Data
- Title: RL unknotter, hard unknots and unknotting number
- Authors: Anne Dranowski, Yura Kabkov and Daniel Tubbenhauer
- Status: preprint. Last update: Mon, 6 Oct 2025 22:36:10 UTC
- Code and (possibly empty) Erratum: Click and Click
- ArXiv link: https://arxiv.org/abs/2603.07955
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.
A few extra words
We train a reinforcement learning agent that treats knot simplification as search in a huge move graph (of Reidemeister moves R1, R2, R3) and learns where to move next.
Crucial is the idea of increase-shuffle, which increases the number of crossings using R1 and R2, and then shuffle them in using R3.
In general, we think of the unknotting as a game where the options are to add or remove cards (via R1 and R2), or to shuffle the deck (via R3).
