Deep multi-task mining Calabi-Yau four-folds

Authors: Harold Erbin, Riccardo Finotello, Robin Schneider and Mohamed Tamaazousti

Preprint number: UUITP-36/21

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 (since it is easy to compute) and taking into account the linear constraint arising from index computations, we get 100% total accuracy.