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. * kieran.bull@seh.ox.ac.uk † hey@maths.ox.ac.uk ‡ vishnu@neo.phys.wits.ac.za

We present a list of Calabi‐Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height (h1,1+h2,1)≤24. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi‐Yau threefolds, most of which were computed in Refs. [] and the remainder in Ref. [], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. []. In view of this and other recent constructions of Calabi‐Yau threefolds with small height, we have produced an updated list.

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either Z 2 or contain Z 4 , Z 2 × Z 2 , Z 3 or Z 5 as a subgroup. The Hodge numbers for the quotients for which the group G contains Z 3 or Z 5 have been computed previously. This paper deals with the remaining cases, for which G ⊇ Z 4 or G ⊇ Z 2 × Z 2 . We also compute the Hodge numbers for 99 of the 166 CICY's which have Z 2 quotients.

Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low h 1,1 geometries for training and validate on geometries with large h 1,1 . Neural networks and Support Vector Machines successfully predict trends in the number of Kähler parameters of CICY threefolds.The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher h 1,1 . * pykb@leeds.ac.uk † hey@maths.ox.ac.uk ‡ vishnu@neo.phys.wits.ac.za