The Expressive Power of Graph Neural Networks: A Survey

2023-08-16

IEEE Transactions on Knowledge and Data Engineering

AI Summary

Existing research on the expressive power of graph neural networks (GNNs) lacks a systematic survey and a unified analytical framework—particularly regarding enhancement strategies tailored to practical tasks such as subgraph identification and connectivity modeling. Method: This work pioneers a tripartite taxonomy—graph feature enhancement, topological enhancement, and architectural enhancement—to systematically review expressivity beyond the Weisfeiler–Lehman (WL) test, covering techniques including positional/structural role encoding, multi-hop aggregation, hypergraph modeling, and higher-order message passing. Contribution/Results: We propose a unified analytical framework that precisely characterizes expressivity boundaries and task-specific applicability for each paradigm; establish a reproducible model classification scheme; release the first open-source GNN expressivity repository; and identify key open challenges. Collectively, these contributions provide a principled, task-aware foundation for designing theoretically grounded and practically effective high-expressivity GNNs.

Abstract

Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power. Early works in this domain mainly focus on studying the graph isomorphism recognition ability of GNNs, and recent works try to leverage the properties such as subgraph counting and connectivity learning to characterize the expressive power of GNNs, which are more practical and closer to real-world. However, no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a first survey for models for enhancing expressive power under different forms of definition. Concretely, the models are reviewed based on three categories, i.e., Graph feature enhancement, Graph topology enhancement, and GNNs architecture enhancement.

Problem

• Graph Neural Networks
• Expressive Power
• Model Enhancement

Innovation

• Enhanced Graph Neural Networks
• Expressive Power
• Comprehensive Review Framework