Deep multi-task mining Calabi-Yau four-folds

• URL: http://arxiv.org/abs/2108.02221v1
• Date: Wed, 4 Aug 2021 18:00:15 GMT
• Title: Deep multi-task mining Calabi-Yau four-folds
• Authors: Harold Erbin, Riccardo Finotello, Robin Schneider and Mohamed Tamaazousti
• Abstract summary: We consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. With 30% (80%) training ratio, we reach an accuracy of 100% for $h (1,1)$ and 97% for $h (2,1)$.
• Score: 6.805575417034372
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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