论文标题
照亮结之间的新关系和已知的关系
Illuminating new and known relations between knot invariants
论文作者
论文摘要
我们自动化结节之间的机器学习相关性过程。对于近200,000组不同的输入结和输出不变的，我们试图通过训练输入不变的神经网络来学习输出不变性。不变性之间的相关性是通过神经网络预测的准确性来衡量的，并且两分或三方相关性是从输入不变式集合中依次滤波的，因此具有较大输入集的实验检查了真正的多方相关性。我们重新发现了多项式，同源和双曲结之间的几个已知关系，同时还发现了新的相关性，这些相关性没有通过结理论中的已知结果来解释。这些无法解释的相关性增强了有关Khovanov与结式同源性之间联系的先前观察结果。我们的结果还指出了量子代数和双曲线不变剂之间的新联系，类似于广义体积的猜想。
We automate the process of machine learning correlations between knot invariants. For nearly 200,000 distinct sets of input knot invariants together with an output invariant, we attempt to learn the output invariant by training a neural network on the input invariants. Correlation between invariants is measured by the accuracy of the neural network prediction, and bipartite or tripartite correlations are sequentially filtered from the input invariant sets so that experiments with larger input sets are checking for true multipartite correlation. We rediscover several known relationships between polynomial, homological, and hyperbolic knot invariants, while also finding novel correlations which are not explained by known results in knot theory. These unexplained correlations strengthen previous observations concerning links between Khovanov and knot Floer homology. Our results also point to a new connection between quantum algebraic and hyperbolic invariants, similar to the generalized volume conjecture.
