ICML 2025

On Measuring Long-Range Interactions in Graph Neural Networks
Jacob Bamberger * 1 Benjamin Gutteridge * 1 Scott le Roux * 1 Michael Bronstein 1 2 Xiaowen Dong 1
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 pro-
posed architectures. However, this is an empirical
approach that lacks both robustness and theoret-
ical underpinning; a more principled characteri-
zation of the long-range problem is required. To
bridge this gap, we formalize long-range interac-
tions in graph tasks, introduce a range measure
for operators on graphs, and validate it with syn-
thetic experiments. We then leverage our measure
to examine commonly used tasks and architec-
tures, 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 evalu-
ation of new datasets and architectures.
1. Introduction
Graphs have emerged as a rich data modality, capable of
modeling pairwise relationships between entities in diverse
applications. Graph neural networks (GNNs) have become
the dominant paradigm for learning from such data, with
message passing neural networks (MPNNs) (Gilmer et al.,
2020) standing out as the most widely used framework.
MPNNs operate by iteratively updating a node’s representa-
tion based on information aggregated from its local neigh-
borhood. This local message-passing mechanism has been
highly effective in a wide range of tasks, such as social net-
works (Monti et al., 2019), computational chemistry (Gilmer
et al., 2017) and recommendation systems (Fan et al., 2019).
*Equal contribution 1University of Oxford 2AITHYRA. Corre-
spondence to: Jacob Bamberger <jacob.bamberger@cs.ox.ac.uk>,
Benjamin Gutteridge <beng@robots.ox.ac.u...