Design of Oscillatory Neural Networks Using Machine-Learned Templates
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsOverall evaluation:
This manuscript presents an Oscillatory Neural Network (ONN) based on the Kuramoto model for classifying handwritten digits from the MNIST dataset. The authors employ a 36-oscillator network, down-sample inputs to 6x6 binary patterns, optimize class prototypes using a genetic algorithm (GA), and determine weights via Hebbian learning. The work demonstrates 99% accuracy for binary classification and 75-76% for the full 10-class problem. The topic is timely and relevant to the neuromorphic computing community, which seeks energy-efficient alternatives to deep learning. However, the manuscript in its current form suffers from significant organizational, methodological, and presentational flaws that must be addressed before it can be considered for publication.
Major concerns:
1. Down-sampling to 6x6: The authors state that higher resolutions yield "marginal accuracy improvements" but provide no data or citation to support this claim. A 6x6 binary grid (36 pixels) discards an enormous amount of structural information from 28x28 MNIST digits. The claim of 99% binary accuracy on such a severely down-sampled dataset is not surprising and may overstate the model's true pattern recognition capability. A comparison with a simple baseline (e.g., a linear classifier or a small MLP on the same 6x6 input) is essential to contextualize the 75-76% 10-class accuracy.
2. Genetic Algorithm Optimization: The GA is used to optimize "prototype patterns" for each class. The fitness function is "classification accuracy from Kuramoto simulations." This risks circular logic: the GA finds prototypes that the specific ONN dynamics can separate, but these may not be representative prototypes of the actual digit classes. How do these GA-evolved prototypes compare to simple averaged or binarized class templates? This needs discussion.
3. Ensemble of 45 Binary Classifiers: The 10-class solution uses a one-vs-one ensemble of 45 binary ONNs. The computational and memory cost of training and storing 45 separate weight matrices (each 36x36) is not negligible. The authors should report the total training time and the inference cost (e.g., total number of ODE integrations) for the full ensemble. Is a single 10-class ONN with 10 output readouts not feasible?
4. The three decision strategies (Energy-based, Reference Matching, Hamming Distance) yield nearly identical accuracies (75%, 75.5%, 76%). The authors claim the Hamming distance is "most effective," but the difference is within a rounding error. Statistical significance testing (e.g., a paired t-test) is required. Without it, this is a weak conclusion.
5. The discussion on scalability (Section 6.1) claims >99.4% accuracy for resolutions up to 14x14. This is a strong claim, but no results, tables, or figures are provided to support it. The manuscript must include these data. Furthermore, using a 14x14 binary input would require a 196-oscillator network, dramatically changing the computational cost – this trade-off is not analyzed.
6. The hardware feasibility discussion (Section 6.2) extrapolates power consumption from a single VO2 device citation [6]. The authors correctly state no hardware experiments were performed, but the estimate of 468 µW for the 6x6 network is presented without accounting for the overhead of the 45 classifiers, the readout circuitry, or the GA training (which is done offline, but still relevant). This section should be significantly condensed or moved to a future work paragraph.
7. The authors state their approach is "simpler and more lightweight" than others (e.g., ClassONN, OscNet). However, they do not provide a direct, apples-to-apples comparison in terms of accuracy, number of oscillators, or energy estimates under similar assumptions. For example, ClassONN [18] claims ~72% accuracy on full-resolution (28x28) MNIST. The present work achieves 75-76% on a severely down-sampled 6x6 input. Which is more impressive? The authors must fairly compare their results to prior work using the same input resolution and task complexity.
8. What's the difference between ONN and HNN or LSM. Compared with other works, what is the key contribution or novelty?
9. The git project should be improved, such as the description, how to use and data preprocessing and GA algorithm.
10. The figures must be improved, such as the text front and size, definition.
Author Response
ANSWERS TO REVIEWER 1
First of all, we thank you for the thorough review of our paper. Below you can find our answers, also the paper has been extensively modified.
1-Down-sampling to 6x6: The authors state that higher resolutions yield "marginal accuracy improvements" but provide no data or citation to support this claim. A 6x6 binary grid (36 pixels) discards an enormous amount of structural information from 28x28 MNIST digits. The claim of 99% binary accuracy on such a severely down-sampled dataset is not surprising and may overstate the model's true pattern recognition capability. A comparison with a simple baseline (e.g., a linear classifier or a small MLP on the same 6x6 input) is essential to contextualize the 75-76% 10-class accuracy.
Response:
We thank the reviewer for this comment. We have addressed both concerns in the revised manuscript by adding a new subsection titled “Scalability, Resolution Analysis, and Baseline Comparison” in the Discussion section. First, we added a resolution analysis demonstrating that accuracy remains above 99% across resolutions from 6×6 to 14×14. Second, we added a comparison with a standard MLP baseline under identical preprocessing conditions (Table 3), showing that the GA‑ONN achieves 99.28% accuracy with only 630 coupling weights compared to 99.39% for the MLP with 1,172 parameters.
The reason we use downsampled MNIST data is that full-resolution data set requires unreasonable large and complex ONNs and also the genetic algorithm would be very time consuming to perform for all cases. The simulations we have done with the high resolution MNIST data suggest that working on the full-resolution images would have been possible. We also note that all scalability and baseline comparison experiments were performed on the binary 0‑vs‑1 classification task, which is among the easiest ones - so the 99% claim will not hold for all comparisons. We mention this in the paper now and formulate the 99% claim in this context.
- Genetic Algorithm Optimization: The GA is used to optimize "prototype patterns" for each class. The fitness function is "classification accuracy from Kuramoto simulations." This risks circular logic: the GA finds prototypes that the specific ONN dynamics can separate, but these may not be representative prototypes of the actual digit classes. How do these GA-evolved prototypes compare to simple averaged or binarized class templates? This needs discussion.
Response:
We thank the reviewer for this valuable comment. We agree that this point required clarification. The following paragraph has been added to the Materials and Methods section, specifically within the subsection "System Architecture and Evolutionary Training Process," after the description of the fitness function:
"The GA-evolved prototype patterns are optimized for phase separability within the Kuramoto dynamics and are not necessarily visually resemble the target digit classes. We observed that for certain digits, such as digit 0, the evolved prototypes retain some resemblance to the actual digit shape, whereas for others, such as digits 1 and 7, the prototypes differ substantially in visual appearance from the corresponding digit. We added the picture prototypes for ‘1’ and ‘7’ the paper to (fig 2)make the above point - they are not at all similar to averaged-out instances.
3-Ensemble of 45 Binary Classifiers: The 10-class solution uses a one-vs-one ensemble of 45 binary ONNs. The computational and memory cost of training and storing 45 separate weight matrices (each 36x36) is not negligible. The authors should report the total training time and the inference cost (e.g., total number of ODE integrations) for the full ensemble. Is a single 10-class ONN with 10 output readouts not feasible?
Response:
We thank the reviewer for this comment. A single 10-class ONN with 10 output readouts not feasible - more sophisticated training algorithms (Rudner et al. (2024)) did not succeed to get reasonable results.
The most time-consuming step is the GA optimization to find the optimal binary prototype patterns for each digit pair. However, they have to be done only ‘once’ and this pays off for inference-heavy tasks.
We emphasize that both the training and the inference can eventually be done on real oscillators (i.e. actual analog circuits) - even if our present study is a computational study on a digital computer. We emphasize this now in the paper.
For the training we distributed 10,000 samples across 32 CPU cores in parallel, requiring 3 to 4 hours in total. The optimized prototype patterns for all 45 digit pairs are provided as supplementary files in our GitHub repository at https://github.com/Mitmoayed/ONN-Classifier-Code.These details have been added to the Implementation Details section of the revised manuscript. Of course, all this heavy computation would be significantly reduced with the actual ONN hardware.
4-The three decision strategies (Energy-based, Reference Matching, Hamming Distance) yield nearly identical accuracies (75%, 75.5%, 76%). The authors claim the Hamming distance is "most effective," but the difference is within a rounding error. Statistical significance testing (e.g., a paired t-test) is required. Without it, this is a weak conclusion.
Response:
Thank you for pointing this out - this was indeed inaccurate wording from our side. Since the accuracy differences are marginal between the samples, by ‘efficiency’ we meant that this is the simplest circuitry to give good results. We phrase it now in the paper:“The end of section 3.3.3”
"Although the three methods yield similar accuracies (75%, 75.5%, and 76%), the Hamming distance approach is preferred due to its simplicity. Unlike the energy-based method, which requires matrix-vector multiplications, both the Hamming distance and reference pattern matching methods rely only on simple comparisons. Among these, the Hamming distance method offers a slight accuracy advantage while maintaining low computational cost."
- The discussion on scalability (Section 6.1) claims >99.4% accuracy for resolutions up to 14x14. This is a strong claim, but no results, tables, or figures are provided to support it. The manuscript must include these data. Furthermore, using a 14x14 binary input would require a 196-oscillator network, dramatically changing the computational cost – this trade-off is not analyzed.
Response:
We thank the reviewer for this comment. We have addressed the concerns in the revised manuscript. A dedicated subsection titled "Scalability, Resolution Analysis, and Baseline Comparison" (Section 4.1) has been added to the Discussion, which includes a classification accuracies above 99% across resolutions from 6×6 to 14×14 (see our reply to the first comment) We also clarify that the reported accuracy refers exclusively to the easy binary classification task (digit 0 vs. digit 1). Furthermore, the computational trade-off between resolution and oscillator count has been explicitly discussed, noting that increasing the input size leads to a significant increase in both simulation time and hardware requirements, and that scaling to a 28×28 input would require approximately 22 times more oscillators than the proposed 6×6 design.
We agree with the reviewer that a 196-oscillator system would be fairly complex for an MNIST-level task, but we found it important to comment on scalability since our architecture could possibly be used to more complex problems such as fashion-MNIST or CIFAR-10 or more real-life problems.
- The hardware feasibility discussion (Section 6.2) extrapolates power consumption from a single VO2 device citation [6]. The authors correctly state no hardware experiments were performed, but the estimate of 468 µW for the 6x6 network is presented without accounting for the overhead of the 45 classifiers, the readout circuitry, or the GA training (which is done offline, but still relevant). This section should be significantly condensed or moved to a future work paragraph.
Response:
We thank the reviewer for this comment. We agree that the hardware feasibility discussion required revision. The section has been condensed in the revised manuscript to the following text: "Based on published VO2 device benchmarks, a 36-oscillator ONN is estimated to consume approximately 468 µW. We note that this estimate is extrapolated from a single oscillator unit and does not account for the overhead of the 45-classifier ensemble or readout circuitry. No hardware experiments were performed in this work, and this figure should be interpreted as a back–of-envelope estimation. Circuit-level validation remains an important direction for future work."
- The authors state their approach is "simpler and more lightweight" than others (e.g., ClassONN, OscNet). However, they do not provide a direct, apples-to-apples comparison in terms of accuracy, number of oscillators, or energy estimates under similar assumptions. For example, ClassONN [18] claims ~72% accuracy on full-resolution (28x28) MNIST. The present work achieves 75-76% on a severely down-sampled 6x6 input. Which is more impressive? The authors must fairly compare their results to prior work using the same input resolution and task complexity.
Response:
We thank the reviewer for this helpful comment. In the revised manuscript, we have clarified the wording to emphasize that our approach is intended to be simple and lightweight, rather than to claim superiority over prior ONN models. The description has been updated accordingly to better reflect the intended scope of the work
“Our approach focuses on a simple and lightweight design, which makes implementation easier while still achieving competitive performance.”
- What's the difference between ONN and HNN or LSM. Compared with other works, what is the key contribution or novelty?
Response:
ONNs are closely related to Hopfield networks (see Hoppensteadt, Frank C., and Eugene M. Izhikevich. "Synchronization of laser oscillators, associativememory, and opticalneurocomputing." PhysicalReview E 62,no. 3(2000): 4010.) and it is possible to build LSMs from oscillators ()https://iopscience.iop.org/article/10.1088/1757-899X/862/5/052062). We mention it in the conclusion now
We emphasize our key conclusion in the future work session to make it clearer. The key novelty of our work is that this is the first time we use GA for optimizing templates for ONN - and this gives remarkably good results while keeping the relatively simple structure of an ONN classifier.
The novelty of our work has been mentioned in two places in the revised manuscript: in the Abstract and in Section 1.3, where we state that this is the first work to integrate genetic algorithm optimization with oscillatory neural networks, replacing manually designed templates with an automated evolutionary process that maximizes phase-based classification accuracy. This combination of GA-based template optimization with Hebbian-trained ONN dynamics has not been previously explored in the literature.
- The git project should be improved, such as the description, how to use and data preprocessing and GA algorithm.
Response:
We thank the reviewer for this suggestion. The GitHub repository has been updated as follows: the README file now includes a detailed project description, installation instructions, usage guide, data preprocessing pipeline, and genetic algorithm parameters. In addition, the optimized prototype patterns for all 45 digit pairs have been added as a supplementary file to the repository at https://github.com/Mitmoayed/ONN-Classifier-Code.
- The figures must be improved, such as the text front and size, definition.
Response:
We thank the reviewer for this comment. We have revised the figures in the manuscript. The font size and text clarity within the figures have been increased and we corrected a bug that displayed Fig 2. with the wrong aspect ratio.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors reported an oscillatory neural network (ONN) approach for handwritten digit classification using the MNIST dataset. They employed Kuramoto dynamics, Hebbian learning, and genetic algorithm optimization to achieve high accuracy on binary classification tasks. This work is interesting and an important topic in neuromorphic computing. However, prior to considering its acceptance, the authors are required to address the following issues with appropriate revisions.
(1) The authors should provide detailed information about the dataset used. Specifically, how many MNIST test samples were utilized to report the 75-76% accuracy?
(2) Sections 2 (Preliminary Work and Basics) and 3 (State of the Art in HNNs and ONNs for Image Classification) fall within the scope of the Introduction. It is recommended to reclassify these two parts as subsections and incorporate them into the Introduction part.
(3) What specific advantage does the GA-optimized approach provide for the ONN framework?
(4) Please provide a summarized table that compares the progress and benchmarks in neuromorphic computing frameworks.
Author Response
ANSWERS TO REVIEWER 2:
First of all, we thank you for the thorough review of our paper. Below you can find our answers, also the paper has been extensively modified.
1- The authors should provide detailed information about the dataset used. Specifically, how many MNIST test samples were utilized to report the 75-76% accuracy?
Response:
We thank the reviewer for the comment. The reported 75–76% multi‑class accuracy was evaluated on the full MNIST test set of 10,000 samples. For GA‑based template optimization, approximately 2,000 training samples per class pair were used, while the standard MNIST training set contains 60,000 images in total.
The requested clarification has been added at the end of the Implementation Details subsection, stating that all reported multi‑class accuracy results were evaluated on the full MNIST test set of 10,000 samples.
2- Sections 2 (Preliminary Work and Basics) and 3 (State of the Art in HNNs and ONNs for Image Classification) fall within the scope of the Introduction. It is recommended to reclassify these two parts as subsections and incorporate them into the Introduction part.
Response: We thank the reviewer for the suggestion. Sections 2 and 3 have been changed to as subsections and incorporated into the Introduction.
3- What specific advantage does the GA-optimized approach provide for the ONN framework?
Response:
We thank the reviewer for the insightful question. The GA‑optimized templates provide a clear advantage by producing class‑specific prototype patterns that maximize phase separability in the ONN. This leads to more robust Hebbian weight matrices and improves the reliability of phase‑based classification.
To clarify this contribution, we have added the following sentence to the System Architecture and Evolutionary Training Process subsection:
“The GA‑optimized templates enhance the ONN by producing class‑specific patterns that maximize phase separability and improve the quality of the Hebbian weight matrix.”
We also show in Fig 2 how simple averaged templates are different from GA-optimized ones.
4- Please provide a summarized table that compares the progress and benchmarks in neuromorphic computing frameworks.
Response :
We thank the reviewer for the helpful suggestion.
A concise summary table has now been added at the end of the State of the Art subsection to provide a clearer comparison of neuromorphic computing frameworks and their reported MNIST benchmarks.
The table is included below for convenience.
Framework MNIST Acc. Key Idea
HNN (Storkey rule) ~61% Energy-based associative memory
Kuramoto ONN (10×10) 59–65% Phase synchronization
ClassONN 70–72% Full-size Kuramoto ONN
This Work 75–76% GA-optimized Kuramoto ONN
Our work is most similar to ClassONN, because it uses similar ONN hardware for the same task. THe important difference is the GA-based optimization that improves accuracy.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis study presents the design of a lightweight, energy-efficient Oscillatory Neural Network (ONN) for image classification. The core system uses 36 coupled oscillators governed by Kuramoto dynamics.
1.What are the key components of the ONN architecture (e.g., number of oscillators, dynamical model)?
2.How does the Genetic Algorithm (GA) optimize the reference (prototype) patterns for each digit class?
3.How does the network performance hold up in the presence of noise?
4.What are the three output classification strategies, and what are their respective accuracies?
5. Some relevant reference should be cited: Nat. Mater. 2026, 25, 275-284. Nat. Nanotechnol. 2026, 21, 571–578.
Author Response
ANSWERS TO REVIEWER 3
First of all, we thank you for the thorough review of our paper. Below you can find our answers, also the paper has been extensively modified.
1-What are the key components of the ONN architecture (e.g., number of oscillators, dynamical model)?
Response:
Thank you for your question. The key components of the proposed ONN architecture are described in the Materials and Methods section. The model is built from a network of phase‑coupled oscillators governed by the Kuramoto dynamical equation. The coupling matrix for each class is constructed using a Hebbian learning rule and subsequently refined through a Genetic Algorithm. These components together define the dynamical behavior and class‑dependent structure of the ONN.For improved clarity, we have added an additional explanatory sentence at the end of Section 2.1 describing the architectural elements more explicitly.
The Kuramoto-based ONN architecture we present here is in fact a model of a real analog circuit . Large ONNs were built for different purposes (such as Insing machines [14 ]), our design is a relatively simple one for classification tasks.
2-How does the Genetic Algorithm (GA) optimize the reference (prototype) patterns for each digit class?
Response:
Thank you for your question. The optimization procedure of the Genetic Algorithm is described in the Materials and Methods section. For clarity, the GA operates on a population of candidate prototype patterns, where each individual encodes a class‑specific reference pattern. The fitness of each candidate is evaluated by measuring how well the resulting Hebbian‑derived coupling matrix separates the target class from the others in terms of phase‑synchronization behavior. The GA iteratively improves these prototypes through selection, crossover, and mutation, converging toward patterns that maximize class separability under the ONN dynamics.To make this process more explicit, we have added a clarifying sentence in Section 2.2.
The GA-evolved prototype patterns are optimized for phase separability within the Kuramoto dynamics and are not necessarily visually resemble the target digit classes. We observed that for certain digits, such as digit 0, the evolved prototypes retain some resemblance to the actual digit shape, whereas for others, such as digits 1 and 7, the prototypes differ substantially in visual appearance from the corresponding digit. We added the picture prototypes for ‘1’ and ‘7’ the paper to (fig 2)make the above point - they are not at all similar to averaged-out instances.
3-How does the network performance hold up in the presence of noise?
Response:
We sincerely thank the reviewer for highlighting the importance of evaluating the network’s behavior under noisy conditions. In response to this comment, we have added a dedicated subsection (Section 2.3.1 – Noise Robustness) to provide a quantitative analysis of the GA‑ONN performance in the presence of input phase perturbations.In this new subsection, we assess robustness by introducing random phase deviations to the input phases in a simple binary (0 vs. 1) classification task. This setup reflects realistic imperfections that may occur in analog implementations, where the programmed initial phases can deviate from their intended values. The updated results, now presented in Figure3, demonstrate that the GA‑ONN maintains stability across a wide range of noise levels: the accuracy remains above 97% for moderate deviations and only decreases to 94.5% at the maximum tested perturbation (σ = 0.8 rad).
4-What are the three output classification strategies, and what are their respective accuracies?
Response:
We thank the reviewer for raising this question. The manuscript already included a complete and clearly separated presentation of the three output classification strategies used in the binary ONN classifiers. Each method was originally provided as its own subsubsection, with full mathematical formulation and decision rules. To further improve clarity and make the performance comparison more visible, we have bold‑highlighted the accuracy values in the subsection titles. No methodological changes were made; this update is to enhance readability.
For completeness, we summarize the three strategies below:
- Energy-Based Classification
This method evaluates the Hopfield/Kuramoto energy of the test output with respect to each stored pattern (and their complements). The label is assigned to the pattern yielding the lower energy. This approach reflects the associative-memory interpretation of the ONN and captures how well the oscillator phases align with each stored attractor.
- Reference Pattern Matching
In this rule-based strategy, the final binary output vector is compared directly to the two reference patterns using exact match, inverse match, and threshold-based similarity (allowing up to six mismatches). This method provides a simple but effective way to interpret the oscillator outputs, especially when small distortions occur.
- Hamming Distance Classification
This approach assigns the label whose reference pattern (or its complement) has the smaller Hamming distance to the test output. Because the ONN outputs are binary, Hamming distance provides a natural and robust metric for classification. Among the three methods, it achieved the highest accuracy.
To provide additional context, we also explain why among the three existing strategies, the Hamming distance method is selected as the final readout in our system.
"Although the three methods yield similar accuracies (75%, 75.5%, and 76%), the Hamming distance approach is preferred due to its simplicity. Unlike the energy-based method, which requires matrix-vector multiplications, both the Hamming distance and reference pattern matching methods rely only on simple comparisons. Among these, the Hamming distance method offers a slight accuracy advantage while maintaining low computational cost."
5-Some relevant reference should be cited: Nat. Mater. 2026, 25, 275-284. Nat. Nanotechnol. 2026, 21, 571–578.
Response:
We thank the reviewer for highlighting these relevant recent works. Both suggested references (Nature Materials, 2026; Nature Nanotechnology, 2026) have now been incorporated into the Introduction section of the revised manuscript. To better situate our ONN framework within recent advances in large‑scale neuromorphic and oscillatory hardware, we added a sentence referencing these studies in the context of scalable oscillatory computing architectures.
The revised text in the Introduction now reads:
“Moreover, recent demonstrations of large‑scale neuromorphic arrays, including wafer‑scale optoelectronic computing devices [6] and monolithic oscillatory chemoreceptive chips [7], further validate the practical scalability of oscillatory computing architectures.”
Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe manuscript presents an interesting application of Oscillatory Neural Networks (ONNs) to classify MNIST digits using Kuramoto dynamics, Hebbian learning, and templates optimized via a genetic algorithm. This topic is relevant to the neuromorphic computing community. However, several issues need to be addressed before it can be accepted for publication.
- The novelty of the proposed approach should be clarified more explicitly. While the manuscript references prior work on ONN design and GA-assisted optimization, it does not clearly articulate how this method differs from previous studies.
- Since no circuit-level simulations or hardware experiments are presented, the limitations of the estimates need to be highlighted more clearly.
- The manuscript would benefit from a more thorough comparison with recent ONN-based image classification approaches, including metrics such as classification accuracy and energy efficiency.
- Providing additional details about the genetic algorithm optimization process would enhance the reproducibility of the results.
- A careful revision of the language is recommended.
- The quality of Figure 2 should be improved.
A careful revision of the language is recommended
Author Response
ANSWERS TO REVIEWER 4
First of all, we thank you for the thorough review of our paper. Below you can find our answers, also the paper has been extensively modified.
1-The novelty of the proposed approach should be clarified more explicitly. While the manuscript references prior work on ONN design and GA-assisted optimization, it does not clearly articulate how this method differs from previous studies.
Response:
We thank the reviewer for this comment. We have clarified the novelty of our approach in the revised manuscript. In the Abstract, we added the following sentence: "To the best of our knowledge, this is the first work to apply genetic algorithm optimization directly to the design of oscillatory neural networks, combining evolutionary template generation with Hebbian-based ONN training for image classification.These additions explicitly distinguish our approach from previous studies, which relied on manually designed or fixed templates rather than evolutionarily optimized ones.
The key novelty of our work is that this is the first time we use GA for optimizing templates for ONN - and this gives remarkably good results while keeping the relatively simple structure of an ONN classifier.
The approach closest to ours is ClassONN, which uses Kuramoto-based ONN dynamics and Hebbian-trained templates Link; a crucial difference is that we use GA‑optimized templates that boost accuracy without adding complexity to the network. Our work is most similar to ClassONN because it employs comparable ONN hardware for the same classification task, while the key distinction lies in the GA-based optimization that enhances accuracy beyond what is achievable with manually designed or Hebbian-only templates.
2-Since no circuit-level simulations or hardware experiments are presented, the limitations of the estimates need to be highlighted more clearly.
The paper uses the Kuramoto model, which itself is not directly related to a physical oscillator model (such as to the circuit-level description of a ring oscillator or relaxation oscillator) but can be ‘translated’ to a real circuit as it was done in several cited papers. With the likely valid assumption that the Kuramoto oscillators can be implemented by ring oscillators, one can make a back of envelope calculation of the net power consumption and on the benefits of ONN hardware. We give our back of envelope estimation in Sec. 4.2.
3-The manuscript would benefit from a more thorough comparison with recent ONN-based image classification approaches, including metrics such as classification accuracy and energy efficiency.
Response:
We thank the reviewer for this suggestion. At the end of Section 1.3, we have added a summary table (Table 1) comparing recent ONN-based and HNN-based image classification approaches, including classification accuracy and key ideas for each method (Belyaev & Velichko, 2020; Abernot & Todri-Sanial, 2023; Sabo & Todri-Sanial, 2024; Cai et al., 2025), in comparison with our proposed work.
4-Providing additional details about the genetic algorithm optimization process would enhance the reproducibility of the results.
We thank the reviewer for this comment. We have dedicated a subsection in the Materials and Methods section to describe the genetic algorithm optimization process, including the key parameters such as population size, number of generations, crossover rate, mutation rate, and fitness function. For full reproducibility, the complete implementation code is publicly available at https://github.com/Mitmoayed/ONN-Classifier-Code.
5-A careful revision of the language is recommended.
We made a few passes on the paper, refining the language, rooting out ambiguous sentences and clarifying the message as much as possible
6-The quality of Figure 2 should be improved.
Response:
Thank you for this helpful comment. The quality of Figure 2 has been improved, we corrected a bug that displayed Fig 2.its aspect ratio shows correctly now.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsI am satisfied with the overall revisions, but the size ratio between Figure 1 and Figure 2 needs to be optimized, which is a bit distorted.
Author Response
Thank you very much for the positive evaluation of our paper! We attempted to fix the aspect ratios and hope that Fig 1 and 2 looks well formatted now.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have adequately addressed all my concerns, and I recommend the acceptance of this manuscript.
Author Response
Thank you for the positive evaluation of our paper!
Reviewer 3 Report
Comments and Suggestions for AuthorsAccept.
Author Response
Thank you!
