arXiv:2609.01440 2026 Architecture 1 ideas extracted · analyzed Sep 2, 2026
The paper develops a finite algebra of local generators whose products have canonical non-crossing labelled arc-diagram representations. The transferable asset is the combination of idempotent local operations, commuting distant operations, confluent local rewrites, and sparse connectivity composition. This can become a structured attention or message-passing module that composes local token interactions into compact non-crossing routes without forming a dense attention matrix. The key experiment is whether this hierarchical routing bias preserves accuracy while reducing attention memory and runtime.
Replace dense token-to-token attention with a learned composition of adjacent routing operators whose connectivity is stored as a non-crossing labelled arc diagram. Canonicalize the composed routing program using the Okada relations, then execute only the surviving sparse token paths.