Get a GRIP, this will be a long TRIP: A Quantifiable Long-Range Framework for Verifying Over-squashing

2026-10-02

AI Summary

This study addresses the lack of verifiability in existing long-range Graph Neural Network (GNN) benchmarks, which are susceptible to saturation by short-range models and inherently tied to specific topologies. We propose the TRIP/GRIP framework, introducing the first certifiable axiom system for long-range dependencies over arbitrary graphs. By leveraging stationary distribution sampling and maximum likelihood estimation, we construct provably long-range tasks and derive closed-form likelihood lower bounds to quantify prior errors, audit benchmarks, and decouple topological from computational bottlenecks. Our analysis reveals critical failure modes in mainstream benchmarks, demonstrates that curvature is uncorrelated with performance, and elucidates the multifactorial origins of oversquashing. Ultimately, this work establishes a rigorous theoretical foundation and analytical paradigm for evaluating long-range dependencies in GNNs.

Abstract

Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validate them genuinely require long-range interactions. The de-facto standard, the Long Range Graph Benchmark, has been repeatedly shown to be saturated by tuned short-range models, with existing synthetic alternatives being tied to specific topologies. As such, there is a lack of principled certificate of long-rangedness on arbitrary graphs. This state reflects the absence of a precise characterization of long-ranged benchmarks. We address this fundamental gap by introducing four verifiable axioms: Predictability, Tightness, Strictly $k$-Range, and Topology-Invariance, that any task claiming to test $k$-hop interactions must satisfy. We formally prove that violating any one of them admits failure modes that undermine conclusions drawn from the task. Based on these axioms, we introduce TRIP (Truly Ranged Interactions Problem) and its generalisation GRIP (Generally Ranged Interactions Problem), constructive procedures that turn any graph into a provably long-ranged task by drawing features from stable distributions. Moreover, by construction, GRIP admits a closed-form, per-range Maximum-Likelihood oracle that yields the first a priori per-range lower bound on test error available on any benchmark. Using our framework, we: (i) audit 4 common long-range benchmarks and identify their failures modes with respect to our axioms; (ii) on TRIP-instantiated topologies, we find a popular notion of curvature is uncorrelated with GNN performance, supporting topological-vs-computational bottleneck distinction; and (iii) we show that a novel benchmark's over-squashing measures factors beyond pure long-rangedness. Code to use the framework and reproduce experiments is released https://github.com/ferranhernandezc/graph-grip.

Problem

• over-squashing
• long-range interactions
• graph neural networks
• benchmark evaluation
• topology-invariance

Innovation

• Over-squashing
• Long-range interactions
• Graph Neural Networks
• Benchmark axioms
• Maximum-Likelihood oracle