Machine learning automorphic forms for black holes

TL;DR

This paper demonstrates that machine learning can effectively predict modular weights from automorphic forms related to black hole degeneracies, aiding the understanding of symmetries in quantum gravity.

Contribution

It introduces a novel approach of applying neural networks to automorphic forms to identify modular weights, advancing automated symmetry detection in gravitational systems.

Findings

Strong performance for negative weight forms

Lower accuracy for positive weights

Potential for automated symmetry identification

Abstract

Modular, Jacobi, and mock-modular forms serve as generating functions for BPS black hole degeneracies. By training feed-forward neural networks on Fourier coefficients of automorphic forms derived from the Dedekind eta function, Eisenstein series, and Jacobi theta functions, we demonstrate that machine learning techniques can accurately predict modular weights from truncated expansions. Our results reveal strong performance for negative weight modular and quasi-modular forms, particularly those arising in exact black hole counting formulae, with lower accuracy for positive weights and more complicated combinations of Jacobi theta functions. This study establishes a proof of concept for using machine learning to identify how data is organized in terms of modular symmetries in gravitational systems and suggests a pathway toward automated detection and verification of symmetries in quantum gravity.