Stochastic Path Sampler For Lattice Field Theory

Abstract

In lattice field theory, target distributions are known only up to normalization, (\tildeπ(ϕ)\propto e^{-S(ϕ)}), while the partition function is intractable. Markov chain Monte Carlo simulations often become inefficient near phase transitions or the continuum limit due to critical slowing down. In this work, we propose a novel sampler based on nonequilibrium thermodynamics, called Stochastic Path Sampler (SPS), which can generate configurations for the unnormalized target distribution without requiring training data. The central idea of SPS is to establish a trajectory-level balance for learnable forward and backward stochastic dynamics between two equilibrium states, namely the prior and target distributions. This is achieved by minimizing the path-space variational free energy, equivalently an entropy-production upper bound, defined by the log-ratio of forward and auxiliary backward trajectory measures, thereby enhancing the reversibility of the forward and backward processes. The learned forward process provides independent proposals, which are subsequently corrected by an extended-space Independence Metropolis--Hastings step. In two-dimensional (ϕ^4) theory, we demonstrate that our neural sampler can achieve the same sampling quality as HMC but with a much shorter autocorrelation time in the critical region. This sampler offers a stochastic-quantization-inspired route to data-free proposal construction for lattice field theory by leveraging a variational free-energy principle derived from path-space irreversibility.