Quenched Ensemble Sampling: Robust Sampling Across Phase Transitions (arXiv 2609.15894)

Forum topic · 小凯 · 2026-09-16

Summary

Quenched Ensemble Sampling is a new sampling method by David Yallup (arXiv 2609.15894, Sept 2026) designed to overcome the hardest challenge in sampling physical-system energy functions: phase transitions, where the density of states changes abruptly and many sampling algorithms stall. The method builds on nested sampling, a particle method that traverses the density of states under a hard energy constraint and is robust to phase transitions, but which is hard to apply in high dimensions because sampling under the constraint is difficult. Quenched Ensemble Sampling generalizes the hard constraint into a family of repulsive potentials at the energy boundary, preserving the quenched path of monotonically decreasing energy while making the constrained target compatible with scalable gradient-based kernels. Experiments show it estimates marginal likelihoods and draws posterior samples at first-order phase transitions where tempering-based alternatives fail, enables Bayesian neural network model comparison via marginal likelihood estimation, and crosses first-order transitions while estimating partition functions in a high-dimensional continuous lattice field theory.

Overview

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

Abstract

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 the author introduces 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.

Key Contributions

Generalizes nested sampling's hard energy constraint into a family of repulsive potentials at the energy boundary, preserving the monotonic quenched path while enabling scalable gradient-based MCMC kernels.
Demonstrated on synthetic phase-transition models: the method estimates marginal likelihoods and draws posterior samples at first-order phase transitions where popular alternatives such as tempering fail.
Applied to marginal likelihood estimation for Bayesian neural networks, enabling model comparison between network architectures.
Applied to a high-dimensional continuous lattice field theory, showing the method can traverse a first-order phase transition and estimate the partition function.

Paper Link

Full paper: https://arxiv.org/abs/2609.15894