Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks
A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a para...
| Authors | Xin Xu, Siru Tao, Kaizhen Tan |
|---|---|
| Primary category | cs.LG |
| Published | 28 July 2026 |
| Last updated at source | 28 July 2026 |
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