Enhancing the Utility of Higher-Order Information in Relational Learning

TL;DR

This paper evaluates hypergraph and graph neural network architectures for relational learning, revealing that graph-level models often outperform hypergraph-level ones and proposing hypergraph encodings that enhance model performance.

Contribution

The study systematically compares hypergraph and graph architectures, introduces hypergraph encodings, and provides theoretical analysis of their representational power.

Findings

Graph-level architectures often outperform hypergraph-level ones.

Hypergraph encodings improve the performance of graph-level models.

Hypergraph encodings increase the representational power of message-passing neural networks.

Abstract

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.