Constant-Depth Rational-Weight GNNs and their Connection to Schanuel's Conjecture
A landmark result states that the expressive power of graph neural networks (GNNs) is bounded from above by the 1-dimensional Weisfeiler-Leman (1-WL) test. We ask whether a constant-depth GNN can match the expressive power of 1-WL while using only rational weights. We prove that this is the case when Schanuel's conjecture, a famous open problem from transcendental number theory, is taken to be true. Our GNN construction works even with integer weights, and more generally with a broad range of rational weights. As the activation function, it may use logistic sigmoid, hyperbolic tangent, or related functions. It is uniform across all graph sizes. We also prove a partial converse: if a GNN w...
| Authors | Daumantas Kojelis, Carsten Lutz |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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