论文标题
矩形结图与深度学习分类
Rectangular knot diagrams classification with deep learning
论文作者
论文摘要
在本文中，我们讨论了神经网络的应用，以识别结，尤其是针对无结的问题。这项研究的动机之一是理解神经网络如何在一个问题的示例中起作用，该问题已知严格的数学算法。我们通过矩形Dynnikov图表示结，并应用神经网络以区分给定图表类别和给定的拓扑类型的有限家族。通过将dynnikov移动应用于初始样本来生成到程序中的数据。使用这些图表和移动的意义在于，在这种情况下，确定图表是否没有打结的问题是对有限的组合空间的有限搜索。
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which rigorous mathematical algorithms for its solution are known. We represent knots by rectangular Dynnikov diagrams and apply neural networks to distinguish a given diagram class from the given finite families of topological types. The data presented to the program is generated by applying Dynnikov moves to initial samples. The significance of using these diagrams and moves is that in this context the problem of determining whether a diagram is unknotted is a finite search of a bounded combinatorial space.
