论文标题
学习解开
Learning to Unknot
论文作者
论文摘要
我们将自然语言处理引入了结理论的研究中，这是由结的编织单词表示制成的。我们研究了确定给定结是否是未结的结节问题。在描述了一种算法以随机生成$ n $ - 跨编织及其结的闭合并讨论了结的先前，我们将二进制分类应用于UNNENNEN KINENT DICACTION问题。我们发现，改革者和共享的QK变形金刚网络架构的表现均优于完全连接的网络，尽管它们都表现良好。也许令人惊讶的是，我们发现准确性随辫子词的长度而提高，并且网络学习了他们的预测信心与琼斯多项式的程度之间的直接相关性。最后，我们利用加固学习（RL）来找到马尔可夫动作和辫子关系的序列，这些序列简化了结，可以通过明确给出一系列无结的动作来识别结的序列。信任区域策略优化（TRPO）在广泛的交叉数字上表现良好，并且彻底胜过其他RL算法和随机步行器。在研究这些行动时，我们发现辫子关系在简化无结论方面比马尔可夫的一项动作更有用。
We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate $N$-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform well. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well for a wide range of crossing numbers and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves.
