Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling
Timothee Leleu, Sam Reifenstein
Abstract
We propose a general framework for a hybrid continuous-discrete algorithm that integrates continuous-time deterministic dynamics with Metropolis-Hastings (MH) steps to combine search dynamics that either preserve or break detailed balance. Our purpose is to study the non-equilibrium dynamics that leads to the ground state of rugged energy landscapes in this general setting. Our results show that MH-driven dynamics reach ``easy'' ground states more quickly, indicating a stronger bias toward these solutions in algorithms using reversible transition probabilities. To validate this, we construct a set of Ising problem instances with a controllable bias in the energy landscape that makes certain degenerate solutions more accessible than others. The constructed hybrid algorithm demonstrates significant improvements in convergence and ground-state sampling accuracy, achieving a 100x speedup on GPU compared to simulated annealing, making it well-suited for large-scale applications.
BibTeX
@inproceedings{
leleu2025nonequilibrium,
title={Non-Equilibrium Dynamics of Hybrid Continuous-Discrete Ground-State Sampling},
author={Timothee Leleu and Sam Reifenstein},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=BlSIKSPhfz}
}