Generative models for scalar field theories: how to deal with poor scaling?

TL;DR

This paper investigates the limitations of current generative models, like normalizing flows, in efficiently generating large-scale lattice gauge configurations, and explores new architectures inspired by effective field theories to improve their scalability.

Contribution

It introduces novel architectures inspired by effective field theories and discusses alternative strategies to address poor scaling and acceptance rates in large lattice models.

Findings

Current models struggle with large lattices due to poor scaling.

New architectures inspired by effective field theories show potential improvements.

Alternative methods can mitigate acceptance rate issues for large lattices.

Abstract

Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof of principle for simple models in two dimensions. However, further studies indicate that the training cost can be, in general, very high for large lattices. The poor scaling traits of current models indicate that moderate-size networks cannot efficiently handle the inherently multi-scale aspects of the problem, especially around critical points. We explore current models with limited acceptance rates for large lattices and examine new architectures inspired by effective field theories to improve scaling traits. We also discuss alternative ways of handling poor acceptance rates for large lattices.