Association Rules Machine Learning complete intersection Calabi-Yau 5-Folds and 6-Folds

TL;DR

This paper applies association rule machine learning to analyze Hodge numbers of complete intersection Calabi-Yau 5-folds and 6-folds, uncovering significant patterns that can inform future research and computations.

Contribution

It introduces the first large-scale application of association rule learning to Calabi-Yau manifolds, revealing hidden patterns in their Hodge numbers.

Findings

60 significant rules for 5-folds with high confidence

160 rules for 6-folds, including universal zero Hodge numbers

patterns can predict missing Hodge numbers and guide future research

Abstract

Association rule machine learning is applied to the dataset of complete intersection Calabi--Yau 5-folds and 6-folds in order to uncover hidden patterns among their Hodge numbers. These Hodge numbers -- six for the 5-folds and nine for the 6-folds -- serve as the items in our analysis. For the 5-folds, we discover 60 significant association rules. For example, within the dataset, if $h_{1,3} = 0$ and $h_{2,2} = 5$, then $h_{1,1} = 3$ with 99.43\% confidence. Similarly, if $h_{2,1} = 0$, $h_{1,3} = 0$, and $h_{2,2} = 5$, then $h_{1,1} = 3$ with 99.42\% confidence. For the 6-folds, we identify 160 association rules across a dataset of 1,482,022 examples. A particularly striking observation is that $h_{1,2} = h_{1,3} = h_{1,4} = h_{2,3} = 0$ for all entries in this dataset. These types of association rules are especially valuable because the Hodge numbers of complete intersection Calabi--Yau 5-folds have only been computed for approximately 53 percent of the dataset, while those of 6-folds remain largely undetermined. The discovered patterns provide predictive insights that can guide future computations and theoretical developments.