mlsanityData to 7 Oct 2026

Can Graph Neural Networks Learn to Solve MaxSAT Problem?

arXiv 2111.07568 ↗First posted 15 Nov 2021cs.AIcited by 5

Not on the map. Why?

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 17 of its 44 references that are in the map. First posted on arXiv 15 Nov 2021.

Builds on

17 of 44 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018How Powerful are Graph Neural Networks?cited by 4,355
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  4. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  5. 2015Pointer Networkscited by 882
  6. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  7. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
  8. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  9. 2018Learning a SAT Solver from Single-Bit Supervisioncited by 198
  10. 2019What Can Neural Networks Reason About?cited by 155
  11. 2020Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspectivecited by 93
  12. 2019Approximation Ratios of Graph Neural Networks for Combinatorial Problemscited by 68
5 more
  1. 2019Guiding High-Performance SAT Solvers with Unsat-Core Predictionscited by 61
  2. 2018Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSPcited by 58
  3. 2019Graph Colouring Meets Deep Learning: Effective Graph Neural Network Models for Combinatorial Problemscited by 40
  4. 2020NLocalSAT: Boosting Local Search with Solution Predictioncited by 25
  5. 2018Learning Heuristics for Quantified Boolean Formulas through Deep Reinforcement Learningcited by 15

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 3; 2024: 0; 2025: 1.

5 papers.

  1. 2023Are Graph Neural Networks Optimal Approximation Algorithms?cited by 10
  2. 2022Analyzing B"uchi Automata with Graph Neural Networkscited by 1
  3. 2023A Unified Pre-training and Adaptation Framework for Combinatorial Optimization on Graphscited by 1
  4. 2025HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problemscited by 1
  5. 2023Machine Learning for SAT: Restricted Heuristics and New Graph Representationscited by 0