Mitton, J. and Murray-Smith, R. (2023) Subgraph permutation equivariant networks. Transactions on Machine Learning Research, (Early Online Publication)
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Abstract
In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of -hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.
| Item Type: | Articles |
|---|---|
| Additional Information: | Joshua Mitton was supported by a University of Glasgow Lord Kelvin Adam Smith Studentship. Roderick Murray-Smith is grateful for EPSRC support through grants EP/T021020/1, EP/R018634/1 and EP/T00097X/1. |
| Status: | Early Online Publication |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Murray-Smith, Professor Roderick and Mitton, Joshua |
| Authors: | Mitton, J., and Murray-Smith, R. |
| College/School: | College of Science and Engineering > School of Computing Science |
| Journal Name: | Transactions on Machine Learning Research |
| Publisher: | Transactions on Machine Learning Research |
| ISSN: | 2835-8856 |
| ISSN (Online): | 2835-8856 |
| Published Online: | 08 September 2023 |
| Copyright Holders: | Copyright © 2023 The Authors |
| First Published: | First published in Transactions on Machine Learning Research |
| Publisher Policy: | Reproduced under a Creative Commons license |
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