pathGCN: Learning General Graph Spatial Operators from Paths

Moshe Eliasof, Eldad Haber, Eran Treister
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:5878-5891, 2022.

Abstract

Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-eliasof22a, title = {path{GCN}: Learning General Graph Spatial Operators from Paths}, author = {Eliasof, Moshe and Haber, Eldad and Treister, Eran}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {5878--5891}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/eliasof22a/eliasof22a.pdf}, url = {https://proceedings.mlr.press/v162/eliasof22a.html}, abstract = {Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.} }
Endnote
%0 Conference Paper %T pathGCN: Learning General Graph Spatial Operators from Paths %A Moshe Eliasof %A Eldad Haber %A Eran Treister %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-eliasof22a %I PMLR %P 5878--5891 %U https://proceedings.mlr.press/v162/eliasof22a.html %V 162 %X Graph Convolutional Networks (GCNs), similarly to Convolutional Neural Networks (CNNs), are typically based on two main operations - spatial and point-wise convolutions. In the context of GCNs, differently from CNNs, a pre-determined spatial operator based on the graph Laplacian is often chosen, allowing only the point-wise operations to be learnt. However, learning a meaningful spatial operator is critical for developing more expressive GCNs for improved performance. In this paper we propose pathGCN, a novel approach to learn the spatial operator from random paths on the graph. We analyze the convergence of our method and its difference from existing GCNs. Furthermore, we discuss several options of combining our learnt spatial operator with point-wise convolutions. Our extensive experiments on numerous datasets suggest that by properly learning both the spatial and point-wise convolutions, phenomena like over-smoothing can be inherently avoided, and new state-of-the-art performance is achieved.
APA
Eliasof, M., Haber, E. & Treister, E.. (2022). pathGCN: Learning General Graph Spatial Operators from Paths. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:5878-5891 Available from https://proceedings.mlr.press/v162/eliasof22a.html.

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