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

Ferran Hernandez Caralt, Simon Heilig, Adrián Bazaga, Asja Fischer, Moshe Eliasof +1

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…