Deep multi-task mining Calabi-Yau four-folds - Archive ouverte HAL
Article Dans Une Revue Machine Learning: Science and Technology Année : 2022

Deep multi-task mining Calabi-Yau four-folds

Résumé

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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Dates et versions

hal-03323024 , version 1 (26-04-2023)

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Citer

Harold Erbin, Riccardo Finotello, Robin Schneider, Mohamed Tamaazousti. Deep multi-task mining Calabi-Yau four-folds. Machine Learning: Science and Technology, 2022, 3 (1), pp.015006. ⟨10.1088/2632-2153/ac37f7⟩. ⟨hal-03323024⟩
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