Machine Learning Calabi-Yau Four-folds

TL;DR

This paper applies machine learning techniques to predict Hodge numbers of Calabi-Yau four-folds, revealing successful predictions for some and suggesting potential unknown formulas for these topological invariants.

Contribution

It demonstrates the effectiveness of neural networks in predicting Hodge numbers of Calabi-Yau four-folds and introduces a novel two-branch network approach for complex predictions.

Findings

h^1,1 can be predicted with 96% accuracy

h^3,1 prediction improved to 98% with complex network

indicates possible existence of unknown formulas for Hodge numbers

Abstract

Hodge numbers of Calabi-Yau manifolds depend non-trivially on the underlying manifold data and they present an interesting challenge for machine learning. In this letter we consider the data set of complete intersection Calabi-Yau four-folds, a set of about 900,000 topological types, and study supervised learning of the Hodge numbers h^1,1 and h^3,1 for these manifolds. We find that h^1,1 can be successfully learned (to 96% precision) by fully connected classifier and regressor networks. While both types of networks fail for h^3,1, we show that a more complicated two-branch network, combined with feature enhancement, can act as an efficient regressor (to 98% precision) for h^3,1, at least for a subset of the data. This hints at the existence of an, as yet unknown, formula for Hodge numbers.