuscript has not effectively captured the interest of a broader audience outside its niche area, which will limit its impact and reach, please revised

2. The introduction can be enriched by briefly describing the state-of-the-art in the title of this study and providing more recently related references to support the foundation of this study and provide a better context for the current research. I will recommend citing recently published related papers;

a. "Semantic Segmentation of the Lung to Examine the Effect of COVID-19 Using UNET Model," in Applied Machine Learningand Data Analytics. AMLDA 2022. Communications in Computer and Information Science, 2023.

b. "Vision transformers for automated detection of pig interactions in groups," Smart Agricultural Technology, vol. 10, p. 100774, 2025.

3. The problem that the author is trying to address in this paper is not clear yet, (clearer motivation for the study is required)

4. In 4-5- lines, authors should summarize the literature gaps identified before starting the methodology (Kindly relate your work in the context of existing work, what are the shortcomings of existing studies?)

5. Author should re-check the correctness of equations, especially from equations 3 to 8

6. More discussion of the results are required

7. Services of language experts are required (be mindful of tenses, typo errors)

8. Image quality needs to be improved (High resolution image suggested)

Reviewer #3: The authors propose 3 methods to increase image classification using Vision Transformers. Namely (1) image patch arrangement (2) period-aware positional encoding and (3) boundary compensation strategy.

They show on several benchmark image datasets that your top 1 accuracy has a small improvement compared to others.

The overall reading style of the paper is good and clear to me. Below I have a few comments / questions / suggestions to improve the paper / understand it better.

On page 2 you claim that you have 30% faster convergence speed (coming from figure 7 I believe).

- Does your method takes more time to train compared to the others?

- Does it takes more GPU memory then the others (model parameters)?

1. On page 2 you say: “ Visualization analysis showed the model’ s identification error for rotational targets decreased by 12.6%. To me this is not explained / supported in the paper. Could you follow up on this?

2. As you claim that your method is better on rotational , symmetrical objects, would it be an idea that you run an experiment for this? Could you find a dataset with mostly rotational , symmetrical objects, and compare your classification score compared to others?

3. The original VIT paper (https://arxiv.org/abs/2010.11929) has a figure (figure 7 in the middle) on their learned positional embeddings, by this they show what the embeddings have learned, and that they correspond to the image patch. Could be a nice additional to your paper as well.

4. You compare yourself to ViT[1] (2022), Swin-T[2](2021), GFPE-ViT[5] (2024). Aren’t there no other recent models as some of these are some years old.

5. As you have 3 methods, it would be nice to see the results of your method in isolation. I believe you try to show this in table 4 and 5, but the numbers are exactly the same as in table 2 where you have put all your methods. Can you clarify?

6. For all tables, it is unclear to me if your experiments have been run once or multiple runs (with seeds). I do not see any st. Dev scores as well. I cannot see if you are better compared to the others due to a lucky run now.

7. In table 3, Swin-T[2] model comparison is not taken into account. Why?

8. For table 4 and 5, you decide to only report on 2 datasets, not all. Why?

9. I think there is a type in table number 1, in the Places 365 row. The sum training set + test set is not equal to total images.

10. It would be interesting to see some more images being divided in different patches as examples.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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PONE-D-25-38700R1MViT: A Vision Transformer with Fractal Path Reordering and Dynamic Positional EncodingPLOS One

Dear Dr. Zhu,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jan 29 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Anil Yaman, Ph.D.

Academic Editor

PLOS One

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If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

Thank you for addressing the comments and questions of the reviewers. All reviewers found the responses and improvements satisfactory. One reviewer pointed out two questions. Could you please address them and asses if there is any revisions to be made in the text?

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors have addressed my concerns, and the experiments have been extended to more types of computer vision tasks. No more comments from my side.

Reviewer #2: The manuscript has has been improved and it is suitable for publication to the best of my knowledge

Reviewer #3: Dear authors,

Thank you for response to my questions, I find them satisfactory. I also liked that you added table 8 which I believe, shows the value of your approach. Nevertheless, I still have two questions below.

Question 1:

In your paper you mention"MViT demonstrates superior performance across various image classification datasets

with different structural complexities, particularly excelling in fine-grained datasets that

are sensitive to structure. As shown in Table 2, MViT achieved an accuracy of 84.08%

on ImageNet-21k and 90.75% on the Stanford Cars dataset, significantly outperforming

both ViT-B/16 and Swin-T."

But looking at table 2, I only see a small improvement. Could you clarify how significance was determined?

Question 2:

The sentence above table 3 states:

"Compared to ViT-B/16, MViT exhibited a 12.6%

reduction in accuracy drop, demonstrating that periodic positional encoding can

maintain phase continuity under rotation, alleviating absolute positional index

mismatches, and thus improving the stability and generalization ability of the model for

rotational and symmetric structures."

It was not clear to me how you found 12.6%.

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Reviewer #1: No

Reviewer #2: Yes: Sunday Adeola Ajagbe

Reviewer #3: Yes: Bob Borsboom

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MViT: A Vision Transformer with Fractal Path Reordering and Dynamic Positional Encoding

PONE-D-25-38700R2

Dear Dr. Zhu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Anil Yaman, Ph.D.

Academic Editor

PLOS One