Quiver mutations, Seiberg duality, and machine learning
Quiver mutations, Seiberg duality, and machine learning
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DOI：
10.1103/physrevd.102.086013
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发表时间：
2020-06
影响因子：
5
通讯作者：
Jiakang Bao;S. Franco;Yang-Hui He;Edward Hirst;Gregg Musiker;Yan Xiao
中科院分区：
文献类型：
--
作者：
Jiakang Bao;S. Franco;Yang-Hui He;Edward Hirst;Gregg Musiker;Yan Xiao
我们开始研究机器学习的应用程序塞伯格对偶，专注于情况下的规范理论，一个问题也感兴趣的数学在集群代数的背景下。在塞伯格对偶的一般主题内，我们定义并探索了各种有趣的问题，大致分为二元确定从一系列对偶类中选出的一对理论是否彼此对偶，以及给定理论所属的对偶类的多类确定。我们研究了机器学习的性能如何取决于几个变量，包括类的数量和突变类型（有限或无限）。此外，我们评估了朴素贝叶斯分类器与卷积神经网络的相对优势。最后，我们还研究了结果是如何影响列入额外的数据，如排名的规范/味群和某些变量的动机的存在下丢番图方程。在考虑的所有问题中，都可以实现高准确性和置信度。
We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the context of cluster algebras. Within the general theme of Seiberg duality, we define and explore a variety of interesting questions, broadly divided into the binary determination of whether a pair of theories picked from a series of duality classes are dual to each other, as well as the multiclass determination of the duality class to which a given theory belongs. We study how the performance of machine learning depends on several variables, including number of classes and mutation type (finite or infinite). In addition, we evaluate the relative advantages of Naive Bayes classifiers versus convolutional neural networks. Finally, we also investigate how the results are affected by the inclusion of additional data, such as ranks of gauge/flavor groups and certain variables motivated by the existence of underlying Diophantine equations. In all questions considered, high accuracy and confidence can be achieved.