RL unknotter, hard unknots and unknotting number

arXiv:2603.07955 · math.GT, cs.LG, stat.ML · Submitted 2026-03-09 · Read on arXiv

math.GT, cs.LG, stat.ML

Submitted: 2026-03-09

Updated: 2026-09-09

Comments: 20 pages, many figures, comments welcome

Code: https://github.com/annedranowski/untangling-number

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reinforcement Learning — 9× in this paper · explained in 4 episodes
• Additivity — 3× in this paper · explained in 1 episode
• Benchmark — 3× in this paper · explained in 2 episodes
• Ablation — 2× in this paper · explained in 1 episode
• Verifier — 2× in this paper · explained in 2 episodes
• Action Space — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Proximal Policy Optimization — 1× in this paper
• Proximal Policy Optimization (PPO) — 1× in this paper · explained in 4 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 24 episodes
• Reward Shaping — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• The unknotting number, hard unknot diagrams, and reinforcement learning
• Unknotting number and connected sums: The knots $4_1$ and $5_1$
• Unknotting number is not additive under connected sum
• On knot detection via picture recognition
• Unknotting Unknots
• On detection probabilities of link invariants
• Big data comparison of quantum invariants
• A remark on the counterexample to the unknotting number conjecture

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