Deep multi-task mining Calabi-Yau four-folds

Code

• github.com/thesfinox/ml-cicy-4folds
  OfficialIn papertf★ 5
• github.com/robin-schneider/cicy-fourfolds
  OfficialIn papertf★ 2

Abstract

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for h^(1,1) and 97% for h^(2,1) (100% for both), 81% (96%) for h^(3,1), and 49% (83%) for h^(2,2). Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

Reproductions