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.

Authors:
; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10303335
Journal Name:
Machine Learning: Science and Technology
Volume:
3
Issue:
1
Page Range or eLocation-ID:
Article No. 015006
ISSN:
2632-2153
Publisher:
IOP Publishing
National Science Foundation
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