Attention as Lattice Gauge Theory: Relations Interact Only Through Wilson Loops
The authors report inferring missing relations without training even when a fifth of the graph’s edges are corrupted.
Their “holonomy attention” method scores relations by composing them around closed loops, preserving the order of composition. Under independent rotations of each entity’s coordinate frame, they show that this loop-based structure is the only permitted form of edge attention in the pure-gauge setting. On sparse graphs of noncommuting S₄ relations, the method scores 0.88, at or slightly below specialist synchronization algorithms; commuting architectures are capped at 0.083. Its loop score also detects corrupted triangles with an AUC of 0.99.
ArXiv · AI/CL/LG's note
Their “holonomy attention” method scores relations by composing them around closed loops, preserving the order of composition. Under independent rotations of each entity’s coordinate frame, they show that this loop-based structure is the only permitted form of edge attention in the pure-gauge setting. On sparse graphs of noncommuting S₄ relations, the method scores 0.88, at or slightly below specialist synchronization algorithms; commuting architectures are capped at 0.083. Its loop score also detects corrupted triangles with an AUC of 0.99.
ArXiv · AI/CL/LG's note
score 4