# Uniform Sampling through the Lov'asz Local Lemma

arXiv: https://arxiv.org/abs/1611.01647 · HTML: https://mlsanity.com/paper/1611.01647/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2016.

## Built on by (most cited first, 9 of 9)

- [Learning Hard-Constrained Models with One Sample](https://mlsanity.com/paper/2311.03332/) (2023)
- [Perfect Sampling from Pairwise Comparisons](https://mlsanity.com/paper/2211.12868/) (2022)
- [Lifted Algorithms for Symmetric Weighted First-Order Model Sampling](https://mlsanity.com/paper/2308.08828/) (2023)
- [On Exact Sampling in the Two-Variable Fragment of First-Order Logic](https://mlsanity.com/paper/2302.02730/) (2023)
- [Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample](https://mlsanity.com/paper/2509.20993/) (2025)
- [Learning Markov Random Fields for Combinatorial Structures via Sampling through Lov'asz Local Lemma](https://mlsanity.com/paper/2212.00296/) (2022)
- [One-Shot Learning for k-SAT](https://mlsanity.com/paper/2502.07135/) (2025)
- [Bypassing orthogonalization in the quantum DPP sampler](https://mlsanity.com/paper/2503.05906/) (2025)
- [Learning CNF Formulas from Uniform Random Solutions: Near-Tight Sample Complexity for Valiant's Algorithm](https://mlsanity.com/paper/2609.15268/) (2026)

## Abstract (arXiv)

We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new connections between the variable framework of the Lov'asz Local Lemma and some classical sampling algorithms such as the "cycle-popping" algorithm for rooted spanning trees. Among other applications, we discover new algorithms to sample satisfying assignments of k-CNF formulas with bounded variable occurrences.