RL unknotter, hard unknots and unknotting number

Abstract

We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on 4_1\#9_10 where we recover the recently established and surprising upper bound of three for the unknotting number.

Reproductions