The World in a Grain of Sand: Condensing the String Vacuum Degeneracy

TL;DR

This paper introduces a machine learning approach using Siamese Neural Networks to efficiently measure similarity among Calabi-Yau manifolds, significantly reducing the search space in string vacuum landscape analysis.

Contribution

It presents a novel application of few-shot learning and neural networks to quantify vacuum degeneracy in string theory, enabling rapid identification of rare manifolds.

Findings

Reduced search space to 1% of original data

Effective similarity measurement with few training examples

Potential to characterize typicality of vacua

Abstract

We propose a novel approach toward the vacuum degeneracy problem of the string landscape, by finding an efficient measure of similarity amongst compactification scenarios. Using a class of some one million Calabi-Yau manifolds as concrete examples, the paradigm of few-shot machine-learning and Siamese Neural Networks represents them as points in R(3) where the similarity score between two manifolds is the Euclidean distance between their R(3) representatives. Using these methods, we can compress the search space for exceedingly rare manifolds to within one percent of the original data by training on only a few hundred data points. We also demonstrate how these methods may be applied to characterize `typicality' for vacuum representatives.