Abstract
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 multi-class 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.
Highlights
To provide the readers with an idea of the machine learning performance at a glance, we provide here a brief description of the problem styles addressed in this paper, a list of the quivers used to generate the mutation classes examined in the investigations, and a table summarizing the investigations’ key results
We first list the conclusions for Naive Bayes (NB) and Mathematica classifier: (i) The number of different mutation classes is the dominant influence in our machine learning
Other factors are outcompeted for influence on the learning when there is a larger number of mutation classes
Summary
To provide the readers with an idea of the machine learning performance at a glance, we provide here a brief description of the problem styles addressed in this paper, a list of the quivers used to generate the mutation classes examined in the investigations, and a table summarizing the investigations’ key results
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