Application of transformer in 2D lattice Yang-Mills theory

A

bstract

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, demonstrating that the Transformer can effectively learn the supervised mapping from loop geometry to analytic results within the training distribution. We note that the 2D theory is exactly solvable and the target expressions belong to a restricted set of polynomial forms, which considerably simplifies the learning task. 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 proof-of-concept study toward extending such methods to higher dimensions and inspiring rigorous analytical derivations.