Deep multi-task mining Calabi–Yau four-folds. Issue 1 (25th November 2021)

• Record Type: Journal Article
• Authors: Erbin, Harold; Finotello, Riccardo; Schneider, Robin; Tamaazousti, Mohamed
• Is Part Of: Machine learning: science and technology. Volume 3:Issue 1(2022)
• Publication Date: 2021-11-25
• Subjects: Calabi–Yau -- Hodge numbers -- string theory -- multi-task learning -- deep mining -- inception modules -- algebraic geometry; 006.31
• DOI: 10.1088/2632-2153/ac37f7
• Languages: English
• ISSNs: 2632-2153

Abstract

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.