Deep multi-task mining Calabi-Yau four-folds

08/04/2021

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by   Harold Erbin, et al.

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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 training ratio, we reach an accuracy of 100 h^(2,1) (100 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