Bridging Theory and Practice in Link Representation with Graph Neural Networks

2025-06-30

AI Summary

Prior theoretical analyses of graph neural networks (GNNs) have predominantly focused on graph-level expressivity, leaving link-level representation power largely unexplored. This work establishes the first systematic theoretical framework for link representation expressivity, introducing a unified $k_phi$-$k_ ho$-$m$ formal model family that characterizes hierarchical expressivity of mainstream GNNs in link prediction. We design the first synthetic evaluation protocol specifically tailored to link-level expressivity, uncovering the critical role of graph symmetry in predictive performance. Based on these insights, we propose a data-aware model selection principle. Theoretical analysis demonstrates that higher-order expressive models substantially outperform basic message-passing GNNs on highly symmetric graphs. By bridging a fundamental gap in the theoretical understanding of link representations, this work provides a novel paradigm for both GNN architecture design and rigorous empirical evaluation.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level representations. In this work, we shift the focus to links and provide the first comprehensive study of GNN expressiveness in link representation. We introduce a unifying framework, the $k_φ$-$k_ρ$-$m$ framework, that subsumes existing message-passing link models and enables formal expressiveness comparisons. Using this framework, we derive a hierarchy of state-of-the-art methods and offer theoretical tools to analyze future architectures. To complement our analysis, we propose a synthetic evaluation protocol comprising the first benchmark specifically designed to assess link-level expressiveness. Finally, we ask: does expressiveness matter in practice? We use a graph symmetry metric that quantifies the difficulty of distinguishing links and show that while expressive models may underperform on standard benchmarks, they significantly outperform simpler ones as symmetry increases, highlighting the need for dataset-aware model selection.

Problem

• Study GNN expressiveness in link representation, not just graph-level.
• Introduce a framework to compare link representation models theoretically.
• Assess practical impact of expressiveness on link prediction performance.

Innovation

• Introduces $k_φ$-$k_ρ$-$m$ framework for link representation
• Proposes synthetic benchmark for link-level expressiveness
• Uses graph symmetry metric for model selection