The unknotting number, hard unknot diagrams, and reinforcement learning
Taylor Applebaum, Sam Blackwell, Alex Davies, Thomas Edlich, András Juhász, Marc Lackenby, Nenad Tomašev, Daniel Zheng
我们已经开发出一种强化学习代理,通常为高达200个交叉的结图找到最小序列的不注意交叉变化,因此在未标记的数字上给出上限。 我们已经用它来确定57k结的unnotting数。 我们用相反签名的签名,绘制了这些结的关联金额图,其中的总和被覆盖。 该代理人发现了一些例子,其中几个交叉变化在一个不明显的交叉收集导致双曲结。 基于此,我们已经证明,给定的结K和K'满足一些温和的假设,有一个图表,它们的连接和u(K) + u(K') 的通量和未标记的交叉,从而改变其中任何一个会导致一个素数结。 作为副产品,我们获得了260万个不同的硬图的数据集;其中大多数在35个交叉点下。 假设不扣数字的附加性,我们已经确定在最多12个交叉结处的不为人知的不为人知的不为人知的不为人知的不为人知的不为人知的不为人知数的。
We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number. We have used this to determine the unknotting number of 57k knots. We took diagrams of connected sums of such knots with oppositely signed signatures, where the summands were overlaid. The agent has found examples where several of the crossing changes in an unknotting collection of cr...