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A group argued edge attention is not a design choice but a symmetry: relations can only interact through closed loops, and it beat commuting baselines ten to one

AspireAI community · arXiv
Relations compose through shared entities and order matters, so verifying a composed relation means closing a loop. Treating each entity's coordinate frame as independently rotatable, the paper derives that relations sharing no cycle cannot interact at all, that the only gauge-invariant score of a triangle is a class function of its holonomy (a Wilson loop), and that the only equivariant edge update has the form U = Psi(H) T. That makes edge attention by Wilson loops the unique form the symmetry permits rather than one option among many. Instantiated as holonomy attention on general relational graphs, and with no training at all, it infers unobserved S4 relations on sparse graphs at 0.88 with a fifth of the edges corrupted, where every commutative architecture is capped at 0.083. Its holonomy score flags corrupted triangles at AUC 0.99 against a 0.76 ceiling for commuting scores, and it separates clusters without labels. It is a 7-page workshop paper at ML4PS 2026, so the theory is the contribution and the evaluation is narrow: one synthetic graph family.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
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