# Preconditioned Discrete-HAMS: A Second-order Irreversible Discrete Sampler

arXiv: https://arxiv.org/abs/2507.21982 · HTML: https://mlsanity.com/paper/2507.21982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 32 references that are in the map.
- First posted on arXiv 29 Jul 2025.

## Builds on (most cited first, 5 of 5)

- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Auxiliary gradient-based sampling algorithms](https://mlsanity.com/paper/1610.09641/) (2016)
- [Enhanced gradient-based MCMC in discrete spaces](https://mlsanity.com/paper/2208.00040/) (2022)
- [Irreversible Samplers from Jump and Continuous Markov Processes](https://mlsanity.com/paper/1608.05973/) (2016)

## Abstract (arXiv)

Gradient-based Markov Chain Monte Carlo methods have recently received much attention for sampling discrete distributions, with notable examples such as Norm Constrained Gradient (NCG), Auxiliary Variable Gradient (AVG), and Discrete Hamiltonian Assisted Metropolis Sampling (DHAMS). In this work, we propose the Preconditioned Discrete-HAMS (PDHAMS) algorithm, which extends DHAMS by incorporating a second-order, quadratic approximation of the potential function, and uses Gaussian integral trick to avoid directly sampling a pairwise Markov random field. The PDHAMS sampler not only satisfies generalized detailed balance, hence enabling irreversible sampling, but also is a rejection-free property for a target distribution with a quadratic potential function. In various numerical experiments, PDHAMS algorithms consistently yield superior performance compared with other methods.