Learning Invariant Representations of Graph Neural Networks via Cluster Generalization

Graph neural networks (GNNs) have become increasingly popular in modeling graph-structured data due to their ability to learn node representations by aggregating local structure information. However, it is widely acknowledged that the test graph structure may differ from the training graph structure, resulting in a structure shift. In this paper, we experimentally find that the performance of GNNs drops significantly when the structure shift happens, suggesting that the learned models may be biased towards specific structure patterns. To address this challenge, we propose the Cluster Information Transfer (CIT) mechanism (Code available at https://github.com/BUPT-GAMMA/CITGNN), which can learn invariant representations for GNNs, thereby improving their generalization ability to various and unknown test graphs with structure shift. The CIT mechanism achieves this by combining different cluster information with the nodes while preserving their cluster-independent information. By generating nodes across different clusters, the mechanism significantly enhances the diversity of the nodes and helps GNNs learn the invariant representations. We provide a theoretical analysis of the CIT mechanism, showing that the impact of changing clusters during structure shift can be mitigated after transfer. Additionally, the proposed mechanism is a plug-in that can be easily used to improve existing GNNs. We comprehensively evaluate our proposed method on three typical structure shift scenarios, demonstrating its effectiveness in enhancing GNNs' performance.

Paper

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Peer review

Reviewer uNQ94/10 · confidence 4/52023-07-04

Summary

This paper aims to handle the structure shift problem in GNN. The paper proposed a novel approach -- Cluster Information Transfer (CIT) to address this challenge. CIT first computes cluster center representation during training. CIT then extract the cluster center from the node embedding to retrieve the cluster-independent information. Finally CIT transfers the cluster-independent information to another random cluster center, allowing the model to learn structure-independent knowledges.

Strengths

+ Previous works like EERM, SR-GNN majorly focus on data distribution shifts on graphs, while this paper focus on graph structural shift which is of potential research interest. + The method proposed in the paper can be applied on various existing GNN backbones, the method can also fit into different type of tasks and graphs. + This paper is well-written and is easy to follow.

Weaknesses

- The CIT method proposed in the paper is not well supported by theorem. Theoretical analysis only shows that CIT weakens the affect of cluster information. However, the paper still need to answer why it is necessary to transfer nodes across clusters using Eq.8 (If the cluster information is harmful, why not just remove it?) and why can the model learn invariant representations from this process. - The method introduces a lot of additional hyper-parameters which are sensitive to the results, which are all tuned by grid-search according to the experiments settings. Finally, the accuracy improvements in the experiments is not remarkable compared with other baselines. - The method is only evaluated on small graphs with several thousand nodes, making it unknown whether the method can be applied to larger graphs.

Questions

Q1:What is the relationship between invariant representations and cluster information and why is transferring a node to another cluster reasonable ? Q2: Can CIT possibly be scaled to larger graphs?

Rating

4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

The reviewer does not see potential negative social impact of the work.

Reviewer 5H2e6/10 · confidence 4/52023-07-04

Summary

The paper introduces a new mechanism called Cluster Information Transfer (CIT) to improve the generalization ability of GNNs to various and unknown test graphs with structure shift. The CIT mechanism enhances the diversity of nodes by combining different cluster information with the nodes, which helps GNNs learn invariant representations. The paper presents experimental results on several benchmark datasets, demonstrating that the proposed CIT-GNN model outperforms existing GNN models in terms of accuracy and macro-F1 score.

Strengths

- The paper is easy to understand. - While the theory analysis is straightforward, it provides theoretically support for the proposed method. - The experiments are extensive and the results look promising.

Weaknesses

- **Fair Novelty:** The proposed method is essentially an embedding transformation function that aims to eliminate the statistic variance between clusters that causes bias and hinders generalization. The novelty comes from the clustering mechanism and the augmented training using adjusted node embeddings. However, the spectral clustering mechanism has been introduced previously, and the transformation is relatively straightforward. - **Assumptions and scope of the solution:** My second concern is about the assumptions of this paper. The paper generally assumes that there exist cluster / structural shifts between training and testing datasets. While structure could change across environments, the node labels remain invariant. The paper also implicitly assumes the node embeddings in different clusters are subject to Multivariate Gaussian distributions. These assumptions should be made explicit and formal. Moreover, the scope of structural shifts needs to be clarified. I understand that the variant of graph density or node degree can be one factor, but do other factors, e.g., edge homophily, also contribute to the shifts? A more general scope should be discussed in order to ensure its applicability. - **More validation about the claim:** The examples in the introduction considers the shifts between sparse and dense graphs. One simple baseline to mitigate it is to augment the datasets or clusters via DropEdge and AddEdge compared to modifying node embeddings. While I understand that the graph structure is complex in the real world, as the authors claimed (Line 57-59), it would be good to experimentally validate the effectiveness of the method with a simple baseline that modifies the graph structure. - **Lack of real datasets with natural shifts**: The experiments are somewhat synthetic in the sense that the training and testing sets are splitted with strong structural shifts. I wonder the performance of this method on datasets with more natural shifts, e.g., ogbn-arxiv, where the training and testing sets are splitted based on the time difference. - **Missing Related Works:** It is unclear how the proposed clustering objective differs from the existing group clustering methods, e.g., Zhou et al. [1]. **Minor:** - I feel Section 2 is not very informative since the setting is simple and the conclusion is not surprising. It would be good to demonstrate the structural shifts in more real settings or just combine this section to the introduction. - In Line139 and 149, $m$ and $M$ are both used to indicate the number of clusters. It's better to make it consistent. In general, the angle of mitigating structure shifts is interesting. However, several things above should be solved or clarified to understand its generality and effectiveness. [1] Towards Deeper Graph Neural Networks with Differentiable Group Normalization. Kaixiong Zhou, Xiao Huang, Yuening Li, Daochen Zha, Rui Chen, Xia Hu.

Questions

- The method considers the embedding space only. Thus, it seems that the method can be extended to other domains, e.g., for images. If that is the case, are there any graph-specific properties that make this solution remains on the graph domain rather than other general domains? - What's the method's performance when removing/adding 5%, 20% edges and not removing/adding any edges? Does the improvement of the method decline with the decreasing ratios?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

2 fair

Limitations

The authors discussed the limitations on the fact that the method could only apply to node-level tasks directly and the theory remain to be fully developed, as well as the limitation that the transfer remains on embedding space but graph topology.

Reviewer Nbx47/10 · confidence 4/52023-07-05

Summary

This paper focuses on the invariant learning of graph neural networks and proposes a cluster information transfer mechanism with two statistics: the mean of cluster and the variance of cluster. The authors prove that with CIT mechanism, the model is able to capture the cluster independent information, so as to improve the generalization ability across different structure shifts. Experiments on different graph benchmarks show promising results of CIT mechanism.

Strengths

Introduction and background parts are clearly written and motivate this study well. The research problem is important, the ideas are clearly clarified and all the technical steps are easy to follow. The paper provides the comprehensive experiments on different kinds of graphs to evaluate the performance of the proposed model.

Weaknesses

No specific discussions on structure shift. Time complexity analysis is not provided. The CIT mechanism is not explained sufficiently.

Questions

1. It seems that most of the graphs used here are not large enough, so what is the time complexity of the proposed model? 3. The authors design several experiments to evaluate the model, e.g., perturbate edges, multiplex graphs. Do all these changes belong to the structure shift? Can the authors provide more discussions on what changes can be considered as structure shift? 4. The paper proves that with CIT mechanism, the cluster information has less influence on the classifier, but what if the cluster information is related with the labels?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

4 excellent

Limitations

N/A

Reviewer nmEc7/10 · confidence 5/52023-07-06

Summary

The paper tackles an important question of learning invariant representations of GNNs. The authors show that once the test graph pattern shifts, the reliability of GNNs becomes compromised. Then they propose the cluster information transfer mechanism, which can be easily combined with current GNNs to improve their robustness on structure shift. The authors present numerical experiments that suggest that the proposed mechanism is effective.

Strengths

1. I enjoyed reading the paper. The presentation is clear and mostly easy to follow. 2. Clear results on different scenarios, well-backed by experiments. 3. The CIT mechanism is interesting and with technical analysis.

Weaknesses

1. In section 2, why GAT performs worse than GCN? 2. In fig.2, the model uses the node representation learned by GNNs to obtain clusters, so does the representation learned by different layers affect the clustering process? 3. The authors mentioned that the graph OOD benchmark is built, so why the datasets used in the experiments are still the traditional graphs?

Questions

It would be beneficial to answer the questions in weakness.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

3 good

Contribution

4 excellent

Limitations

N/A

Reviewer QyZE7/10 · confidence 5/52023-07-07

Summary

The paper introduces a novel Cluster Information Transfer (CIT) mechanism to enhance the generalization capability of Graph Neural Networks (GNNs) in the presence of structural shifts. The authors provide theoretical analysis, showing that the impact of cluster information on the classifier diminishes during transfer. They demonstrate that the CIT mechanism can be easily incorporated into existing models and showcase its effectiveness through extensive experiments. Overall, the paper highlights the value of the CIT mechanism in improving GNN generalization and supports its claims with comprehensive empirical evidence.

Strengths

- The paper includes both theoretical analysis and numerical results, providing a well-rounded evaluation of the proposed approach. - The idea presented in the paper is clear and well-motivated, addressing an important problem. - The experiments conducted in the paper are extensive and provide convincing evidence to support the claims made by the authors.

Weaknesses

- The experiments in section 2 are not sufficient. - The descriptions of the experimental settings are unclear and could benefit from more detailed and precise explanations. - There are some typos present in the paper that should be addressed for improved clarity and readability.

Questions

- In Section 2, the authors focus on presenting results specifically for the GCN and GAT models, but they do not mention the evaluation of other GNN models. It would be beneficial for the authors to clarify if they have considered or conducted experiments with other GNN models as well. - The authors introduce different structure shifts in their experiments, but it would be helpful to provide a clearer distinction between their approach and the OOD graph benchmarks proposed in [1]. Additionally, the paper could benefit from providing standard settings for structure shifts and including information on the label rate used in training the models. - There are several typos in the paper, such as "less affect" in line 321, "bulids" in line 315, and "Initial residual and Identity mapping two effective techniques on GCN" in line 305. These errors should be addressed to improve the clarity and accuracy of the paper. [1] Shurui Gui, Xiner Li, Limei Wang, and Shuiwang Ji. Good: A graph out-of-distribution benchmark. arXiv preprint arXiv:2206.08452, 2022.

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

4 excellent

Presentation

3 good

Contribution

4 excellent

Limitations

The authors have discussed the limitation and potential negative societal impact.

Reviewer 5H2e2023-08-12

Re author rebuttal

Thanks for the authors's response which solved part of my concerns. One concern that hasn't been addressed is that, the scope of the solution is based on the assumption of the cluster structure shifts. And I feel the response "Therefore, a structure shift might correlate to a shift in these local properties of a node, which could manifest as variations in node degree, edge density, graph size, or homophily" is not accurate, how does looking into different clusters of nodes mitigates the distribution shifts on graph size (which is global information)? Still, I prefer the author to make the assumptions more explicit and discuss how common the cluster structure shifts happen in the real-world graph datasets. Secondly, I think the authors may misunderstand my concern on Related Works. I wasn't asking about the difference between the specific clustering method and your method, but in a more general context - graph clustering methods, since it's also a crucial componant in your framework and could largely affect the performance.

Authorsrebuttal2023-08-14

We sincerely thank the Reviewer for the valuable opinions and concerns about our work. To address your concerns, we will give more explicit explanations. Here, we think that the structure shift is highly related with the local structure shift of nodes, resulting in the changes in information aggregated by nodes. For graph data, cluster information captures information from similar and connected nodes, closely related to the local properties of nodes. Meanwhile, cluster information is determined by both features and structure. When there are changes in the structure, the cluster information also changes. Thus, we utilize cluster information to model the local properties of nodes, and characterize changes in the structure through variations in clusters. And in the real world, it is also common for cluster information to change intuitively. For instance, in adversarial attack scenarios, manipulating the edges of targeted nodes can result in changes to node cluster information. Similarly, in social networks, the cluster information of users can shift based on diverse social behaviors and interactions, among other factors. As for the issue of graph size, what we want to convey is that changes in the local information of nodes may be reflected in the variation of the number of nodes, such as an increase or decrease in neighbors of the node. In this scenario, the change in the graph size is still caused by the change in the local information of nodes. Therefore, although we didn't model the graph size information explicitly, we can still enhance the performance of model in cases with shifts in graph size by making the model more robust to changes in local information. Our experiment (for details, please refer to Section 4.3) also includes this case. We train the model on the graph with 6549 nodes, while the testing graphs have both more and fewer nodes than it, and experimental results demonstrate that we have improved the performance of the models. We sincerely thank the Reviewer for spending time and providing valuable feedback, and we will make it more explicit in our paper. We are really sorry for misunderstanding your concerns about the Related Works. For the clustering part, we employed an existing spectral clustering method that falls within the scope of graph clustering methods. But the clustering method used here needs to be differentiable and capable of preventing cluster collapse to integrate with our framework. Technically, the clustering component could be substituted with other types of clustering methods to achieve different effects, which is well worth exploring and can be considered as future work. Thank you very much for your suggestions; we will add the related work on graph clustering in our paper.

Reviewer 5H2e2023-08-14

Response

I appreciate the authors' response. I agree the point that it's challenging to reasonably model domain information of graphs. The assumptions still seem a bit blurry to me but the examples make sense to me. I also read other reviewers' comments and I think it's true that the hyperparameters are a bit sensitive. I am willing to raise my score to weak accept given some of my concerns are solved.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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