# RL unknotter, hard unknots and unknotting number

arXiv: https://arxiv.org/abs/2603.07955 · HTML: https://mlsanity.com/paper/2603.07955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 5 of 5)

- [Big data approach to Kazhdan-Lusztig polynomials](https://mlsanity.com/paper/2412.01283/) (2024)
- [Big data comparison of quantum invariants](https://mlsanity.com/paper/2503.15810/) (2025)
- [The unknotting number, hard unknot diagrams, and reinforcement learning](https://mlsanity.com/paper/2409.09032/) (2024)
- [On detection probabilities of link invariants](https://mlsanity.com/paper/2509.05574/) (2025)
- [On knot detection via picture recognition](https://mlsanity.com/paper/2510.06284/) (2025)

## Abstract (arXiv)

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 41#910 where we investigate 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 prime knots.