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流程。训练后的智能体能够学习移动提议和用于导航雷德迈斯特移动的价值启发式算法。该流程适用于任意纽结与链环；我们在“极难”解结图上进行了测试，并利用图解膨胀法在$4_1\#9_{10}$上恢复了近期确立的令人惊讶的解结数上界三。此外，我们解释了一种自改进的工作簿驱动扩展，该系统性地改进了素纽结列表上解结数的上界。