Expressive Higher-Order Link Prediction through Hypergraph Symmetry Breaking
Abstract: A hypergraph consists of a set of nodes along with a collection of subsets of the nodes called hyperedges. Higher order link prediction is the task of predicting the existence of a missing hyperedge in a hypergraph. A hyperedge representation learned for higher order link prediction is fully expressive when it does not lose distinguishing power up to an isomorphism. Many existing hypergraph representation learners, are bounded in expressive power by the Generalized Weisfeiler Lehman-1 (GWL-1) algorithm, a generalization of the Weisfeiler Lehman-1 (WL-1) algorithm. The WL-1 algorithm can approximately decide whether two graphs are isomorphic. However, GWL-1 has limited expressive power. In fact, GWL-1 can only view the hypergraph as a collection of trees rooted at each of the nodes in the hypergraph. Furthermore, message passing on hypergraphs can already be computationally expensive, particularly with limited GPU device memory. To address these limitations, we devise a preprocessing algorithm that can identify certain regular subhypergraphs exhibiting symmetry with respect to GWL-1. Our preprocessing algorithm runs once with the time complexity linear in the size of the input hypergraph. During training, we randomly drop the hyperedges of the subhypergraphs identifed by the algorithm and add covering hyperedges to break symmetry. We show that our method improves the expressivity of GWL-1. Our extensive experiments 1 also demonstrate the effectiveness of our approach for higher-order link prediction on both graph and hypergraph datasets with negligible change in computation.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=nyp4vOJbED&nesting=2&sort=date-desc
Changes Since Last Submission: We would like to thank the expert reviewers and the action editor for their reviewing.
These are the latest revisions:
* The paper is deanonymized
* Link to the code is available
Video: https://youtu.be/ZRiaYiN6BNw
Code: https://github.com/simonzhang00/HypergraphSymmetryBreaking
Assigned Action Editor: ~Jeff_Phillips1
Submission Number: 2999
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