Accelerating Discrete Langevin Samplers via Continuous Intermediates

TMLR Paper5824 Authors

Abstract: Sampling from discrete distributions remains a challenge in machine learning, with traditional Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling suffering from inefficiency due to single-coordinate updates. Recent gradient-based discrete samplers have improved performance but remain constrained by the original discrete structures, which potentially hinder the convergence. To address this issue, we propose a hybrid approach that enables more global and informed proposals by introducing a continuous exploratory intermediate before the discrete update. This method, called Discrete Langevin Samplers via Continuous intermediates (cDLS), bridges the gap between discrete and continuous sampling and significantly accelerates convergence while maintaining theoretical guarantees. We develop variants of cDLS to ensure broad applicability, including unadjusted and Metropolis-adjusted versions. Experiments on Ising models, restricted Boltzmann machines, deep energy-based models, and Bayesian binary neural networks validate the superior performance of cDLS compared to existing methods. Our results highlight the potential of hybrid continuous-discrete exploration for advancing general discrete sampling.

Submission Length: Long submission (more than 12 pages of main content)

Changes Since Last Submission:

1. We have corrected all typos and issues related to formula notation in the manuscript.

2. We have rewritten the description of our contributions to more clearly highlight the novelty and unique aspects of our work.

3. We have added further discussion on the extensibility of our method.

4. In response to the reviewers’ comments, we have provided additional clarifications for parts of the main text that were previously insufficiently explained.

5. We have included in the appendix a detailed description of how the key hyperparameters of the sampler are selected.

Assigned Action Editor: ~Andreas_Lehrmann1

Submission Number: 5824