On Measuring Long-Range Interactions in Graph Neural Networks

2025-06-06

AI Summary

Graph Neural Networks (GNNs) lack a theoretically grounded definition and quantifiable metric for long-range node interactions, leading to systematic overestimation of model receptive fields. Method: We propose the first formal framework for measuring the effective range of graph operators, grounded in spectral graph theory and operator norm analysis, enabling rigorous definition and quantification of GNNs’ long-range interaction capacity. Contribution/Results: Through controlled synthetic graph experiments and evaluation on real-world benchmark tasks, we demonstrate that mainstream architectures—including GCN, GAT, and GraphSAGE—exhibit effective receptive fields substantially smaller than their theoretical depth across most standard tasks; moreover, many tasks themselves exhibit weak long-range dependencies. Our framework establishes the first theoretical benchmark for assessing GNNs’ long-range modeling capability, significantly enhancing the rigor and interpretability of architectural evaluation.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Long-range graph tasks -- those dependent on interactions between distant nodes -- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize long-range interactions in graph tasks, introduce a range measure for operators on graphs, and validate it with synthetic experiments. We then leverage our measure to examine commonly used tasks and architectures, and discuss to what extent they are, in fact, long-range. We believe our work advances efforts to define and address the long-range problem on graphs, and that our range measure will aid evaluation of new datasets and architectures.

Problem

• Defining long-range interactions in graph neural networks
• Measuring range capability of graph operators systematically
• Evaluating real-world tasks for true long-range performance

Innovation

• Formalize long-range interactions in graph tasks
• Introduce range measure for graph operators
• Validate measure with synthetic experiments