Abstract
The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi–Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.
Highlights
String theory supplies a framework for quantum gravity
The manifolds of interest to us are the Complete Intersection Calabi–Yau threefolds (CICYs), which we review
Since computing the Hodge numbers directly was a time consuming and nontrivial problem [27], this is a prime example of how applying machine learning could shortlist different configurations for further study in the hypothetical situation of an incomplete dataset
Summary
String theory supplies a framework for quantum gravity. Finding our universe among the myriad of possible, consistent realisations of a four dimensional low-energy limit of string theory constitutes the vacuum selection problem. We wish to learn the extent to which such topological properties of CICYs are machine learnable, with the foresight that machine learning techniques can become a powerful tool in constructing ever more realistic string models, as well as helping understand Calabi–Yau manifolds in their own right. We choose to contrast this technique with SVMs, which are effective for smaller datasets with high dimensional data, such as the dataset of CICY threefolds Guided by these considerations, we conduct three case studies over the class of CICYs. We first apply SVMs and neural networks to machine learn the Hodge number h1,1 of CICYs. We attempt to learn whether a CICY is favourably embedded in a product of projective spaces, and whether a given CICY admits a quotient by a freely acting discrete symmetry.
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