AI for Pattern Hunter: Application in Wilson Loop of 2D Lattice Yang-Mills Theory

TL;DR

This paper demonstrates that Transformer models can effectively learn and predict the expectation values of Wilson loops in 2D lattice Yang-Mills theory by analyzing their geometric shapes, offering a new analytical approach.

Contribution

It introduces a novel application of Transformer models to capture the analytical structure of Wilson loops in lattice gauge theory, differing from traditional numerical methods.

Findings

High prediction accuracy of Wilson loop expectation values

Model performance varies with hyperparameters and data size

Potential extension to higher-dimensional theories

Abstract

We employ the Transformer to learn patterns in two-dimensional lattice Yang-Mills theory. Specifically, we represent both Wilson loops and their expectation values as tokenized sequences. Taking the shape of Wilson loops as input, the model successfully predicts expectation values with high accuracy, indicating a meaningful connection between loop geometry and physical results. Our study differs from prior machine learning applications in lattice QCD by emphasizing analytical structures rather than numerical computations. We explore model performance under varying hyperparameters, training data sizes, and sequence lengths. This work serves as a first step toward extending such methods to higher dimensions and inspiring rigorous analytical derivations.