Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them
Researchers have demonstrated that the Weisfeiler-Leman (WL) test, a common method for graph isomorphism testing, is incomplete for graphs with simple spectra. This limitation extends to Graph Neural Networks (GNNs) that rely on the WL hierarchy. To address this, a new method called PRiSM has been developed, which provides a provably complete canonicalization for simple-spectrum eigendecompositions. When integrated with models like DeepSets or Transformers, PRiSM enables universal approximation on these types of graphs. AI
IMPACT This research could lead to more powerful and accurate graph neural networks by providing a complete canonicalization method for specific graph types.