Hyperbolic Graph Neural Networks at Scale: A Meta Learning Approach

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper, we aim to alleviate these issues by learning generalizable inductive biases from the nodes' local subgraph and transfer them for faster learning over new subgraphs with a disjoint set of nodes, edges, and labels in a few-shot setting. We introduce a novel method, Hyperbolic GRAph Meta Learner (H-GRAM), that, for the tasks of node classification and link prediction, learns transferable information from a set of support local subgraphs in the form of hyperbolic meta gradients and label hyperbolic protonets to enable faster learning over a query set of new tasks dealing with disjoint subgraphs. Furthermore, we show that an extension of our meta-learning framework also mitigates the scalability challenges seen in HNNs faced by existing approaches. Our comparative analysis shows that H-GRAM effectively learns and transfers information in multiple challenging few-shot settings compared to other state-of-the-art baselines. Additionally, we demonstrate that, unlike standard HNNs, our approach is able to scale over large graph datasets and improve performance over its Euclidean counterparts.

Paper

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Peer review

Reviewer Ft7q5/10 · confidence 4/52023-06-16

Summary

This paper introduces the model, Hyperbolic GRAph Meta Learner (H-GRAM), that learns transferable information from a set of support local subgraphs using hyperbolic meta gradients and label hyperbolic protonets to enable faster learning over a query set of new tasks disjoint subgraphs. The model is evaluated on downstream tasks of both node classification and link prediction. The experiments and ablation studies show that H-GRAM effectively learns and transfers information in few-shot settings and outperforms its Euclidean counterparts.

Strengths

In general, the paper is well written and the model introduces some novel contributions. Further, regarding experiment results, the model seems outperform all the baselines consistently on tasks of link prediction and node classification. The ablation studies from varying the base HNN model and deleting individual meta-learning components are informative to better understand the influence of the various components in the model and the final proposed architecture.

Weaknesses

- In the Related Work section on Hyperbolic Neural Networks, the following important reference is missing regarding HNNs for large scale datasets (from the knowledge graph domain) from recent work: [KDD 2022] Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '22). Association for Computing Machinery, New York, NY, USA, 676–686. https://doi.org/10.1145/3534678.3539350 - In the problem setup section, can the authors more clearly explain the properties of the graph (e.g., directed/undirected, what do the nodes/edges represent etc.)? - Regarding experiments, it would be useful to see the model performance on both inductive as well as transductive tasks. Furthermore, can the authors provide more details on the dataset statistics such as number of vertices and edges and the domain of the dataset to get a better indication of the data size? - I also have a concern about the scalability of the model especially since non-Euclidean space embedding models tend to converge very slowly and Mobius computations are more computationally expensive compared to the Euclidean space. Can the authors provide some model complexity analysis (e.g., runtime/memory complexity)?

Questions

Please see weaknesses section above.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited 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

3 good

Presentation

2 fair

Contribution

3 good

Limitations

Authors have sufficiently identified limitations of the prior work and addressed it in their proposed model. It would also be helpful if the authors provide future directions for their work.

Reviewer Urvd5/10 · confidence 3/52023-07-05

Summary

This submitted work identifies an important research problem of existing works, scalability of hyperbolic neural network to large graphs and previously unseen graphs. To achieve these two goals, this work first proves that node classification and link prediction can be done with a node's local neighborhood only. Based on this insight, this work designs a meta-learning mechanism for hyperbolic graph neural networks to scale on large graphs. Experiments on both small and large graphs show the effectiveness of the proposed model.

Strengths

1. This paper proposes an interesting and important research problem, scalability of hyperbolic graph neural networks on large datasets. With a theoretical analysis and a meta-learning based model achitecture, this paper shows promising performance over baseline models. 2. This paper is self-contained, with enough introduction to background knowledge, such as meta-learning and operations in hyperbolic space, in Appendix. 3. Experiments are comprehensive with both small and large graphs, with baselines from different categories, and with both node classification and link prediction tasks.

Weaknesses

1. Introduction section contains too much redundant content. Introduction section should provide a general and overall picture of the paper, while this submitted work introduces too much model architecture and details in the Intro section. I suggest authors to remove some content and better emphasize the key innovation proposed in the paper. Paper writing can be imporved. 2. I can see standard deviation of experiment results in most of the tables, but Table 1 doesn't have std. dev.

Questions

1. Why is standard deviation at Table 1 absent? 2. This paper uses Poincare ball as the hyperbolic model for illustration. I am wondering if the proposed model is also applicable when Hyperboloid model is used.

Rating

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

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

I can't see any potential negative societal impact of their work.

Reviewer qW7m5/10 · confidence 4/52023-07-05

Summary

The paper introduces a method, Hyperbolic GRAph Meta Learner (H-GRAM), to improve the scalability and generalization of Hyperbolic Neural Networks (HNNs). H-GRAM learns from local subgraphs and transfers this learning to new, disjoint subgraphs in a few-shot setting. The authors demonstrate that H-GRAM outperforms existing methods in various few-shot settings and scales effectively over large graph datasets.

Strengths

The paper presents a new approach, H-GRAM, that combines meta-learning with hyperbolic neural networks (HNNs) to address their scalability and generalization issues. The quality of the work is evident in the detailed explanation of H-GRAM and its demonstrated effectiveness in comparison with baselines.

Weaknesses

* There are a few areas where it could potentially be improved: * Comparison with Other Meta-Learning Approaches: The paper could include a comparison of H-GRAM with other meta-learning approaches in table 2 and 3, not just with other HNNs. This would provide a broader context for understanding the performance and advantages of H-GRAM. * Limited contribution * This work seems just extend paper[1]'s work to hyperbolic and present some trivial definitions and theorem. * Lack of important references [2-4] to make comparisons. [1]Huang, Kexin, and Marinka Zitnik. "Graph meta-learning via local subgraphs." Advances in neural information processing systems 33 (2020): 5862-5874. The proposed method is close to this paper. Please make a detailed comparison with the method. [2] Yu, Tao, and Christopher De Sa. "Random Laplacian Features for Learning with Hyperbolic Space." arXiv preprint arXiv:2202.06854 (2022). They also said that their method is scalable. Please compare with their method. [3] Zhang, Yiding, et al. "Lorentzian graph convolutional networks." Proceedings of the Web Conference 2021. 2021. They developed a new HGNN with the aggregation in the manifold, could you provide your definition and theorem in such a case? [4] Yang, Menglin, et al. HGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning. KDD 2023. They also derive the node influence in the case of tangent space.

Questions

see weaknesses Additionally, a lot of HNN or HGNNs are formulated within the manifold. Could you deduce the node influence and establish the information loss without utilizing a logarithmic map (i.e., relying on tangent space)? If you use a logarithmic map, could you derive the conclusion using a local reference point other than the origin point since you say that "we use the local tangent space of Poincare ball model to prove that the local neighborhood policy holds better for HNN models?"

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited 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

3 good

Presentation

3 good

Contribution

2 fair

Limitations

not mentioned.

Reviewer UWvg8/10 · confidence 4/52023-07-05

Summary

The authors propose applying the MAML methodology to hyperbolic GNNs in a novel local manner, along with continuous label prototypes, that enables them to scale the HNN approach from a few thousand nodes to a few million nodes. The authors provide theoretical justification for this local H-GRAM approach via theorems 1 and 2 and demonstrate its efficacy via a large set of experimental comparisons in Sec. 4 and 5.

Strengths

1. The four research questions from Sec. 4 regarding the novel HGRAM approach are comprehensively answered via comparison on multiple different datasets with competing Euclidean MAML approaches, standard hyperbolic baselines, other graph MAML approaches such as G-Meta [17], Meta-GNN [38], protoNET[29] and ablation studies. H-GRAM clearly outperforms competing meta-learning / protoNET approaches on large graphs in Table 1 and is comparable with competing hyperbolic approaches on small graphs in Table 2. 2. The authors provide theoretical justification for their local H-GRAM approach via theorems 1 and 2.

Weaknesses

1. Some of the mathematical presentation could be shortened, e.g., the same symbol $D_{g\mu}^{p_i}$ is defined in both theorems 1 and 2. 2. The authors limit their meta-learning enhancements to hyperbolic neural networks, but it is not clear if their enhancements can be applied to superior pseudo-Riemannian approaches, e.g., Pseudo-Riemannian Graph Convolutional Networks, NeurIPS 2022, and Ultrahyperbolic Neural Networks, NeurIPS 2021. 3. The authors' approach seems quite similar to G-Meta [17], although their experimental results seem to be slightly better in Table 1. Presumably it is the hyperbolic modeling (and RSGD) or the continuous label prototypes that allows H-GRAM to outperform G-Meta, but such explanations or other explanations are not discussed. 4. In Sec. 5.4, it is not discussed why HGCN outperforms HMLP and HAT. In other studies, attention-based GNNs sometimes outperform GCNs, so some explanation appears to be necessary. The SG, SL setting on the Cora dataset from Table 2 could be considered in the ablation study in Table 3 to help answer this question.

Questions

Please note the questions inherent in weakness 2, 3 and 4.

Rating

8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and 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

4 excellent

Presentation

3 good

Contribution

3 good

Limitations

It is not clear if weakness 2 above constitutes a limitation or whether it is simply a case where no theoretical justification can be provided for an ulterhyperbolic-GRAM variant, for example.

Reviewer 4N275/10 · confidence 2/52023-07-07

Summary

This paper introduces H-GRAM, a novel meta-learning model for scalable Hyperbolic Graph Neural Networks. H-GRAM leverages meta-learning techniques to learn from from local subgraphs and adapt quickly to new tasks. The authors theoretically establish that HNNs are dependent on the local neighborhood of nodes for prediction and formulate HNNs to encode node-centric local subgraphs using the locality of tangent space transformations. Experiments conducted on various benchmark datasets to illustrate that H-GRAM addresses several HNNs tasks such as inductive learning, over-smoothing elimination, and few-shot learning in various demanding situations.

Strengths

- The paper presents a novel approach that combines hyperbolic geometry and meta-learning techniques, which is innovative and interesting. - The proposed H-GRAM is scalable and efficient compared to previous HNN techniques. - Extensive and carefully designed experiments have been conducted to demonstrate the effectiveness of H-GRAM

Weaknesses

For results listed in table 2, why did H-GRAM never achieve the best performances for both of node classification and link prediction at the same time among all datasets? Could you explain the reason behind this discrepancy between tasks?

Questions

I don't have further questions.

Rating

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

Confidence

2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

2 fair

Contribution

2 fair

Limitations

The authors adequately addressed the limitations.

Reviewer UWvg2023-08-16

Thank you for your response

I want to thank the authors for their thoughtful rebuttals to all reviewers. I am satisfied by their responses to all my concerns. Although I have rated this submission more positively than any other reviewer, I wish to retain my original rating.

Reviewer qW7m2023-08-17

Thanks for the response

Thanks to the author for their reply. My concerns have been addressed and i could like to raise my score

Authorsrebuttal2023-08-18

Thanks a lot for your consideration

Dear Reviewer, We truly appreciate your active participation and the constructive feedback you've provided. Your thoughtful review has played a pivotal role in enhancing the quality of our manuscript. As we approach the final stages of our interaction, we're here to continue our exchange of ideas if you have any more inputs to offer prior to the impending deadline.

Authorsrebuttal2023-08-18

Gentle Reminder

Dear Reviewer, We extend our heartfelt gratitude for your valuable engagement and insightful feedback! As we near the conclusion of the author-reviewer discourse, we kindly request your consideration for a potential upward revision of your evaluation, given our responses. We remain open to further dialogue should you have additional insights to share before the impending deadline.

Authorsrebuttal2023-08-18

Gentle Reminder

Dear Reviewer, We truly appreciate your active participation and the constructive feedback you've provided. Your thoughtful review has played a pivotal role in enhancing the quality of our manuscript. As we approach the final stages of our interaction, we cordially inquire if you might be inclined to reconsider your assessment, considering the comprehensive responses. We're here to continue our exchange of ideas if you have any more inputs to offer prior to the impending deadline.

Authorsrebuttal2023-08-18

Gentle Reminder

Dear Reviewer, We sincerely thank you again for your insightful review. We have worked hard to comprehensively address your comments in the rebuttal, including new requested results, as well as providing appropriate responses addressing other questions. The impact of your discerning review is unmistakable. With the conclusion of our author-reviewer interactions drawing near, we respectfully inquire whether you might consider revising your assessment upwards, given our responses. Your continued insights are of great value to us, and we welcome any additional thoughts before the impending deadline.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

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