# Can Graph Neural Networks Learn to Solve MaxSAT Problem?

arXiv: https://arxiv.org/abs/2111.07568 · HTML: https://mlsanity.com/paper/2111.07568/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Approximation Ratios of Graph Neural Networks for Combinatorial Problems](https://mlsanity.com/paper/1905.10261/) (2019)
- [Guiding High-Performance SAT Solvers with Unsat-Core Predictions](https://mlsanity.com/paper/1903.04671/) (2019)
- [Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSP](https://mlsanity.com/paper/1809.02721/) (2018)
- [Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problems](https://mlsanity.com/paper/1903.04598/) (2019)
- [NLocalSAT: Boosting Local Search with Solution Prediction](https://mlsanity.com/paper/2001.09398/) (2020)
- [Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learning](https://mlsanity.com/paper/1807.08058/) (2018)

## Built on by (most cited first, 5 of 5)

- [Are Graph Neural Networks Optimal Approximation Algorithms?](https://mlsanity.com/paper/2310.00526/) (2023)
- [Analyzing B"uchi Automata with Graph Neural Networks](https://mlsanity.com/paper/2206.09619/) (2022)
- [A Unified Pre-training and Adaptation Framework for Combinatorial Optimization on Graphs](https://mlsanity.com/paper/2312.11547/) (2023)
- [HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems](https://mlsanity.com/paper/2504.11885/) (2025)
- [Machine Learning for SAT: Restricted Heuristics and New Graph Representations](https://mlsanity.com/paper/2307.09141/) (2023)

## Abstract (arXiv)

With the rapid development of deep learning techniques, various recent work has tried to apply graph neural networks (GNNs) to solve NP-hard problems such as Boolean Satisfiability (SAT), which shows the potential in bridging the gap between machine learning and symbolic reasoning. However, the quality of solutions predicted by GNNs has not been well investigated in the literature. In this paper, we study the capability of GNNs in learning to solve Maximum Satisfiability (MaxSAT) problem, both from theoretical and practical perspectives. We build two kinds of GNN models to learn the solution of MaxSAT instances from benchmarks, and show that GNNs have attractive potential to solve MaxSAT problem through experimental evaluation. We also present a theoretical explanation of the effect that GNNs can learn to solve MaxSAT problem to some extent for the first time, based on the algorithmic alignment theory.