Papers › Deep multi-task mining Calabi-Yau four-folds
Deep multi-task mining Calabi-Yau four-folds
Harold Erbin, Riccardo Finotello, Robin Schneider, Mohamed Tamaazousti
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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