Enhancing the Utility of Higher-Order Information in Relational Learning
This work addresses the problem of effectively leveraging higher-order information in relational learning for domains like social networks or biology, though it is incremental in comparing existing methods.
The paper systematically evaluated hypergraph and graph neural network architectures for relational learning, finding that graph-level models applied to hypergraph expansions often outperform hypergraph-level ones, and proposed hypergraph-level encodings that yield substantial performance gains when combined with graph-level models, with theoretical analysis showing increased representational power.
Higher-order information is crucial for relational learning in many domains where relationships extend beyond pairwise interactions. Hypergraphs provide a natural framework for modeling such relationships, which has motivated recent extensions of graph neural network architectures to hypergraphs. However, comparisons between hypergraph architectures and standard graph-level models remain limited. In this work, we systematically evaluate a selection of hypergraph-level and graph-level architectures, to determine their effectiveness in leveraging higher-order information in relational learning. Our results show that graph-level architectures applied to hypergraph expansions often outperform hypergraph-level ones, even on inputs that are naturally parametrized as hypergraphs. As an alternative approach for leveraging higher-order information, we propose hypergraph-level encodings based on classical hypergraph characteristics. While these encodings do not significantly improve hypergraph architectures, they yield substantial performance gains when combined with graph-level models. Our theoretical analysis shows that hypergraph-level encodings provably increase the representational power of message-passing graph neural networks beyond that of their graph-level counterparts.