LRIM: a Physics-Based Benchmark for Provably Evaluating Long-Range Capabilities in Graph Learning

Accurately modeling long-range dependencies in graph-structured data is critical for many real-world applications. However, incorporating long-range interactions beyond the nodes' immediate neighborhood in a $\textit{scalable}$ manner remains an open challenge for graph machine learning models. Existing benchmarks for evaluating long-range capabilities either cannot $\textit{guarantee}$ that their tasks actually depend on long-range information or are rather limited. Therefore, claims of long-range modeling improvements based on said performance remain questionable. We introduce the Long-Range Ising Model Graph Benchmark, a physics-based benchmark utilizing the well-studied Ising model whose ground truth $\textit{provably}$ depends on long-range dependencies. Our benchmark consists of ten datasets that scale from 256 to 65k nodes per graph, and provide controllable long-range dependencies through tunable parameters, allowing precise control over the hardness and ``long-rangedness". We provide model-agnostic evidence that local information is insufficient, further validating the design choices of our benchmark. Via experiments on classical message-passing architectures and graph transformers, we show that both perform far from the optimum, especially those with scalable complexity. Our goal is that our benchmark will foster the development of scalable methodologies that effectively model long-range interactions in graphs.