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Deep multi-task mining Calabi–Yau four-folds

https://doi.org/10.1088/2632-2153/ac37f7

Erbin, Harold; Finotello, Riccardo; Schneider, Robin; Tamaazousti, Mohamed (November 2021, Machine Learning: Science and Technology)

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.

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