Learning Trivializing Gradient Flows for Lattice Gauge Theories

Abstract

We propose a unifying approach that starts from the perturbative construction of trivializing maps by Lüscher 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.

10 pages, 4 figures, 1 table

References in corpus (7)

• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Flow-based sampling for fermionic lattice field theories
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Stochastic normalizing flows as non-equilibrium transformations
• Flow-based sampling in the lattice Schwinger model at criticality
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse
• Applications of Lattice Gauge Equivariant Neural Networks

Cited by in corpus (14)

• FLAG Review 2024
• Learning Lattice Quantum Field Theories with Equivariant Continuous Flows
• Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics
• Diffusion Models as Stochastic Quantization in Lattice Field Theory
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Sampling U(1) gauge theory using a re-trainable conditional flow-based model
• Gauge covariant neural network for quarks and gluons
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Non-Perturbative Trivializing Flows for Lattice Gauge Theories
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Applications of flow models to the generation of correlated lattice QCD ensembles