Spectral Limits of Polynomial Graph Filters on the Long-Range Ising Model Benchmark
The Long-Range Ising Model benchmark (LRIM) guarantees long-range dependence by construction: each label is the node's spin times the spin field convolved with a power-law coupling, so any model's distance from the target is measurable. We prove that a readout whose filter is a polynomial in the adjacency, the linear core of isotropic message passing and spectral graph networks, leaves an error floor that no degree lowers, because the target varies along a level set of the spectrum on which every such filter is constant. Computed exactly, the floor and the best filter of each degree predict two spectral networks adapted from published architectures to within a tenth of a decade. A filter ...
| Authors | Amin Najafgholizadeh, Mohsen Afsharchi |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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