Deep Multi-task Mining Calabi-Yau Four-folds
Published in Mach. Learn.: Sci. Technol. 3 015006, 2021
Cite as: H. Erbin, R. Finotello, R. Schneider, M. Tamaazousti. 'Deep Multi-task Mining Calabi-Yau Four-folds'. Mach. Learn.: Sci. Technol. 3 01500. https://doi.org/10.1088/2632-2153/ac37f7
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, asit is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.