Quenched Ensemble Sampling: Robust MCMC Through Phase Transitions

Forum topic · 小凯 · 2026-09-16

Summary

A paper by David Yallup (arXiv:2609.15894, posted 2026-09-14) introduces Quenched Ensemble Sampling, a method for sampling energy functions of physical systems across phase transitions, where density-of-states changes abruptly and many algorithms stall. Nested sampling is robust to such transitions but struggles in high dimensions due to the hard energy constraint. The new method generalizes that hard constraint into a family of repulsive potentials at the energy boundary, preserving a quenched path of monotonically decreasing energy while making the constrained target compatible with scalable gradient-based kernels. Experiments show the method estimates marginal likelihoods and draws posterior samples at first-order phase transitions on synthetic models, where tempering-based alternatives fail. It is applied to Bayesian neural networks for marginal likelihood estimation enabling model comparison across architectures, and demonstrated on a high-dimensional continuous lattice field theory, traversing a first-order transition and estimating the partition function.

Overview

Field: Machine Learning
Author: David Yallup
Posted: 2026-09-14
arXiv: 2609.15894

Abstract (Original)

Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that the method estimates marginal likelihoods and draws posterior samples at first-order phase transitions where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation for Bayesian neural networks, enabling model comparison across network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that the method crosses a first-order phase transition and estimates the partition function.

Highlights

Generalizes nested sampling's hard energy constraint to a family of repulsive potentials at the energy boundary.
Maintains the quenched path of monotonically decreasing energy while supporting scalable gradient-based kernels.
Outperforms tempering-based methods at first-order phase transitions on synthetic benchmarks.
Enables marginal likelihood estimation and model comparison for Bayesian neural networks.
Demonstrated on a high-dimensional continuous lattice field theory, crossing a first-order transition and estimating the partition function.

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