Review Reports - Grade Inflation in Generative Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript introduces the concept of “grade inflation” in quality metrics for generative models and proposes the Eden score, an equidensity-based measure that compares overlap across density contours. The distinction between equipoint and equidensity scoring is interesting, and the Eden score is intuitive and well illustrated. The human-evaluation component and the discussion of sampling uncertainty are also useful additions. However, the current validation design does not yet provide sufficiently strong evidence for some of the manuscript’s broader claims. I therefore recommend Major Revision.

The human-validation set is selected in a way that may favor Eden.
The manuscript states that plots were selected such that the plot with the higher Eden score received a lower score according to at least one competing metric. This creates a selected disagreement set rather than an independently sampled benchmark. Such a design is useful for studying cases where metrics disagree, but it does not by itself establish that Eden agrees better with human judgment overall. The authors should add an independently selected or randomly sampled evaluation set that is constructed without reference to Eden or the comparator scores.

2. The human-rating instruction is closely aligned with the definition of Eden.
Raters were explicitly instructed to choose the plot in which the contours matched better while considering all contours. Since Eden is itself defined by averaging overlap across density contours, this may partially favor the proposed metric. A more neutral instruction, such as asking which synthetic distribution better matches the reference distribution overall, would provide stronger validation. The term “gold standard” should also be used more cautiously; “human-reference evaluation” or “expert visual assessment” would be more appropriate.

3. The human-validation sample is small, and the statistical comparison should be revised.

Although 39 plot pairs were evaluated, these correspond to only 13 unique pairs repeated three times with rotations or color changes. This limits the diversity of independent test cases. In addition, the manuscript compares Cohen’s k values across scoring methods using the Mann–Whitney U test. Because the same raters contribute k values for each scoring method, the observations are paired rather than independent. A paired test, such as the Wilcoxon signed-rank test or a paired permutation test, may be more appropriate. Multiple comparisons should also be controlled.

4. The robustness of Eden to KDE and implementation choices should be evaluated.

Eden depends directly on KDE contours, yet the current implementation fixes the seaborn KDE, Scott bandwidth, five contour levels, and five annuli. The authors should evaluate sensitivity to bandwidth, number of contour levels, number of annuli, tail-mass exclusion, Monte Carlo resolution, and sample size. This is particularly important because the manuscript itself shows that oversampling can substantially change the KDE and reduce the Eden score from 0.452 to 0.160 for the same underlying model.

5. The comparator set should be broadened and defined more carefully.

The current evaluation is limited to correlation, earth-mover’s, Jaccard, KL, and Eden. Additional distribution-comparison methods such as Jensen–Shannon divergence, Hellinger distance, MMD, energy distance, or sliced Wasserstein distance would provide a stronger benchmark. The KL divergence used here is asymmetric, whereas Eden is symmetric, so symmetric KL or Jensen–Shannon would be particularly informative. In addition, the reported “Jaccard score” is a KDE-based modification that defines intersection using a relative-density threshold of 0.1.

This should be clearly identified as a modified Jaccard score, and sensitivity to this threshold should be assessed.

6. The general claims should be weakened unless supported by broader theoretical or empirical evidence.

The manuscript suggests that all equipoint scores will suffer grade inflation and that reasonable equidensity scores will avoid it. However, only a small number of metrics and example distributions are examined. These statements should be framed consistently as hypotheses rather than general conclusions.

7. Reproducibility and ethics reporting should be improved

Several implementation details needed to reproduce the Eden score are missing, including the number of Monte Carlo points, bounding-box definition, random seeds, EMD histogram settings, and full specifications of the in-house datasets and models. The Methods currently describe only “a large number” of uniformly distributed Monte Carlo points. Public release of the implementation would substantially strengthen the paper. In addition, the study involves 20 human raters, but the manuscript does not appear to report IRB approval, exemption, or informed-consent procedures.

8. Several typographical errors should be corrected, including “can to lead,” “intialized,” “the the,” “perenially,” “nonparameteric,” and “Renyi diverence.” The Methods describe repeated rotated/color-swapped evaluations intended to assess within-rater consistency, but the corresponding consistency results should be reported. Also, qualitative labels such as “excellent,” “moderate,” and “low” agreement for Cohen’s k should either be supported by a reference or omitted.

Author Response

We thank the reviewers for their very helpful comments, which we feel have improved the manuscript. We address each point below (reviewers’ points in bold; all points are numbered). In addition, we found and fixed a bug in our code for the earth mover’s score, and have updated the results accordingly; this did not meaningfully affect the manuscript.

Comment 1-1. The human-validation set is selected in a way that may favor Eden. The manuscript states that plots were selected such that the plot with the higher Eden score received a lower score according to at least one competing metric. This creates a selected disagreement set rather than an independently sampled benchmark. Such a design is useful for studying cases where metrics disagree, but it does not by itself establish that Eden agrees better with human judgment overall. The authors should add an independently selected or randomly sampled evaluation set that is constructed without reference to Eden or the comparator scores.

Response 1-1. This is not what was done; we apologize for the confusion and have updated the text to clarify (Section 2.4). Plots were selected only for having differences, not for the Eden score being higher. In other words, each pair included a plot where Eden was lower than (at least) one of the other scores and another plot where Eden was higher. We then compare the preference for each method (the plot with higher score) with human raters’ choices to find the method showing the highest consistency. Thus, this was an unbiased test of agreement between human raters and each of the scores.

Comment 1-2. The human-rating instruction is closely aligned with the definition of Eden. Raters were explicitly instructed to choose the plot in which the contours matched better while considering all contours. Since Eden is itself defined by averaging overlap across density contours, this may partially favor the proposed metric. A more neutral instruction, such as asking which synthetic distribution better matches the reference distribution overall, would provide stronger validation. The term “gold standard” should also be used more cautiously; “human-reference evaluation” or “expert visual assessment” would be more appropriate.

Response 1-2. This is a good point, unfortunately left for future work in the interest of time, which we have now added as a limitation. We appreciate the suggestion of more cautious use of “gold standard” and have now moved away from this term. We now evoke the common usage of visual inspection by experts in generative model inspection to motivate the validation.

Comment 1-3. The human-validation sample is small, and the statistical comparison should be revised. Although 39 plot pairs were evaluated, these correspond to only 13 unique pairs repeated three times with rotations or color changes. This limits the diversity of independent test cases. In addition, the manuscript compares Cohen’s k values across scoring methods using the Mann–Whitney U test. Because the same raters contribute k values for each scoring method, the observations are paired rather than independent. A paired test, such as the Wilcoxon signed-rank test or a paired permutation test, may be more appropriate. Multiple comparisons should also be controlled.

Response 1-3. The main consideration for not including more images was to ensure the focus of raters, especially with 3 repetitions to minimize effect of color and angle on rater’s choice. In the 13 pairs of plots, we included fits from 6 different datasets of various fitting quality (Eden score ranging from 0.14 to 0.77). A new figure 2 is added to demonstrate the diversity of plots included. We agree that Wilcoxon signed-rank is a better test for the paired data and have updated the results with the new tests. In the results we control multiple comparison by only taking the majority choice in the 3 repetitions. We have now added sample size as a limitation.

Comment 1-4. The robustness of Eden to KDE and implementation choices should be evaluated. Eden depends directly on KDE contours, yet the current implementation fixes the seaborn KDE, Scott bandwidth, five contour levels, and five annuli. The authors should evaluate sensitivity to bandwidth, number of contour levels, number of annuli, tail-mass exclusion, Monte Carlo resolution, and sample size. This is particularly important because the manuscript itself shows that oversampling can substantially change the KDE and reduce the Eden score from 0.452 to 0.160 for the same underlying model.

Response 1-4. We have now added this analysis in a new Appendix B, where we study how the Eden score varies with the number of annuli, the choice of bandwidth, the threshold for tail-mass exclusion, and the Monte-Carlo resolution.

Comment 1-5. The comparator set should be broadened and defined more carefully. The current evaluation is limited to correlation, earth-mover’s, Jaccard, KL, and Eden. Additional distribution- comparison methods such as Jensen–Shannon divergence, Hellinger distance, MMD, energy distance, or sliced Wasserstein distance would provide a stronger benchmark. The KL divergence used here is asymmetric, whereas Eden is symmetric, so symmetric KL or Jensen–Shannon would be particularly informative. In addition, the reported “Jaccard score” is a KDE-based modification that defines intersection using a relative-density threshold of 0.1. This should be clearly identified as a modified Jaccard score, and sensitivity to this threshold should be assessed.

Response 1-5. Two new symmetric measures have been added as comparators: scores based on the Jensen-Shannon divergence and on the Cauchy-Schwarz divergence. We now say explicitly at the end of section 2.3.3 that our Jaccard score is a modified version of the traditional Jaccard score, which is defined for discrete sets rather than samples from continuous probability distributions.

Our new sensitivity study has shown that threshold on KDE in general doesn’t influence the score as much, and we believe this will hold for Jaccard score as well (see more in response to point 1-4).

Comment 1-6. The general claims should be weakened unless sup- ported by broader theoretical or empirical evidence. The manuscript suggests that all equipoint scores will suffer grade inflation and that reasonable equidensity scores will avoid it. However, only a small number of metrics and example distributions are examined. These statements should be framed consistently as hypotheses rather than general conclusions.

Response 1-6. We appreciate the point that current empirical research does not definitively prove that all equipoint scores suffer from grade inflation. We have softened ”propose” to ”suggest” in the abstract, and in the discussion (Section 4.1) we suggest future research to explore other measures resistance to grade inflation.

Comment 1-7. Reproducibility and ethics reporting should be improved. Several implementation details needed to reproduce the Eden score are missing, including the number of Monte Carlo points, bounding-box definition, random seeds, EMD histogram settings, and full specifications of the in-house datasets and models. The Methods currently describe only “a large number” of uniformly distributed Monte Carlo points. Public release of the implementation would substantially strengthen the paper. In addition, the study involves 20 human raters, but the manuscript does not appear to report IRB approval, exemption, or informed-consent procedures.

Response 1-8. We now have the Python implementation code as part of a new Appendix A. Datasets and implementation of the other scoring methods are now available on GitHub (https://github.com/ArnaoutLab/Grade-Inflation). This study is IRB exempt with exemption type 4 (45 CFR 46.104(d)(4)(ii)). We have added this information to the Methods section.

Comment 1-8. Several typographical errors should be corrected, including “can to lead,” “intialized,” “the the,” “perenially,” “nonparameteric,” and “Renyi diverence.” The Methods describe repeated rotated/color-swapped evaluations intended to assess within-rater consistency, but the corresponding consistency results should be reported. Also, qualitative labels such as “excellent,” “moderate,” and “low” agreement for Cohen’s k should either be supported by a reference or omitted.

Response 1-8. We have fixed the typos and added references for the qualitative labels.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript identifies an important and potentially underappreciated problem in evaluating generative models: commonly used similarity scores may produce deceptively high scores for poor distributional matches, which the authors call “grade inflation.” The paper compares correlation, earthmover’s, Jaccard, and KL-based scores and introduces the Eden score, which evaluates similarity across density contours rather than weighting datapoints according to their frequency. The authors report that Eden both avoids the observed grade inflation and agrees more closely with human judgments in a blind evaluation. However, I have several substantial concerns about the experimental design, the definition and implementation of Eden, the scope of the conclusions, and the human validation. In its current form, the manuscript supports the claim that Eden is promising for the particular two-dimensional examples studied, but it does not yet establish the broader claim that equidensity scores generally outperform equipoint scores for generative-model evaluation.

1 The manuscript states that the 39 test pairs were deliberately selected so that “the plot with the higher Eden score received a lower score according to at least one of the other scores.” This means the evaluation set was constructed in advance around disagreements involving Eden.

That is a reasonable way to create challenging test cases, but it is not a neutral validation of Eden. It can enrich the dataset for exactly the circumstances in which Eden differs from competing metrics.

The paper therefore should distinguish between:

demonstrating that Eden resolves disagreement cases that were specifically selected to favor disagreement with other metrics, and
demonstrating that Eden has better general validity on an independently sampled benchmark.

I strongly recommend adding an evaluation set constructed without reference to the scores being compared. Ideally, the authors should report results separately for a preregistered/independently selected test set and the current disagreement-enriched set.

2. Related work on higher-dimensional entropy/divergence measures is incomplete. The discussion of Rényi entropy, diversity, and distribution comparison would benefit from citing relevant work on matrix-based Rényi’s α\alpha-order entropy, Cauchy–Schwarz divergence, and representation comparison/visualization. The manuscript currently discusses connections between equidensity scores and Rényi entropy, including negative-order Rényi entropy , but the related literature could be broadened to include approaches developed for multivariate and high-dimensional representations. Relevant examples include [1] Yu et al., “Multivariate Extension of Matrix-Based Rényi's α-Order Entropy Functional,” IEEE TPAMI (2019/2020); [2] Jenssen, “Map It to Visualize Representations,” ICLR 2024. A brief discussion of these related approaches would better position Eden within the broader literature on information-theoretic comparison and visualization of complex distributions and representations, particularly given the manuscript's discussion of dimensionality reduction and potential extensions beyond two dimensions.

Author Response

Comment 2-1. The manuscript states that the 39 test pairs were deliberately selected so that “the plot with the higher Eden score received a lower score according to at least one of the other scores.”

This means the evaluation set was constructed in advance around disagreements involving Eden. That is a reasonable way to create challenging test cases, but it is not a neutral validation of Eden. It can enrich the dataset for exactly the circumstances in which Eden differs from competing metrics. The paper therefore should distinguish between: demonstrating that Eden resolves disagreement cases that were specifically selected to favor disagreement with other metrics, and demonstrating that Eden has better general validity on an independently sampled benchmark.

Response 2-1. We realized our previous description might have been somewhat confusing and have clarified accordingly (see also under the response to point 1-1). Randomly selecting comparison pairs would require larger number of tests to sufficiently power the study and ensure difference between scoring methods can be observed, whereas there is a limit as to how long raters can realistically be expected to maintain attention. See also the response to point 1-3.

Comment 2-2. Related work on higher-dimensional entropy/divergence measures is incomplete. The discussion of R´enyi entropy, diversity, and distribution comparison would benefit from citing relevant work on matrix-based R´enyi’s α-order entropy, Cauchy–Schwarz divergence, and representation comparison/visualization. The manuscript currently discusses connections between equidensity scores and R´enyi entropy, including negative-order Rényi entropy , but the related literature could be broadened to include approaches developed for multivariate and high-dimensional representations. Relevant examples include Yu et al., “Multivariate Extension of Matrix-Based Rényi’s α-Order Entropy Functional,” IEEE TPAMI (2019/2020); Jenssen, “Map It to Visualize Representations,” ICLR 2024. A brief discussion of these related approaches would better position Eden within the broader literature on information-theoretic comparison and visualization of complex distributions and representations, particularly given the manuscript’s discussion of dimensionality reduction and potential extensions beyond two dimensions.

Response 2-2. We have now added a score based on the Cauchy-Schwarz divergence as comparator. This work focuses on two dimensions, the most common application in print; we have discussed potential considerations for higher dimensions but leave it as a problem for future work. We elaborate more on this in Section 4.6. We have also added a reference to Yu et al IEEE TPAMI (2019/2020) in Section 4.4 to Jenssen ICLR 2024 in Section 4.6.

Reviewer 3 Report

Comments and Suggestions for Authors

- How well does the Eden score scale to higher-dimensional data? Could the curse of dimensionality reduce its effectiveness?

- How sensitive is the Eden score to KDE bandwidth? Would different contour choices significantly change the results? Please elaborate.

- The Methods section should provide more details on the dataset sources, study limitations, computational trade-offs, and other relevant experimental settings.

- The mathematical derivations should have a clear purpose and objective, with all variables and parameters explicitly defined.

- Please elaborate on the future research directions and conclusion, and clearly document all additional setup parameters used in the study.

Author Response

Response 3-1. While the study of higher-dimensional Eden scores is left for future work, but yes, we expect the curse of dimensionality to reduce its effectiveness (as it does for many other measures). We elaborate on this in Section 4.6.

Comment 3-2. How sensitive is the Eden score to KDE bandwidth? Would different contour choices significantly change the results? Please elaborate.

Response 3-2. We have added a sensitivity analysis on parameters including number of annuli and KDE bandwidth in a new Appendix B. Also see the response to point 1-4 above.

Comment 3-3. The Methods section should provide more details on the dataset sources, study limitations, computational trade-offs, and other relevant experimental settings.

Response 3-3. We now include a python script for implementation of Eden score and a summary table of data source with plot examples in the manuscript. Datasets and implementation of the other scoring methods are now available on GitHub (https://github.com/ArnaoutLab/Grade-Inflation).

Comment 3-4. The mathematical derivations should have a clear purpose and objective, with all variables and parameters explicitly defined.

Response 3.4. We have now stated the meanings of all mathematical symbols in Methods section more explicitly, and code is up on GitHub. Please let us know if anything remains unclear.

Comment 3-5. Please elaborate on the future research directions and conclusion, and clearly document all additional setup parameters used in the study.

Response 3.5. Please see the response under point 3-3 above.

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript addresses the grade inflation problem in generative models and proposes the Eden score as an alternative approach to evaluate the outcome of the data. However, several aspects of the manuscript need to be improved to strengthen the quality as :

1- Abstract
The abstract needs to include the outcome of the comparison to demonstrate the effectiveness of the proposed Eden score.

2- Introduction
The main contributions and novelty of the work should be stated more clearly in the introduction which is not clearly presented in the current manuscript. I recommend adding a concise list of the major contributions, including the proposed Eden score, benchmark datasets, generative models, and evaluation metrics considered in the study.

3- Related Work
The current manuscript lacks one of the most element of the research. it should be included in more depth to understand how the proposed approach is positioned relative to existing methods. Also, The authors should discuss previous studies on generative-model evaluation and distribution-similarity metrics.

4-Methodology

The authors describe the datasets used in the experiments; however, the presentation could be improved. I recommend including a summary table of all datasets. the author also should add proposed algorithm to how the input data is work with Eden score to evaluate the outcome.

5-xperimental and Environment Setup
The experimental setup requires further clarification. The manuscript should provide a more structured description of the evaluation metrics, generative models, implementation environment, and parameter settings used in the experiments. For example, what value is used in the hyperparameters and experimental configurations should be reported to ensure that the experiments can be reproduced

6-Conclusion and Future Work
The conclusion should make it more clearly summarizing the main findings, contributions, and limitations of the study. In addition, a more detailed discussion of future research directions should be provided, particularly regarding further validation of the Eden score

Author Response

Response 4-1. We have now edited the abstract section to explicitly state ”We find that Eden avoids grade inflation and show the highest consistency with human perception of goodness-of-fit compared to the equipoint scores above.”

Comment 4-2. Introduction: The main contributions and novelty of the work should be stated more clearly in the introduction which is not clearly presented in the current manuscript. I recommend adding a concise list of the major contributions, including the proposed Eden score, benchmark datasets, generative models, and evaluation metrics considered in the study.

Response 4-2. We now include a list of main contributions at the end of the Introduction section.

Comment 4-3. Related Work: The current manuscript lacks one of the most element of the research. it should be included in more depth to understand how the proposed approach is positioned relative to existing methods. Also, The authors should discuss previous studies on generative-model evaluation and distribution-similarity metrics.

Response 4-3. We have included discussion of previous work as part of the Introduction and Methods sections, with an emphasis on the many comparator measures that we evaluate (with references). MAKE’s author instructions do not include a ”Related Work” section in its manuscripts (https://www.mdpi.com/journal/make/instructions#prep ). We understand this is not uncommon.

Comment 4-4. Methodology: The authors describe the datasets used in the experiments; however, the presentation could be improved. I recommend including a summary table of all datasets. the author also should add proposed algorithm to how the input data is work with Eden score to evaluate the outcome.

Response 4-4. We now include a summary table of datasets used and examples of plots in the blind test. A Python script is also included for better evaluation (Appendix A). Datasets and implementations of the other scoring methods are now available on GitHub (https://github.com/ArnaoutLab/Grade-Inflation).

Comment 4-5. Experimental and Environment Setup: The experimental setup requires further clarification. The manuscript should provide a more structured description of the evaluation metrics, generative models, implementation environment, and parameter settings used in the experiments. For example, what value is used in the hyperparameters and experimental configurations should be reported to ensure that the experiments can be reproduced.

Response 4-5. Details of experiments are now made available on GitHub: https://github.com/ArnaoutLab/G
Inflation .

Comment 4-6. Conclusion and Future Work: The conclusion should make it more clearly summarizing the main findings, contributions, and limitations of the study. In addition, a more detailed discussion of future research directions should be provided, particularly regarding further validation of the Eden score.

Response 4-6. We have added a paragraph to this effect at the beginning of Section 4.6, and discuss directions for future research there and elsewhere (for example, Section 4.3 mentions the possibility choosing the number of annuli based on sample size). We have now added sensitivity testing; see above under response 1-4 and expanded on directions for future exploration.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for the revisions. The additional comparator metrics, sensitivity analysis, implementation code, and use of a paired statistical test have improved the manuscript. The Eden score remains an interesting approach to comparing two-dimensional distributions. I recommend minor revision, subject to the following clarifications.

Please correct the treatment of multiple comparisons.

Taking the majority choice across three repeated presentations is a reasonable way to summarize each rater’s preference, but it does not control multiple testing across comparisons between scoring methods. Please define the family of comparisons, apply an appropriate correction, such as the Holm method, and report the adjusted p-values. Any statements about statistically significant superiority should be updated accordingly.

Please limit the human-validation conclusions to the evaluation performed.

The clarification about plot selection is helpful. However, selecting pairs because Eden disagrees with at least one comparator still produces a selected disagreement set rather than an independently sampled benchmark. The evaluation also contains only 13 unique plot pairs, and the instruction to consider all contours is closely related to Eden’s construction. These limitations do not remove the value of the experiment, but they restrict what can be concluded from it. A new human study is not essential for this revision if the abstract, results, and conclusions consistently describe the findings as agreement with human judgments on the selected contour-comparison cases. Broader superiority should remain a hypothesis for future validation.

Please reconcile the number of annuli in the description and implementation.

The Methods state that five annuli were used. However, Appendix A sets n_of_levels=5 and calculates the average using range(self.n_of_levels − 1), which appears to include four annular regions. Please clarify the relationship between contour levels and scored annuli, specify the actual setting used for the reported experiments, and make the text and code consistent.

Author Response

Comment 1-1: Please correct the treatment of multiple comparisons. Taking the majority choice across three repeated presentations is a reasonable way to summarize each rater’s preference, but it does not control multiple testing across comparisons between scoring methods. Please define the family of comparisons, apply an appropriate correction, such as the Holm method, and report the adjusted p-values. Any statements about statistically significant superiority should be updated accordingly.

Response 1-1: We appreciate this suggestion and made the following changes to the statistical tests for the validation experiment (see changes in Section 2.4): we check whether Eden score agrees with human raters more than the other scoring methods, thus conducting a one-sided Wilcoxon’s signed-rank test adjusted by Holm method. The family of comparisons are thus the six pairwise comparison between Eden and the other scoring methods. Changes of p-value and method are now updated in the manuscript as well as the plots.

Comment 1-2: Please limit the human-validation conclusions to the evaluation performed. The clarification about plot selection is helpful. However, selecting pairs because Eden disagrees with at least one comparator still produces a selected disagreement set rather than an independently sampled benchmark. The evaluation also contains only 13 unique plot pairs, and the instruction to consider all contours is closely related to Eden’s construction. These limitations do not remove the value of the experiment, but they restrict what can be concluded from it. A new human study is not essential for this revision if the abstract, results, and conclusions consistently describe the findings as agreement with human judgments on the selected contour-comparison cases. Broader superiority should remain a hypothesis for future validation.

Response 1-2: We thank the reviewer for this observation. We have now made it more explicit in both the Abstract and Results sections that the visual tests are with KDE plots. In the Discussion section, we further address this limitation by adding, ”For the simplicity of visual inspection, this work only represented contours for raters to compare the goodness-of-fit of two synthetic data. [...] Such studies would further validate the Eden score’s robustness in general settings” (Section 4.6).

Comment 1-3. Please reconcile the number of annuli in the description and implementation. The Methods state that five annuli were used. However, Appendix A sets n of levels=5 and calculates the average using range(self.n of levels-1), which appears to include four annular regions. Please clarify the relationship between contour levels and scored annuli, specify the actual setting used for the reported experiments, and make the text and code consistent.

Response 1-3: We thank the reviewer for pointing out this ambiguity. We have revised subsection 2.3.7 of the Methods section to clarify that n of levels specifies the number of contour levels, and that n annuli = n of levels - 1, because the outermost contour level does not contribute to the Eden score. We have also explicitly stated that n of levels = 5 was used throughout the reported experiments, corresponding to 4 scored annular regions. The code and reported results remain unchanged.

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you so much for authors' detailed responses, it solved all my concerns and I recommend accepting the paper.

Author Response

Thank you for your help in strengthening our paper!

Reviewer 4 Report

Comments and Suggestions for Authors

The revised manuscript has addressed all my previous comments. I am pleased with the revisions and recommend accepting the manuscript in its current form.

Author Response

Thank you for your help strengthening our manuscript!