Reachability is not enough: Diagnosing long-range behavior in GNNs
Graph neural networks (GNNs) are often called long-range because their architecture can connect distant nodes, but this does not show whether they use distant information correctly. We introduce a framework that measures how strongly inputs at each graph distance affect predictions and separates limitations due to architecture, finite approximation, training, and numerical execution. Our analysis shows that local message-passing can spread influence slowly, so a finite implementation may rely mainly on nearby inputs even when the ideal computation uses the whole graph. We also explain why mathematically equivalent filters can differ in how easily they are learned and how reliably they run...
| Authors | Filippo Maria Bianchi |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 27 September 2026 |
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