Statistical Predictions in String Theory and Deep Generative Models

Abstract

Generative models in deep learning allow for sampling probability distributions that approximate data distributions. We propose using generative models for making approximate statistical predictions in the string theory landscape. For vacua admitting a Lagrangian description this can be thought of as learning random tensor approximations of couplings. As a concrete proof-of-principle, we demonstrate in a large ensemble of Calabi-Yau manifolds that Kahler metrics evaluated at points in Kahler moduli space are well-approximated by ensembles of matrices produced by a deep convolutional Wasserstein GAN. Accurate approximations of the Kahler metric eigenspectra are achieved with far fewer than $h^{11}$ Gaussian draws. Accurate extrapolation to values of $h^{11}$ outside the training set are achieved via a conditional GAN. Together, these results implicitly suggest the existence of strong correlations in the data, as might be expected if Reid's fantasy is correct.

14 pages, 4 figures

References in corpus (9)

• Computational complexity of the landscape I
• Machine Learning in the String Landscape
• Evolving neural networks with genetic algorithms to study the String Landscape
• Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
• Searching the Landscape of Flux Vacua with Genetic Algorithms
• Heavy Tails in Calabi-Yau Moduli Spaces
• Getting CICY High
• Distinguishing Elliptic Fibrations with AI
• Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape

Cited by in corpus (10)

• Deep learning black hole metrics from shear viscosity
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• Machine Learning Lie Structures & Applications to Physics
• Hilbert Series, Machine Learning, and Applications to Physics
• The landscape of promising non-supersymmetric string models
• Disentangling a Deep Learned Volume Formula
• Predicting the orbifold origin of the MSSM
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Metastable vacua from torsion and machine learning
• Generative AI for Brane Configurations and Coamoeba