PCSY-D-24-00084

Cyclic image generation using chaotic dynamics

PLOS Complex Systems

Dear Dr. Yamaguti,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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.

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We look forward to receiving your revised manuscript.

Kind regards,

Jin Liu

Academic Editor

PLOS Complex Systems

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Additional Editor Comments (if provided):

The authors introduce a novel image generator based on CycleGAN and show that successive image transformation can be considered as being a dynamical system. The research and findings are interesting, and this work can be accepted after minor edits addressing the reviewers’ concerns.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: I don't know

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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

Reviewer #4: Yes

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

PLOS Complex Systems 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

Reviewer #4: 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: The authors present a very interesting study in which they introduce a novel image generator using generative adversarial networks. They build on the popular CycleGAN and show that their modification gives rise to intriguing dynamics in image space that are reminiscent of chaos, i.e., sensitivity to initial conditions and convergence of phase space dynamics towards a finite set of states. They argue that this demonstrates the model's potential to simulate associative memory. The model is validated using two paradigmatic example datasets. To me, the findings appear relevant and compatible with the scope of PLOS Complex Systems. Code is made publicly available. As the paper clearly requires multidisciplinary expertise (deep learning, neuroscience and nonlinear dynamics), I focussed on the aspects touching on the latter as this most closely matches my own expertise.

Overall, the authors give a clear and concise description of the implemented method as well as how they apply it to the selected numerical examples. This is well supplemented by suppl. figures that further contribute to the overall clarity of the manuscript. The authors employ UMAP for dimensionality reduction, enabling them to visually display the exhibited model dynamics in a simplified fashion. While I have not myself used UMAP before, I am missing some demonstration that transformed representation of the data effectively captures the high-dimensional dynamics. Other standard methods for dimensionality reduction/compression, e.g., derive the explained variance or quantify the achieved separation of components. As the remainder of the analysis strongly depends on this representation, I'd argue that this would be quite important.

The authors reveal that, i), sequences of images starting from different initial conditions show strong sensitivity and, ii), image sequences converge to a constrained subspace of the full image space. They investigate in more detail whether this hints at chaotic dynamics, using Lyapunov exponents and vectors. While I think that it is an important first step to derive the Lyapunov exponents with two different techniques, I wonder whether another fully independent method for classifying a system as chaotic would agree with this finding. Numerical Lyapunov exponent estimation methods are known to perform rather poorly for "short" time series (often, anything less than several 100k of data points). Common alternative approaches (e.g., symbolic dynamics) are less sensitive to time series length. Since many off-the-shelf Python implementations exist, I would suggest that the authors consider demonstrating the robustness of this key finding using an independent chaos classification method. If the model indeed generates chaotic dynamics, I am left to wonder which property of the model is responsible for this behaviour. While this question would likely reach beyond the scope of this manuscript, a more simple question (to me as a non-expert of image generators) would be a direct comparison to CycleGAN: Does CycleGAN also exhibit chaotic dynamics in some sense? Does the third category included here play a role?

One of the most interesting findings is clearly the existence of attractors and the corresponding low recall values. Could the authors elaborate whether (and if so, how) the finiteness of the generated sequences may affect this finding? I also wonder whether the exhibited samples possess any specific features that render them distinct to the not exhibited samples? I do, however, understand that this would probably require further investigations (likely beyond the reduced UMAP representation) and that it thus could be beyond the scope of this work.

Finally, the authors' claim that their model could bear relevance for associative memory modelling, as of now, seems to stand as a mere hypothesis. So far, the outlook of the paper is limited to rather technical considerations for future work. I think it would be valuable to at least comment on, i), how future studies could investigate the scope of the method with more challenging real-world examples and, ii), what would be required to link it to associative memory processes.

After addressing these considerations appropriately, I am positive to recommend the study for publication in PLOS Complex Systems.

Reviewer #2: This study extends CycleGAN to cyclically transform images among three categories, generating diverse images through chaotic dynamics and demonstrating high precision but relatively low recall, suggesting future improvements to balance image quality and diversity. The paper is well-written and the idea is well presented. The source codes are available on GitHub for public use and verification. Just one minor suggestion: numbers such as 70000 could be written using scientific notation.

Reviewer #3: In this manuscript, the authors extended CycleGAN to cyclically transform images among three categories, aiming to generate diverse images. They claim the model's effectiveness was confirmed through visualization and clustering of generated images. The authors framed the process as a dynamical system, suggesting that chaotic dynamics enabled varied image generation. They report that precision metrics indicated high accuracy, though recall metrics showed limited distribution coverage. The Lyapunov spectrum and attractor dimension analyses purportedly suggest that the generated images exhibited chaotic behavior and high-dimensional complexity similar to the training data. The work falls within the scope of journal and can be accepted for publication.

Reviewer #4: The authors present an extension of Machine Learning Application to produce images in a cyclical manner to generate variants by running Convolution Neural Networks with a generator-discriminator setup. The authors use chaos theory measurements to argue for a better distribution of the resulting images. To this end, two measures are utilized to estimate its performance. The presentation is tractable but and the probability estimations seam correct. Yet I have the following comments and concerns.

1. The chaotic nature of the proposed model is only based on Lyapunov exponents therefore it maybe just an indication of chaotic behavior. Additionally, the basic idea in unclear, the results of a numerical model with out a verifiable equation, calls for a time-series based calculation, as such, the numerical effects and the length of the time series are important. A particular aspect is the dimension of the reconstructed delayed coordinates in your results are 15 or larger dimensions, is that a concern taken into consideration here? Also note that for chaos the presence of a positive Lyapunov exponent is a good indicator, but for most of your results the exponents are negative, is the positive results at the beginning a numerical artifact, or are they sufficient to declare the underlining system chaotic? This point is very questionable and borderline technically incorrect.

2. The numerical results are interesting and provide a good illustration of the applications of the proposed application of LM, however, the authors do in fact include information as time series and programs but the main problem I find with the presentation is that it is an extension of an application package TensorFlow, that uses a prefabricated model for the neural network, then is unclear that most of the basic aspects of the results are not due to its original programming and the additional processing proposed by the authors makes basically no difference. Please elaborate on the significance of the changes proposed. Also, perhaps a just comparison of the results maybe useful.

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Reviewer #1: Yes: T. Braun

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

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Cyclic image generation using chaotic dynamics

PCSY-D-24-00084R1

Dear Dr. Yamaguti,

We are pleased to inform you that your manuscript 'Cyclic image generation using chaotic dynamics' has been provisionally accepted for publication in PLOS Complex Systems.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow-up email from a member of our team. 

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they'll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact complexsystems@plos.org.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Complex Systems.

Best regards,

Jin Liu

Academic Editor

PLOS Complex Systems

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This manuscript can be accepted now, the authors may take a thorough check on typos in the final typesetting.

Reviewer Comments (if any, and for reference):

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 #5: All comments have been addressed

Reviewer #6: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #5: Yes

Reviewer #6: Yes

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #5: Yes

Reviewer #6: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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 #5: Yes

Reviewer #6: Yes

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

PLOS Complex Systems 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 #5: Yes

Reviewer #6: Yes

**********

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 adequately addressed all of my concerns. I recommend the manuscript for publication in PLOS Complex Systems.

Reviewer #2: (No Response)

Reviewer #5: The authors have responded well to previous comments, and I have no further comments.

Reviewer #6: All comments have been addressed. However, the revised version of the manuscript in response to Reviewer #1’s comment #1 contains an inaccuracy. The name Adjusted Rand Score is used incorrectly; the correct name is Adjusted Rand Index, commonly known as ARI. The use of the term Adjusted Rand Score introduces terminological inconsistency and confusion into the existing literature. Additionally, the analysis would be enhanced by the incorporation of supplementary calculations pertaining to the Normalized Mutual Information (NMI).

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #5: No

Reviewer #6: No

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