Deep multi-task mining Calabi-Yau four-folds

• 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)) 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.

Ämnesord

NATURVETENSKAP  -- Fysik -- Subatomär fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Subatomic Physics (hsv//eng)

Nyckelord

Calabi-Yau

Hodge numbers

string theory

multi-task learning

deep mining

inception modules

algebraic geometry

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