Deep multi-task mining Calabi-Yau four-folds. (arXiv:2108.02221v1 [hep-th])

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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