ENAHPool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks

Zhehan Zhao, Lu Bai, Lixin Cui, Ming Li, Ziyu Lyu, Lixiang Xu, Yue Wang, Edwin Hancock
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:77310-77320, 2025.

Abstract

Graph Neural Networks (GNNs) have emerged as powerful tools for graph learning, and one key challenge arising in GNNs is the development of effective pooling operations for learning meaningful graph representations. In this paper, we propose a novel Edge-Node Attention-based Hierarchical Pooling (ENAHPool) operation for GNNs. Unlike existing cluster-based pooling methods that suffer from ambiguous node assignments and uniform edge-node information aggregation, ENAHPool assigns each node exclusively to a cluster and employs attention mechanisms to perform weighted aggregation of both node features within clusters and edge connectivity strengths between clusters, resulting in more informative hierarchical representations. To further enhance the model performance, we introduce a Multi-Distance Message Passing Neural Network (MD-MPNN) that utilizes edge connectivity strength information to enable direct and selective message propagation across multiple distances, effectively mitigating the over-squashing problem in classical MPNNs. Experimental results demonstrate the effectiveness of the proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhao25b, title = {{ENAHP}ool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks}, author = {Zhao, Zhehan and Bai, Lu and Cui, Lixin and Li, Ming and Lyu, Ziyu and Xu, Lixiang and Wang, Yue and Hancock, Edwin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {77310--77320}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhao25b/zhao25b.pdf}, url = {https://proceedings.mlr.press/v267/zhao25b.html}, abstract = {Graph Neural Networks (GNNs) have emerged as powerful tools for graph learning, and one key challenge arising in GNNs is the development of effective pooling operations for learning meaningful graph representations. In this paper, we propose a novel Edge-Node Attention-based Hierarchical Pooling (ENAHPool) operation for GNNs. Unlike existing cluster-based pooling methods that suffer from ambiguous node assignments and uniform edge-node information aggregation, ENAHPool assigns each node exclusively to a cluster and employs attention mechanisms to perform weighted aggregation of both node features within clusters and edge connectivity strengths between clusters, resulting in more informative hierarchical representations. To further enhance the model performance, we introduce a Multi-Distance Message Passing Neural Network (MD-MPNN) that utilizes edge connectivity strength information to enable direct and selective message propagation across multiple distances, effectively mitigating the over-squashing problem in classical MPNNs. Experimental results demonstrate the effectiveness of the proposed method.} }
Endnote
%0 Conference Paper %T ENAHPool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks %A Zhehan Zhao %A Lu Bai %A Lixin Cui %A Ming Li %A Ziyu Lyu %A Lixiang Xu %A Yue Wang %A Edwin Hancock %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhao25b %I PMLR %P 77310--77320 %U https://proceedings.mlr.press/v267/zhao25b.html %V 267 %X Graph Neural Networks (GNNs) have emerged as powerful tools for graph learning, and one key challenge arising in GNNs is the development of effective pooling operations for learning meaningful graph representations. In this paper, we propose a novel Edge-Node Attention-based Hierarchical Pooling (ENAHPool) operation for GNNs. Unlike existing cluster-based pooling methods that suffer from ambiguous node assignments and uniform edge-node information aggregation, ENAHPool assigns each node exclusively to a cluster and employs attention mechanisms to perform weighted aggregation of both node features within clusters and edge connectivity strengths between clusters, resulting in more informative hierarchical representations. To further enhance the model performance, we introduce a Multi-Distance Message Passing Neural Network (MD-MPNN) that utilizes edge connectivity strength information to enable direct and selective message propagation across multiple distances, effectively mitigating the over-squashing problem in classical MPNNs. Experimental results demonstrate the effectiveness of the proposed method.
APA
Zhao, Z., Bai, L., Cui, L., Li, M., Lyu, Z., Xu, L., Wang, Y. & Hancock, E.. (2025). ENAHPool: The Edge-Node Attention-based Hierarchical Pooling for Graph Neural Networks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:77310-77320 Available from https://proceedings.mlr.press/v267/zhao25b.html.

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