Machine Learning Free Quotients of CICYs

Free quotients of Calabi-Yau manifolds play an important role in string compactification. In this paper, we explore machine learning techniques, such as fully connected neural networks and multi-head attention (MHA) models, as a potential approach to detect $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$ and $\mathbb{Z}_2\times\mathbb{Z}_2$ free quotients of CICYs. When tested on unseen examples, both models successfully identified almost all free quotients for $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$ and $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. These results demonstrate that well-trained machine learning models can effectively generalize to new Calabi-Yau manifolds and may aid in the broader classification of free quotients in the future.