Learning Trivializing Gradient Flows for Lattice Gauge Theories

TL;DR

This paper introduces a novel continuous normalizing flow model for lattice gauge theories that is highly efficient, requiring significantly fewer parameters than existing methods, and offers improved training speed and interpretability.

Contribution

It unifies the perturbative construction of trivializing maps with learning techniques, creating a more efficient and scalable approach for lattice gauge theories.

Findings

Achieves competitive performance with only 14 parameters.

Requires several orders of magnitude fewer parameters than existing models.

Facilitates faster training and better interpretability.

Abstract

We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of lattice field theory and requires several orders of magnitude fewer parameters than any existing machine learning approach. Specifically, our model can achieve competitive performance with as few as 14 parameters while existing deep-learning models have around 1 million parameters for $SU(3)$ Yang--Mills theory on a $16^2$ lattice. This has obvious consequences for training speed and interpretability. It also provides a plausible path for scaling machine-learning approaches toward realistic theories.