Long-range dependence is hard to build into graph benchmarks, but the Long-Range Ising Model (LRIM) does it by construction. In LRIM, each label comes from a node's spin multiplied by a spin field convolved with a power-law coupling, so the target itself encodes interactions that decay slowly across the graph.
A new arXiv preprint (2610.22713v1) studies polynomial graph filters on this benchmark. These filters are common in graph neural networks because they are simple functions of the graph operator, but their spectral behavior is constrained. On LRIM, those constraints become visible: the paper identifies spectral limits that separate polynomial filters from the long-range target.
The abstract is truncated before it states the full conclusion, so the exact quantitative results are not available from the source alone. What is clear is the framing: LRIM is designed to make long-range dependence the thing being measured, and polynomial graph filters are the models being tested.