Neural Field Transformations for Hybrid Monte Carlo: Architectural Design and Scaling

TL;DR

This paper investigates neural field transformations integrated with Hybrid Monte Carlo to improve sampling efficiency in lattice gauge theories, emphasizing architectural choices and scalability for future high-dimensional applications.

Contribution

It systematically evaluates neural architectures within NTHMC, identifying design principles that enhance sampling and scalability in gauge theory simulations.

Findings

Neural architectures with wider receptive fields improve autocorrelation reduction.

Channel-dependent activations contribute to better topological tunneling.

Good designs maintain favorable scaling to larger volumes and finer lattices.

Abstract

Critical slowing down, where autocorrelation grows rapidly near the continuum limit due to Hybrid Monte Carlo (HMC) moving through configuration space inefficiently, still challenges lattice gauge theory simulations. Combining neural field transformations with HMC (NTHMC) can reshape the energy landscape and accelerate sampling, but the choice of neural architectures has yet to be studied systematically. We evaluate NTHMC on a two-dimensional U(1) gauge theory, analyzing how it scales and transfers to larger volumes and smaller lattice spacing. Controlled comparisons let us isolate architectural contributions to sampling efficiency. Good designs can reduce autocorrelation and boost topological tunneling while maintaining favorable scaling. More broadly, our study highlights emerging design guides, such as wider receptive fields and channel-dependent activations, paving the way for systematic extensions to four-dimensional SU(3) gauge theory.