A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This is a paper devoted to machine learning techniques in the context of
high energy particle collisions at the LHC at Cern. In particular, graph neural
networks (GNNs) in the task of jet tagging are derived with classical algorithms or quantum algorithms (QGNNs). The later networks are found to be much better but are 100 times as long to train than their classical counterparts. The paper comprises an introduction with the state of the art, a section on Data as used at the LHC, a section on Models (4 models) and sections on Results and Conclusions. Appendixs A, B and C complete the description.
In general, the paper has a good structure, is not difficult to read, contains
all the necessary material. The work seems fully original. The presentation is
well written and I failed to find weak points or points to improve.
My only recommendation is to provide the meaning of some short hand
notations in the abstract: AU and APIs.

Author Response

Comment: This is a paper devoted to machine learning techniques in the context of high energy particle collisions at the LHC at Cern. In particular, graph neural
networks (GNNs) in the task of jet tagging are derived with classical algorithms or quantum algorithms (QGNNs). The later networks are found to be much better but are 100 times as long to train than their classical counterparts. The paper comprises an introduction with the state of the art, a section on Data as used at the LHC, a section on Models (4 models) and sections on Results and Conclusions. Appendixs A, B and C complete the description.
In general, the paper has a good structure, is not difficult to read, contains
all the necessary material. The work seems fully original. The presentation is
well written and I failed to find weak points or points to improve.
My only recommendation is to provide the meaning of some short hand
notations in the abstract: AU and APIs.

 

Response: We thank the reviewer for the feedback. We have now defined the abbreviations in the abstract on page 1.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper provide interesting comparison between graph neural networks for specific use case. But, it can improve the quality of work if the authors provide a more detailed conclusion and discussion about the result in the section, result and analysis. In addition, authors can provide more details about the dataset. 

If the authors change the place of figures in the article (for example fig 6 is better to move to the end of page), it can improve the structure of paper.

Author Response

Comment: The paper provide interesting comparison between graph neural networks for specific use case. But, it can improve the quality of work if the authors provide a more detailed conclusion and discussion about the result in the section, result and analysis. In addition, authors can provide more details about the dataset. 

 

Response: We thank the reviewer for the feedback. In response to comments of the reviewers, we have made numerous changes throughout the text which are highlighted with the changes package.

 

Comment: If the authors change the place of figures in the article (for example fig 6 is better to move to the end of page), it can improve the structure of paper.

 

Response: We thank the reviewer for the suggestion. We have moved Figure 6 to the bottom of page 8.

Reviewer 3 Report

Comments and Suggestions for Authors

These manuscript explores the effectiveness of classical and quantum graph neural networks (GNNs) in processing data from high-energy particle collisions, especially in the use of invariant and equivariant techniques within these networks. 

Comments:

1. Although the idea is interesting, the motivation is missing in the paper. The authors are suggested to give more theoretical discussions and an intuitionistic example to strongly motivate the work.

2. The paper extensively discusses the longer training times of quantum networks without offering concrete solutions to mitigate these issues, which may limit the practicality of quantum GNNs in the near term.

3. Although equivariance is identified as a key factor in model performance, the paper provides limited insight into how equivariance principles could be more effectively leveraged within GNN architectures. Further exploration could strengthen the theoretical and practical contributions of the study.

4. The method for initializing quantum states and encoding classical data into these states is critical for quantum GNNs. However, the paper does not provide a comprehensive explanation of the encoding process or discuss potential limitations and biases introduced by this step. A more detailed exploration of the encoding strategies and their implications on the model's ability to generalize would strengthen the paper.

5. While the paper mentions the adaptation of models to handle graphs with different numbers of nodes, it does not fully address the challenge of varying graph sizes and topologies, especially in the quantum context where scalability is a significant concern. A deeper discussion on how the models maintain performance across these variations would be beneficial.

6. The conclusions of this work are heavily predicated on anticipated advancements in quantum computing. While forward-looking, this perspective might overly optimistic, considering the unpredictable pace of technological developments in quantum computing.

 

Comments on the Quality of English Language

1. Ensuring consistent use of technical terms related to both classical and quantum computing would help in avoiding confusion and improving the reader's comprehension.

2. Some sentences are overly complex or lengthy, which may hinder understanding. Simplifying these sentences could make the information more accessible to readers. 

Author Response

Comments and Suggestions for Authors

1. Comments: Although the idea is interesting, the motivation is missing in the paper. The authors are suggested to give more theoretical discussions and an intuitionistic example to strongly motivate the work.

Response: We thank the referee for the feedback. We discussed the motivation in the fifth paragraph of the introduction. We added additional details and an additional reference in lines 66-70.

2. Comments: The paper extensively discusses the longer training times of quantum networks without offering concrete solutions to mitigate these issues, which may limit the practicality of quantum GNNs in the near term.

Response: We thank the reviewer for this comment. We have added a discussion in the first paragraph of the conclusion on page 9 in lines 235-240.

3. Comments: Although equivariance is identified as a key factor in model performance, the paper provides limited insight into how equivariance principles could be more effectively leveraged within GNN architectures. Further exploration could strengthen the theoretical and practical contributions of the study.

Response: We thank the referee for the feedback. We have added an additional reference in paragraph four of the introduction on page two in line 58. We already discussed other ideas of equivariance in paragraph two of section 3.1 in lines 153-156. A more detailed study is underway and will be presented in a future publication.

4. Comments: The method for initializing quantum states and encoding classical data into these states is critical for quantum GNNs. However, the paper does not provide a comprehensive explanation of the encoding process or discuss potential limitations and biases introduced by this step. A more detailed exploration of the encoding strategies and their implications on the model's ability to generalize would strengthen the paper.

Response: We thank the referee for the recommendation. We discuss the encoding process in the first paragraph of section 3.4 on page 7 in lines 183-187.  We agree with the referee that there are alternative encoding methods, but their detailed comparison is beyond the scope of this paper.

5. Comments: While the paper mentions the adaptation of models to handle graphs with different numbers of nodes, it does not fully address the challenge of varying graph sizes and topologies, especially in the quantum context where scalability is a significant concern. A deeper discussion on how the models maintain performance across these variations would be beneficial.

Response: We thank the reviewer for their insight. We mention a solution to this in the second to last paragraph of the introduction on page 3 lines 85-87. We justified our use of reduced graph sizes by truncating particles which are too soft to be relevant for the experimental analysis.

6. Comments: The conclusions of this work are heavily predicated on anticipated advancements in quantum computing. While forward-looking, this perspective might overly optimistic, considering the unpredictable pace of technological developments in quantum computing.

Response: We thank the referee for the comment with which we agree. As a result, we shall track the progress and development of quantum hardware and software to check these concerns in the future.

Comments on the Quality of English Language

Ensuring consistent use of technical terms related to both classical and quantum computing would help in avoiding confusion and improving the reader's comprehension. Some sentences are overly complex or lengthy, which may hinder understanding. Simplifying these sentences could make the information more accessible to readers. 

We thank the referee for the feedback. We have proofread the paper and made numerous edits to clarify the terminology and language.