Aspects of scaling and scalability for flow-based sampling of lattice QCD

TL;DR

This paper investigates the scalability of flow-based sampling methods for lattice QCD, emphasizing that their effectiveness at large scales must be evaluated through experiments rather than simple cost models.

Contribution

It highlights the limitations of traditional scaling laws for flow-based methods and advocates for experimental assessment of their scalability in lattice QCD.

Findings

Flow-based sampling methods have diverse scaling properties.

Traditional cost laws are limited for evaluating flow-based approaches.

Experimental evaluation is essential for assessing scalability.

Abstract

Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. However, these demonstrations have been at the scale of toy models, and it remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations. Assessing the viability of sampling algorithms for lattice field theory at scale has traditionally been accomplished using simple cost scaling laws, but as we discuss in this work, their utility is limited for flow-based approaches. We conclude that flow-based approaches to sampling are better thought of as a broad family of algorithms with different scaling properties, and that scalability must be assessed experimentally.