Spectral Limits of Polynomial Graph Filters on the Long-Range Ising Model Benchmark
Read the original on arXiv Machine Learning →The paper introduces the Long‑Range Ising Model (LRIM) benchmark, which ensures long‑range dependence by defining each label as a node’s spin multiplied by a power‑law coupled spin field. It proves that polynomial filters on the adjacency matrix—used in isotropic message passing and spectral graph networks—cannot reduce the error floor because the target lies on a spectral level set where such filters are constant. The authors show that a strided filter with about fifty coefficients, trained on the labels, achieves a test error 52 times lower than the best published network, while a dilated convolutional network outperforms prior results at 256 nodes and matches them at 1,024 nodes, providing the first in‑domain results for larger sizes.
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