Weisfeiler-Leman Is Incomplete on Simple Spectrum Graphs, so Canonicalize Them
Graphs with a simple spectrum admit cubic-time isomorphism testing, yet we prove that for every natural number $k$, the $k$-Weisfeiler-Leman ($k$-WL) test cannot distinguish all non-isomorphic graphs with a simple spectrum. As the WL hierarchy upper-bounds the distinguishing power of widely-used Graph Neural Networks (GNNs), this incompleteness applies to all such GNNs, ruling out completeness for every $k$-WL-aligned GNN family. To close this gap, we introduce PRiSM (Partition, Refine, Solve, Match), the first provably complete canonicalization of simple-spectrum eigendecompositions. PRiSM obtains the completeness guarantee that prior canonicalizations provably lack, and resolves the ope...
| Authors | Snir Hordan, Nadav Dym, Tim Seppelt |
|---|---|
| Primary category | cs.LG |
| Published | 22 May 2026 |
| Last updated at source | 22 May 2026 |
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