Particle Monte Carlo methods for Lattice Field Theory

TL;DR

This paper demonstrates that GPU-accelerated particle methods like SMC and nested sampling serve as effective classical benchmarks for lattice field theory, matching or surpassing neural samplers in quality and efficiency while also estimating partition functions.

Contribution

It introduces GPU-accelerated particle methods as strong classical baselines for lattice field theory sampling, outperforming neural methods without needing problem-specific tuning.

Findings

Particle methods match or outperform neural samplers in quality.

They provide efficient partition function estimates.

Single covariance tuning suffices for competitive performance.

Abstract

High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and nested sampling, provide a strong classical baseline that matches or outperforms state-of-the-art neural samplers in sample quality and wall-clock time on standard scalar field theory benchmarks, while also estimating the partition function. Using only a single data-driven covariance for tuning, these methods achieve competitive performance without problem-specific structure, raising the bar for when learned proposals justify their training cost.