Enhancing the Utility of Higher-Order Information in Relational Learning

2025-02-13

AI Summary

This paper addresses the challenge of effectively modeling higher-order interactions—beyond pairwise—in relational learning. While hypergraphs naturally represent such interactions, their integration with graph neural networks (GNNs) lacks systematic architectural and theoretical analysis. To bridge this gap, the authors propose a lightweight higher-order structural encoding grounded in classical hypergraph spectral features. Crucially, they provide the first theoretical proof that incorporating this encoding into standard message-passing GNNs strictly enhances their expressive power. Empirical evaluation demonstrates that augmenting graph-level GNNs with this hypergraph encoding consistently outperforms state-of-the-art hypergraph neural networks across multiple benchmarks—achieving superior accuracy, lower computational complexity, and improved generalization. The core contribution lies in establishing that *encoding higher-order information* into conventional GNNs is more efficient and principled than designing specialized hypergraph architectures—backed by both rigorous theoretical guarantees and practical implementation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 net- work 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.

Problem

• Evaluate hypergraph vs. graph architectures
• Leverage higher-order relational information
• Enhance message-passing neural networks

Innovation

• Hypergraph architectures for relational learning
• Graph-level models outperform hypergraph expansions
• Hypergraph encodings enhance message-passing neural networks