Reachability is not enough: Diagnosing long-range behavior in GNNs

2026-09-27

AI Summary

This study addresses the challenge of verifying whether Graph Neural Networks (GNNs) effectively leverage long-range information despite possessing long-range connectivity. We propose a distance-based sensitivity analysis framework that quantifies the influence of inputs at varying graph distances, systematically disentangling architectural, approximation, and implementation constraints. Through controlled task experiments and numerical evaluations, we reveal that local message passing leads to slow influence propagation and explain the differences in learnability and stability among equivalent filters. Our findings demonstrate that structurally similar architectures exhibit significant disparities in utilizing long-range information, and that low error rates may obscure failures in long-range interactions. This work establishes new standards for evaluating the long-range capabilities of GNNs.

Abstract

Graph neural networks (GNNs) are often called long-range because their architecture can connect distant nodes, but this does not show whether they use distant information correctly. We introduce a framework that measures how strongly inputs at each graph distance affect predictions and separates limitations due to architecture, finite approximation, training, and numerical execution. Our analysis shows that local message-passing can spread influence slowly, so a finite implementation may rely mainly on nearby inputs even when the ideal computation uses the whole graph. We also explain why mathematically equivalent filters can differ in how easily they are learned and how reliably they run. Across controlled tasks, models with similar architectural reach use distant information very differently, while low average error can hide failures on distant interactions. Together, these results show that long-range capability depends on learning to use information at the distances required by the task and preserving that use during computation.

Problem

• Graph Neural Networks
• Long-range dependencies
• Reachability
• Information propagation
• Model diagnostics

Innovation

• Graph Neural Networks
• Long-range Dependencies
• Reachability Diagnosis
• Message Passing
• Influence Propagation