Over-Squashing in GNNs and Causal Inference of Rewiring Strategies

2025-08-12

AI Summary

Graph Neural Networks (GNNs) suffer from the *over-squashing* problem—exponential decay of node-pair mutual sensitivity with distance—severely limiting expressive power. Prior work lacks interpretable, quantitative empirical metrics to assess over-squashing or evaluate rewiring strategies. This paper introduces the first fine-grained topological metric system grounded in mutual sensitivity decay rates between node pairs. Integrating graph-level statistics (prevalence, intensity, variability, extremity) with an intrinsic graph causal design, it establishes a *pre-training diagnostic framework* for over-squashing. Experiments reveal significant over-squashing across most graph classification benchmarks; moderate rewiring alleviates it and improves performance. In contrast, rewiring yields marginal gains in node classification and can degrade performance when excessive.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

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
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Graph neural networks (GNNs) have exhibited state-of-the-art performance across wide-range of domains such as recommender systems, material design, and drug repurposing. Yet message-passing GNNs suffer from over-squashing -- exponential compression of long-range information from distant nodes -- which limits expressivity. Rewiring techniques can ease this bottleneck; but their practical impacts are unclear due to the lack of a direct empirical over-squashing metric. We propose a rigorous, topology-focused method for assessing over-squashing between node pairs using the decay rate of their mutual sensitivity. We then extend these pairwise assessments to four graph-level statistics (prevalence, intensity, variability, extremity). Coupling these metrics with a within-graph causal design, we quantify how rewiring strategies affect over-squashing on diverse graph- and node-classification benchmarks. Our extensive empirical analyses show that most graph classification datasets suffer from over-squashing (but to various extents), and rewiring effectively mitigates it -- though the degree of mitigation, and its translation into performance gains, varies by dataset and method. We also found that over-squashing is less notable in node classification datasets, where rewiring often increases over-squashing, and performance variations are uncorrelated with over-squashing changes. These findings suggest that rewiring is most beneficial when over-squashing is both substantial and corrected with restraint -- while overly aggressive rewiring, or rewiring applied to minimally over-squashed graphs, is unlikely to help and may even harm performance. Our plug-and-play diagnostic tool lets practitioners decide -- before any training -- whether rewiring is likely to pay off.

Problem

• Measure over-squashing in GNNs using mutual sensitivity decay
• Evaluate rewiring strategies' impact on over-squashing
• Diagnose when rewiring benefits graph performance

Innovation

• Proposes mutual sensitivity decay rate metric
• Introduces four graph-level over-squashing statistics
• Develops plug-and-play rewiring diagnostic tool