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.

翻译：我们开发了一种用于简化纽结图解的强化学习管道。经过训练的智能体学习移动提议和用于导航Reidemeister移动的价值启发式方法。该管道适用于任意纽结与链环；我们在“极难”平凡结图解上对其进行测试，并利用图解膨胀方法在$4_1\#9_{10}$上恢复了最近发现且令人惊讶的解结数上界三。此外，我们解释了该管道的自改进工作簿驱动扩展，该扩展可系统性地提升素纽结列表上的解结数上界。