Paper frames relational attention as lattice gauge theory
Original title: Attention as Lattice Gauge Theory: Relations Interact Only Through Wilson Loops
Untrained holonomy attention infers unobserved S4 relations at 0.88 with a fifth of edges corrupted.
The paper argues that, under per-entity frame freedom, relations interact only through Wilson loops and that edge attention of that form is the unique equivariant update. It links the idea to knowledge-graph embeddings, AlphaFold's triangle update, the Edge Transformer, and lattice QCD. An untrained holonomy-attention instantiation on relational graphs is reported to infer relations and flag corrupted triangles better than commutative architectures.
- With one-fifth of edges corrupted, accuracy is 0.88 versus a 0.083 commutative cap.
- Holonomy scores flag corrupted triangles at AUC 0.99; commuting scores cap at 0.76.
- The method uses composition alone and no training.
- It also separates clusters without labels.
- Products
- AlphaFoldEdge Transformer
From the original article
1 min read at arxiv.orgRelations compose through the entity they share - Alice is Bob's mother and Bob is Carol's father, so Alice is Carol's grandmother - and the order matters, since a father's mother is not a mother's father; verifying a composed relation means closing the loop. We show that if each entity's coordinate frame may be rotated independently (per-entity frame freedom), three things follow.
By Aakash Sarkar · arxiv.org
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