Non-convolutional Graph Neural Networks

Rethink convolution-based graph neural networks (GNN) -- they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a simple graph learning module entirely free of convolution operators, coined random walk with unifying memory (RUM) neural network, where an RNN merges the topological and semantic graph features along the random walks terminating at each node. Relating the rich literature on RNN behavior and graph topology, we theoretically show and experimentally verify that RUM attenuates the aforementioned symptoms and is more expressive than the Weisfeiler-Lehman (WL) isomorphism test. On a variety of node- and graph-level classification and regression tasks, RUM not only achieves competitive performance, but is also robust, memory-efficient, scalable, and faster than the simplest convolutional GNNs.

Paper

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Peer review

Reviewer jBUd6/10 · confidence 2/52024-06-26

Summary

This paper proposes a random walk-based graph neural network, where an RNN is used to combine the topological and semantic graph features along the walks. The proposed RUM model is free of convolution operators and does not suffer from the limited expressiveness, over-smoothing, and over-squashing, which are commonly faced issues in convolution-based GNNs.

Strengths

This paper proposes a non-convolutional GNN, named RUM. The benefits of this model over convolutional GNNs are elaborated both theoretically and empirically.

Weaknesses

Empirically, the gains with RUM are marginal and in some cases, RUM is worse than the baselines. The organization and the presentation of the paper can be further improved. 1. There are too many hyper-references. Most of the hyper-references in Section 1 and Section 2 are unnecessary, especially when reading the paper for the first time. 2. There are too many supplementary demonstrations (...) Some additional information could be helpful, but too many will hinder the reading. It would be better to reorganize the sentences to make the presentation smoother. 3. There are some grammar mistakes, like in line 244. Proofreading is needed.

Questions

1. In Lemma 6, the author shows that RUM increases Dirichlet energy. Why would this be helpful intuitively? As for homophily graphs, GNNs should decrease the Dirichlet energy. This phenomenon is also analyzed in [1,2]. It seems RUM is not just alleviating over-smoothing, but is anti-smoothing. 2. In line 243, the author claims that RUM almost always outperforms SOTA architectures, this is not true according to the results. [1] Interpreting and unifying graph neural networks with an optimization framework [2] A Unified View on Graph Neural Networks as Graph Signal Denoising

Rating

6

Confidence

2

Soundness

3

Presentation

2

Contribution

3

Limitations

The authors adequately discussed the limitations.

Authorsrebuttal2024-08-08

Clarification on the over-smoothing behavior

Dear Reviewer `jBUd`, Please let us know if our rebuttal has addressed your concerns, especially about the clarification on the over-smoothing behavior. Thank you!

Reviewer jBUd2024-08-10

Official Comment by Reviewer jBUd

Thank you for the detailed responses. Your clarifications relieve most of my concerns. I have increased the score.

Authorsrebuttal2024-08-10

Thank you!

Thank you, Reviewer `jBUd`, for your comment and for raising the score. Please don't hesitate to let us know if you have any further questions!

Reviewer xhjS6/10 · confidence 3/52024-07-07

Summary

The paper introduces Random Walk with Unifying Memory (RUM), a non-convolutional graph neural network (GNN) that addresses limitations like limited expressiveness, over-smoothing, and over-squashing typically associated with convolution-based GNNs. RUM leverages random walks and recurrent neural networks (RNNs) to merge topological and semantic graph features, theoretically showing and experimentally verifying its enhanced expressiveness over traditional methods like the Weisfeiler-Lehman (WL) isomorphism test. It demonstrates competitive performance on node- and graph-level tasks while offering advantages in efficiency and scalability.

Strengths

1. RUM introduces a new paradigm in GNNs by eliminating convolutions and leveraging random walks and RNNs for enhanced graph representation. 2. The presentation of the paper is generally clear and coherent. The authors effectively contextualize their work relative to existing literature, highlighting the novelty of RUM and its contributions to the field of graph representation learning. 3. The theoretical advancements (e.g., expressiveness proofs) and empirical results clearly demonstrate the advantages of RUM over traditional convolutional GNNs. The findings are valuable for advancing graph representation learning techniques and are likely to influence future research directions.

Weaknesses

The paper lacks detailed exploration on how varying random walk lengths impact RUM's performance across diverse tasks and whether optimal lengths are identified for different types of graphs or datasets. Additionally, while the paper highlights RUM's superiority over expressive GNNs in specific scenarios, it overlooks potential limitations when compared to these models, such as not thoroughly investigating upper bounds on the WL test, which could gauge RUM's discriminative power against more expressive GNNs.

Questions

1. Can you elaborate on how the choice of random walk length $𝑙$ impacts the performance of RUM across different tasks? Are there optimal lengths identified for specific types of graphs or datasets? 2. In practical applications, how does RUM handle graph datasets with varying degrees of sparsity? Are there specific strategies employed to ensure robust performance across different graph structures? 3. While the paper demonstrates that RUM outperforms expressive GNNs in certain scenarios, it lacks exploration of scenarios where RUM might face challenges or limitations compared to expressive GNNs. For instance, it does not thoroughly investigate potential upper bounds on the WL test, which is a standard measure of graph isomorphism and could provide insights into the discriminative power of RUM compared to more expressive GNNs.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes, The authors have addressed several limitations in the Limitations section.

Reviewer wXB77/10 · confidence 4/52024-07-12

Summary

The paper introduced a new graph neural network that is not based on convolution but on the random walk. Based on the results of the extensive experiment, the proposed architecture is effective for heterophilic graphs and long-range graphs.

Strengths

1. The experiment results include different tasks on different graphs, also, it is faster than baselines. 2. Theoretical analysis is conducted to show that the proposed architecture is more expressive. 3. Theoretical analysis shows that the proposed architecture is effective in overcoming over-squashing and over-smoothing issues.

Weaknesses

Currently, the proposed architecture only works on unweighted and undirected graphs.

Questions

Can the proposed method work well on directed and weighted graphs?

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

N/A

Reviewer P1Jd7/10 · confidence 4/52024-07-28

Summary

The authors of the paper proposed a non-convolution based approach to solve graph learning tasks using random walks and recurrent neural networks (RNNs), namely a random walk neural network with unifying memory (RUM). Random walks, together with the “anonymous experiment” function, allow to extract topological and semantic information from the graph, while an RNN and a feed-forward neural network take care of “unifying” the features collected from the walks. Research questions on the ability of the model to be more expressive than classical GNNs and to reduce oversmoothing and oversquashing have been answered positively both theoretically and experimentally. The experimental section, along with the appendix section, presents several experiments, ablation studies, training details, and theorem proofs. The code is available.

Strengths

Originality: Novelty is fair/good. The proposed approach can be considered original by choosing to propose a model that does not use the graph convolution operator at all, which is the most widely used approach in the state of the art. In this way, it alleviates the problems associated with convolutions (e.g., oversmoothing, oversquashing) while maintaining or even improving performance. Random walks and RNNs (more specifically GRUs) are not new methodologies, but they are combined in an original way on graph learning. Quality: The quality of the proposed paper is good. The claims and solutions are technically sound. They present theoretical and experimental proofs of their proposed approach. Clarity: The clarity of the paper is good. It is well written and organized. The best results in the tables should be in bold or more visible. Significance: The significance of the paper is medium-high. They proposed an effective method to avoid convolutions in GNNs that effectively outperforms and competes with SOTA methodologies.

Weaknesses

Weakness: The paper lacks a discussion on the proposed method and Graph Transformer architectures. Although they are present in the experimental comparisons on the node classification task in Table 9, Graph Transformer is actually a well-known solution that does not rely on convolutions and can mitigate the over-squashing and oversmoothing problems [1,2]; the discussion should also considering the different computational costs of the two approaches. Ref. [1] "Attending to Graph Transformers", Luis Müller and Mikhail Galkin and Christopher Morris and Ladislav Rampášek, 2024, https://arxiv.org/abs/2302.04181 [2] "Do Transformers Really Perform Bad for Graph Representation?", Chengxuan Ying et. al., 2021, https://arxiv.org/abs/2106.05234

Questions

1) At Table.5, showing Graph Regression comparisons on ESOL, FreeSolv and Lipophilicity datasets, it seems to me that for the MoleculeNet [1] benchmark you used the results presented in their papers about the XGBoost model (best performing among conventional methods) with (0.99, 1.74, 0.799) RMSE scores, respectively to the three datasets, instead using them from the best performing graph-based methods which are (0.58,1.15) for ESOL and FreeSolv datasets by using the MPNN model and 0.655 for Lipophilicity dataset by using GC model, which are the best models in these datasets. This is in contrast on what you said in the caption of Table. 5, since those presented are not the best results and models of [1]. Ref. [1] "MoleculeNet: a benchmark for molecular machine learning", Wu, Zhenqin and et. al., "Chem. Sci.",2018, doi:10.1039/C7SC02664A, url:http://dx.doi.org/10.1039/C7SC02664A

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors have adequately discussed the potential negative societal impact and the current limitations of their work.

Authorsrebuttal2024-08-07

Clarification on the concept of "upper bounds of the WL test"

Hi Reviewer `xhjS`, Thanks again for your feedback! We had a question on the meaning of "upper bounds of the WL test", does it mean the dimension of the $k$-WL test? If that's the case, in the rebuttal we had reworked our **Corollary 4.1** to incorporate a comparison with the $k$-WL test. Please let us know if we have interpreted your comments correctly. We will provide more thorough comparison and discussion to further address your comments if that is not the case. Thank you!

Authorsrebuttal2024-08-10

Correction: to remove the length condition in the new Corollary 4.1

After careful checking, we find that the condition of walk length $k$ has to be removed in the new Corollary 4.1 reworked during the rebuttal. (See this [post](https://openreview.net/forum?id=JDAQwysFOc&noteId=GFBlZllWUU)) We would be grateful if you could cast more light on the concept of "upper bounds of the WL test" and whether a comparison with the $k$-WL test would be sufficient.

Reviewer xhjS2024-08-10

Satisfied with the answers

Thank you for your update and for revisiting Corollary 4.1. I appreciate the authors' detailed response. I am satisfied with the answers and will maintain my original score.

Authorsrebuttal2024-08-11

Thank you!

Thanks again, Reviewer `xhjS`! Please let us know if you have any further questions, or if you think of more ways to characterize the WL upper bound.

Authorsrebuttal2024-08-08

Directed and weighted graphs

Dear Reviewer `wXB7`, We believe that our rebuttal has sufficiently addressed your concern around the limitations when it comes to the weighted and directed graphs---both of which are possible with some slight modifications. Please let us know if you have any further questions!

Reviewer wXB72024-08-10

Thanks authors for the response. I don't have other concerns, so I keep my score.

Authorsrebuttal2024-08-08

Comparison with graph transformers

Dear Reviewer `P1Jd`, We have included extensive conceptual discussion and additional experiments to incorporate your suggestion of comparing with graph transformer models. Please let us know if you have further questions, we will make sure to address them in the discussion period!

Authorsrebuttal2024-08-11

Conceptual and experimental comparison with graph transformers

Dear Reviewer `P1Jd`, As the discussion period is drawing to a close, we just wanted to bring your attention to the new conceptual and experimental comparison with graph transformers. Since this was the main part of the **weaknesses** section in your review, we would be grateful to know whether this concern has been addressed and if you would consider raising the score. If your concerns have not been addressed, please let us know and we will strive to provide more analysis, experiments, and discussion to provide more clarification! Thanks again for your valuable input!

Reviewer P1Jd2024-08-11

Thank you authors. I don't have any concerns. Based on your response and modification, I've increased the score.

Authorsrebuttal2024-08-11

Thank you!

Thank you, Reviewer `P1Jd` for your comment and for raising the score!

Authorsrebuttal2024-08-09

Please let us know if we have addressed your concerns

Dear Reviewers and Area Chairs, Please let us know if the rebuttal we provided has addressed your concerns. If you have more pending questions, we would be more than happy to carry out more analysis and experiments in the discussion period to address them! Thank you again for your valuable suggestions!

Area Chair bArP2024-08-10

As the authors suggest (and due to the size of the rebuttal), I invite all reviewers to share their main concerns before the rebuttal deadline, to have sufficient time for discussion. I'd be especially interested in feedback from reviewer `jBUd`, who gave the most negative review as of now. Thanks, the AC

Authorsrebuttal2024-08-10

Thank you!

Thank you, Area Chair `bArP`, for inviting all reviewers to discuss the remaining concerns!

Authorsrebuttal2024-08-10

Correction: to remove the length condition in the new Corollary 4.1

After careful checking, we find that the condition of walk length $k$ has to be removed in the new Corollary 4.1 reworked during the rebuttal: **Corollary 4.1** (RUM is more expressive than k-WL-test.) Up to the Reconstruction Conjecture, two graphs with $G_1 , G_2$ labeled as non-isomorphic by the $k$-dimensional Weisfeiler-Lehman ($k$-WL) isomorphism test, is the necessary, but not sufficient condition that RUM can distinguish them.

Program Chairsdecision2024-09-25

Decision

Accept (spotlight)

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