Algebraic Geometry and Computer Vision: Inception Neural Network for Calabi-Yau Manifolds

Computing topological properties of Calabi-Yau manifolds is, in general, a challenging mathematical task: traditional methods lead to complicated algorithms, without expressions in closed form in most cases. At the same time, recent years have witnessed the rising use of deep learning as a method for exploration of large sets of data, to learn their patterns and properties. This is specifically interesting when it comes to unravel complicated geometrical structures, as it is a central issue both in mathematics and theoretical physics, as well as in the development of trustworthy AI methods. Motivated by their distinguished role in string theory for the study of compactifications, we compute the Hodge numbers of Complete Intersection Calabi-Yau (CICY) manifolds using deep neural networks. Specifically, we introduce new regression architectures, inspired by Google’s Inception network and multi-task learning, which leverage the theoretical knowledge on the inputs with recent advancements in AI. This shows the potential of deep learning to learn from geometrical data, and it proves the versatility of architectures developed in different contexts, which may therefore find their way in theoretical physics and mathematics for exploration and inference.