Revisiting the Message Passing in Heterophilous Graph Neural Networks

Graph Neural Networks (GNNs) have demonstrated strong performance in graph mining tasks due to their message-passing mechanism, which is aligned with the homophily assumption that adjacent nodes exhibit similar behaviors. However, in many real-world graphs, connected nodes may display contrasting behaviors, termed as heterophilous patterns, which has attracted increased interest in heterophilous GNNs (HTGNNs). Although the message-passing mechanism seems unsuitable for heterophilous graphs due to the propagation of class-irrelevant information, it is still widely used in many existing HTGNNs and consistently achieves notable success. This raises the question: why does message passing remain effective on heterophilous graphs? To answer this question, in this paper, we revisit the message-passing mechanisms in heterophilous graph neural networks and reformulate them into a unified heterophilious message-passing (HTMP) mechanism. Based on HTMP and empirical analysis, we reveal that the success of message passing in existing HTGNNs is attributed to implicitly enhancing the compatibility matrix among classes. Moreover, we argue that the full potential of the compatibility matrix is not completely achieved due to the existence of incomplete and noisy semantic neighborhoods in real-world heterophilous graphs. To bridge this gap, we introduce a new approach named CMGNN, which operates within the HTMP mechanism to explicitly leverage and improve the compatibility matrix. A thorough evaluation involving 10 benchmark datasets and comparative analysis against 13 well-established baselines highlights the superior performance of the HTMP mechanism and CMGNN method.

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Reviewer Fk2z5/10 · confidence 3/52024-06-29

Summary

1. The paper unifies existing heterophilous graph neural networks (HTGNNs) into a Heterophilous Message-Passing (HTMP) mechanism. 2. The authors reveal that the effectiveness of HTMP is due to increasing differences among node representations belonging to different classes. 3. Guided by this revelation, the paper then introduces Compatibility Matrix-aware Graph Neural Network (CMGNN) to further enhance HTGNNs. 4. The authors conduct fair evaluations and comparative analysis on multiple benchmark datasets, highlighting the superior performance of the HTMP mechanism and the proposed CMGNN method.

Strengths

1. The claims are supported empirically by a detailed comparison across multiple benchmark datasets. 2. The paper is well-written and clearly structured, with each section logically building on the previous ones.

Weaknesses

1. Several research publications [1, 2, 3] have used compatible matrices to boost the effectiveness of GNNs on heterophilic graphs. In-depth qualitative and quantitative comparisons are missing from this submission. Including such analyses would significantly increase the importance of the contributions. 2. Some claims made in the paper, such as Observation 1 and Observation 2 in Section 4, would benefit from additional analysis. For instance, including theoretical analysis with formal notations would provide more rigorous support for these claims. 3. Existing survey articles have unified and categorised message passing on heterophilic graphs [4,5,6]. This submission should compare and position the proposed HTMP unification against these categorisations. 4. The experiments lack a comparison of training times with baseline models. Including an analysis of the tradeoff between accuracy and training time would greatly enhance the results. References: 1. Simplifying Node Classification on Heterophilous Graphs with Compatible Label Propagation, In TMLR'22, 2. Explicit pairwise factorized graph neural network for semi-supervised node classification, In UAI'21, 3. Graph Neural Networks with Heterophily, In AAAI'21, 4. Graph Neural Networks for Graphs with Heterophily: A Survey, 5. Learning from Graphs with Heterophily: Progress and Future, 6. Heterophily and Graph Neural Networks: Past, Present and Future. **Edit post Rebuttal:** The authors have promised to include detailed comparisons in a future revised version. Since these details cannot be verified within the review period, I will lower my confidence from 4 to 3. However, given that other major concerns have been addressed, I will raise my rating by one point from 4 to 5.

Questions

1. Were there insights on how the compatible matrices utilised in CMGNN compared with the methods in the referenced publications [1, 2, 3]? What were the pros and cons of CMGNN to tackle heterophily with existing methods that use compatibility matrices? 2. Were there theoretical foundations that support Observation 1 and Observation 2? What formal notations and theoretical analyses could be included to strengthen the support for these observations? 3. How did the proposed HTMP unification differ from the categorisations presented in the existing survey articles [4, 5, 6]? What unique insights did the HTMP unification offer compared to existing unifications? 4. What did the tradeoff between accuracy and training times of the proposed methods and the baselines look like?

Rating

5

Confidence

3

Soundness

2

Presentation

2

Contribution

2

Limitations

The authors have provided some discussion on the limitations of their work (for instance, see section 7 on Page 9). Potential negative societal impacts are not relevant to this study.

Authorsrebuttal2024-08-13

Thank you

Thank you for engaging in the discussion. We greatly appreciate your constructive comments, which have contributed to the improvement and solidity of our work! Best regards!

Reviewer GM4Z5/10 · confidence 3/52024-07-08

Summary

This work revisits the message-passing mechanisms in existing HTGNNs and reformulates them into a unified heterophilous message-passing (HTMP) mechanism. Based on HTMP, the authors propose a new framework named CMGNN. Experiments on 10 datasets with 13 different baseline models demonstrate the effectiveness of the proposed framework.

Strengths

1. This work proposes a unified heterophilous message-passing (HTMP) mechanism, which could be a guideline for further research on heterophilous GNN. 2. Based on the HTMP mechanism, this work proposes a new framework named CMGNN, which is novel and has basic value. 3. The effectiveness of the HTMP mechanism and CMGNN framework is well supported by experiment results.

Weaknesses

1. Paper presentation could be further improved. For example, the conception of "good" heterophily and "bad" homophily deserves further explanation. There are some spelling mistakes, such as "heterophilious" in line 12. 2. If space permits, I feel like moving experiments in Appendix C to the main body would be better for the introduction of *Observation 1*. 3. It might be hard to follow as this paper has so many equations, especially those about CMGNN. So I suggest providing a flow chart or a pseudo algorithm for better understanding. 4. Conclusions in this paper are mainly based on experiment results. It would be better if corresponding theoretical analysis or proofs are provided.

Questions

1. What are the contributions to the newly built benchmark datasets? It seems that this work just collects 10 existing datasets and sets them with the same train-valid-test split ratio. 2. The weighting function (Eq.9) seems to be quite empirical. Is it possible to further discuss it?

Rating

5

Confidence

3

Soundness

3

Presentation

2

Contribution

3

Limitations

As the authors mentioned, this work mainly focuses on semi-supervised settings, which could be further generalized.

Reviewer cjsi6/10 · confidence 5/52024-07-13

Summary

This paper aims to address the question of "why does message passing remain effective on heterophilous graphs" and proposes a unified framework called heterophilous message-passing (HTMP) mechanism. It extensively reviews the architecture of existing heterophilous GNNs under this framework. It then moves on to discuss the empirical observation that the success of message passing in existing heterophilous GNNs is attributed to their implicitly enhancement of the compatibility matrix among classes, and proposed a new GNN approach called CMGNN to further enhance the separability of the compatibility matrix for different classes in the message passing process. The paper includes an extensive empirical analysis involving 10 benchmark datasets and 13 well-established baseline GNNs, and show that the proposed CMGNN approach has the best overall performance against the baselines.

Strengths

- The writing is clear and well-organized for most parts of the paper; - The paper gives an extensive survey of existing message-passing GNNs under the HTMP mechanism in Table 1 and Appendix A. - The experiments are well-thought and extensive: it addresses the drawbacks of the previous homophilous and heterophilous node classification benchmarks identified in previous works by using more recent benchmark datasets, and include 13 baselines for a comprehensive evaluation of the proposed method. - The proposed approach, CMGNN, has the best overall performance against 13 baselines on 10 benchmark datasets.

Weaknesses

- This work builds upon the findings of several previous works regarding the effective designs for GNNs under heterophily and when is heterophily challenging (or in other words, "bad") for GNNs. While the authors cited these works in some parts of the paper ([6,9,12,18] in References), I feel that **some of the observations in the paper overlapped with the findings in previous works, and their connections and differences are not clearly stated in the paper**. - For example, Observation 1 seems to overlap with the previous observations made in [6] ("to ensure that the neighborhood patterns for nodes with different labels are distinguishable, the inter- class similarity should be low") and [9] ("two key factors, low-degree nodes and complex compatibility matrices, deteriorate the distinguishability of the neighborhood label distributions when coupled with heterophily, thus making heterophily a unique challenge for GNNs in most cases"). - Given this, I also think that the claim in the related work section (line 732-734) that "these reviews ... not exploring the reason behind the effectiveness of message passing in heterophilous graphs" is inaccurate, as this paper is in fact built upon these analyses regarding the effectiveness of message passing in heterophilous graphs. - Section 5 (method) is too condensed to present a clear picture of how the proposed Compatibility Matrix-Aware GNN (CMGNN) works for the readers. For example, it is unclear what "topology structure" that the authors are considering as "additional available node features", and the term in Eq. 7 is not well explained. The authors also didn't explain clearly in the main paper how is the "soft pseudo labels" being generated for the model. It will help with the understanding if the authors can include a figure showing the architecture of the proposed CMGNN model. I feel the "method" section is the most novel part in the paper and deserves more length in the paper. - It would be good to analyze the computational complexity and/or compare the empirical runtime of the model with the baselines. - As a minor point, the "Norm" term in Eq. 3 should be explained as "L1 normalization for matrix row vectors" to avoid the confusion that the normalization is done with the L1 norm for *matrix* (instead of for vectors).

Questions

- As per Weakness point 1, can you describe how the observations in the paper are connected to, and different with, prior observations in [6,9,12,18]? - As per Weakness point 2, what is the "topology structure" that you considered as "additional available node features"? How does the use of these features affect the performance of the proposed model? - Can you provide some analysis regarding the computational complexity and/or the empirical runtime of the model?

Rating

6

Confidence

5

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors acknowledged the limitation that the proposed HTMP framework is only applicable to GNNs following the message-passing mechanism. One additional limitation is that the paper is mostly empirical and does not give theoretical underpinnings.

Reviewer Fk2z2024-08-12

Thanks for the Rebuttal

Thanks to the authors for the rebuttal. The responses mostly address the concerns raised. The paper should include in-depth qualitative and quantitative comparisons with existing methods that use compatibility matrices. This should involve performance metrics, robustness tests, and case studies to highlight the differences and advantages of the proposed method compared to similar methods in the literature. The authors have promised to include these comparisons in a future revised version. Since these details cannot be verified within the review period, I will lower my confidence. However, given that all other concerns have been addressed, I will raise my rating by one point.

Reviewer cjsi2024-08-13

Response to Authors' Rebuttal

I appreciate the authors detailed response to my questions and comments. After reading authors' response, I decide to keep my original rating.

Program Chairsdecision2024-09-25

Decision

Reject

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