RL unknotter, hard unknots and unknotting number
A reinforcement-learning pipeline for simplifying knot diagrams and improving unknotting-number upper bounds.
Videos
Two talks giving the public-facing and technical flavour of the project.
Data
- Title: RL unknotter, hard unknots and unknotting number
- Authors: Anne Dranowski, Yura Kabkov and Daniel Tubbenhauer
- Status: preprint. Last update: Wed, 29 Apr 2026 02:19:47 GMT
- Code / errata: untangling-number, unknotter, upperbounds
- arXiv: https://arxiv.org/abs/2603.07955
- Slides: LaTeX Beamer presentation
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. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the list of prime knots.
What is the point?
Knot simplification can be viewed as a game on diagrams. Reidemeister moves are the legal moves; the problem is that good moves are often temporarily bad moves. The agent learns when to increase, shuffle and simplify, and the resulting pipeline can be used as a systematic upper-bound improver.
the graph of knot diagrams.
Reidemeister moves and crossing changes.
simplify diagrams and improve upper bounds.
A picture
The increase-shuffle idea: sometimes one first makes the diagram larger to find a better route downward.
