# Rapid mixing in positively weighted restricted Boltzmann machines

arXiv: https://arxiv.org/abs/2604.00963 · HTML: https://mlsanity.com/paper/2604.00963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Builds on (most cited first, 18 of 18)

- [Localization Schemes: A Framework for Proving Mixing Bounds for Markov Chains](https://mlsanity.com/paper/2203.04163/) (2022)
- [Optimal Mixing of Glauber Dynamics: Entropy Factorization via High-Dimensional Expansion](https://mlsanity.com/paper/2011.02075/) (2020)
- [Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model](https://mlsanity.com/paper/2001.00303/) (2020)
- [Rapid Mixing of Glauber Dynamics up to Uniqueness via Contraction](https://mlsanity.com/paper/2004.09083/) (2020)
- [Random cluster dynamics for the Ising model is rapidly mixing](https://mlsanity.com/paper/1605.00139/) (2016)
- [Layerwise Systematic Scan: Deep Boltzmann Machines and Beyond](https://mlsanity.com/paper/1705.05154/) (2017)
- [Rapid mixing of Glauber dynamics via spectral independence for all degrees](https://mlsanity.com/paper/2105.15005/) (2021)
- [Optimal mixing for two-state anti-ferromagnetic spin systems](https://mlsanity.com/paper/2203.07771/) (2022)
- [Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields](https://mlsanity.com/paper/2205.01985/) (2022)
- [A Near-Linear Time Sampler for the Ising Model with External Field](https://mlsanity.com/paper/2207.09391/) (2022)
- [The Complexity of Ferromagnetic Two-spin Systems with External Fields](https://mlsanity.com/paper/1402.4346/) (2014)
- [Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems](https://mlsanity.com/paper/1511.00493/) (2015)
- [Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials](https://mlsanity.com/paper/1607.01167/) (2016)
- [Swendsen-Wang Dynamics for General Graphs in the Tree Uniqueness Region](https://mlsanity.com/paper/1806.04602/) (2018)
- [Zeros of ferromagnetic 2-spin systems](https://mlsanity.com/paper/1907.06156/) (2019)
- [Contraction: a Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems](https://mlsanity.com/paper/1909.04244/) (2019)
- [A phase transition in sampling from Restricted Boltzmann Machines](https://mlsanity.com/paper/2410.08423/) (2024)
- [Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence](https://mlsanity.com/paper/2507.11031/) (2025)

## Abstract (arXiv)

We show polylogarithmic mixing time bounds for the alternating-scan sampler for positively weighted restricted Boltzmann machines. This is done via analysing the same chain and the Glauber dynamics for ferromagnetic two-spin systems, where we obtain new mixing time bounds up to the critical thresholds.