A scalable flow-based approach to mitigate topological freezing

2026-01-28

AI Summary

This work addresses the topological freezing problem in lattice gauge theories at the continuum limit, where autocorrelation times of topological observables diverge in Markov chain Monte Carlo simulations. While existing open-boundary approaches mitigate freezing, they break translational invariance and introduce unphysical boundary artifacts. The authors propose a scalable and exact method based on stochastic normalizing flows (SNFs), uniquely integrating local gauge-equivariant defect-coupling layers with SNFs. By alternating nonequilibrium Monte Carlo updates and mask-parameterized stout smearing operations, the method constructs a highly reversible mapping from a prior distribution with boundary defects to the full periodic ensemble. Trained to minimize the average dissipative work, the approach effectively eliminates boundary artifacts, restores topological ergodicity, and successfully reproduces benchmark results for the topological susceptibility in four-dimensional SU(3) Yang–Mills theory, demonstrating both efficacy and scalability.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Social Networks and Social Media: Computational social science

Abstract

As lattice gauge theories with non-trivial topological features are driven towards the continuum limit, standard Markov Chain Monte Carlo simulations suffer for topological freezing, i.e., a dramatic growth of autocorrelations in topological observables. A widely used strategy is the adoption of Open Boundary Conditions (OBC), which restores ergodic sampling of topology but at the price of breaking translation invariance and introducing unphysical boundary artifacts. In this contribution we summarize a scalable, exact flow-based strategy to remove them by transporting configurations from a prior with a OBC defect to a fully periodic ensemble, and apply it to 4d SU(3) Yang--Mills theory. The method is based on a Stochastic Normalizing Flow (SNF) that alternates non-equilibrium Monte Carlo updates with localized, gauge-equivariant defect coupling layers implemented via masked parametric stout smearing. Training is performed by minimizing the average dissipated work, equivalent to a Kullback--Leibler divergence between forward and reverse non-equilibrium path measures, to achieve more reversible trajectories and improved efficiency. We discuss the scaling with the number of degrees of freedom affected by the defect and show that defect SNFs achieve better performances than purely stochastic non-equilibrium methods at comparable cost. Finally, we validate the approach by reproducing reference results for the topological susceptibility.

Problem

• topological freezing
• lattice gauge theories
• Open Boundary Conditions
• autocorrelations
• translation invariance

Innovation

• Stochastic Normalizing Flow
• topological freezing
• Open Boundary Conditions
• gauge-equivariant
• non-equilibrium Monte Carlo