We review advancements in deep learning techniques for complete intersection
Calabi-Yau (CICY) 3- and 4-folds, with the aim of understanding better how to
handle algebraic topological data with machine learning. We first discuss
methodological aspects and data analysis, before describing neural networks
architectures. Then, we describe the state-of-the art accuracy in predicting
Hodge numbers. We include new results on extrapolating predictions from low to
high Hodge numbers, and conversely.

我们回顾了关于使用深度学习技术处理完全交联 Calabi-Yau（CICY）3 - 和 4 - 褶曲的研究进展，目的是更好地了解如何使用机器学习处理代数拓扑数据。我们首先讨论了方法学方面和数据分析，然后描述了神经网络的架构。接着，我们描述了在预测 Hodge 数方面的最新准确性。我们还包括了从低到高 Hodge 数的外推预测及其相反情况的新结果。

深度学习完全交叉 Calabi-Yau 流形

Deep learning complete intersection Calabi-Yau manifolds

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.

利用神经网络和支持向量机技术，研究完全交叉 Calabi-Yau（CICY）三次流形的几何性质，探讨基于平稳 CICY 的紧致化的准现实弦模型，并通过神经网络的优化超参数展示了快速诊断工具的优势。

机器学习 CICY 三维流形

Machine Learning CICY Threefolds

It is known that many Calabi-Yau manifolds form a connected web. The question
of whether all Calabi-Yau manifolds form a single web depends on the degree of
singularity that is permitted for the varieties that connect the distinct
families of smooth manifolds. If only conifolds are allowed then, since
shrinking two-spheres and three-spheres to points cannot affect the fundamental
group, manifolds with different fundamental groups will form disconnected webs.
We examine these webs for the tip of the distribution of Calabi-Yau manifolds
where the Hodge numbers (h^{11}, h^{21}) are both small. In the tip of the
distribution the quotient manifolds play an important role. We generate via
conifold transitions from these quotients a number of new manifolds. These
include a manifold with \chi =-6 and manifolds with an attractive structure
that may prove of interest for string phenomenology. We also examine the
relation of some of these manifolds to the remarkable Gross-Popescu manifolds
that have Euler number zero.

该研究探讨了 Calabi-Yau 流形之间的连通性，特别关注了 Hodge 数值很小的 Quotient 流形及其通过 conifold 转换生成的流形之间的关系，其中包含了一些具有吸引性结构、对字符串现象学有意义的流形，以及一些与有零 Euler 数的 Gross-Popescu 流形的关系。