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.

翻译：我们开发了一种用于简化纽结图的强化学习流程。经过训练的智能体学习移动建议和用于导航Reidemeister移动的价值启发式方法。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，并通过图膨胀技术应用于$4_1\#9_{10}$纽结，成功恢复了近期确立且令人惊讶的解结数上界——三。