mlsanityData to 14 Oct 2026

Goal-Aware Neural SAT Solver

arXiv 2106.07162 ↗First posted 14 Jun 2021cs.LG cs.AIcited by 28

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Abstract (arXiv)

Modern neural networks obtain information about the problem and calculate the output solely from the input values. We argue that it is not always optimal, and the network's performance can be significantly improved by augmenting it with a query mechanism that allows the network at run time to make several solution trials and get feedback on the loss value on each trial. To demonstrate the capabilities of the query mechanism, we formulate an unsupervised (not depending on labels) loss function for Boolean Satisfiability Problem (SAT) and theoretically show that it allows the network to extract rich information about the problem. We then propose a neural SAT solver with a query mechanism called QuerySAT and show that it outperforms the neural baseline on a wide range of SAT tasks.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 14 of its 28 references that are in the map. First posted on arXiv 14 Jun 2021.

Builds on

14 of 28 references.

References · 14

  1. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  2. 2016Learning to learn by gradient descent by gradient descentcited by 620
  3. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  4. 2020AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradientscited by 283
  5. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  6. 2018Learning a SAT Solver from Single-Bit Supervisioncited by 200
  7. 2017Recurrent Relational Networkscited by 72
  8. 2019Guiding High-Performance SAT Solvers with Unsat-Core Predictionscited by 62
  9. 2019CLN2INV: Learning Loop Invariants with Continuous Logic Networkscited by 20
  10. 2019PDP: A General Neural Framework for Learning Constraint Satisfaction Solverscited by 14
  11. 2019FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraintscited by 12
  12. 2019Can Q-Learning with Graph Networks Learn a Generalizable Branching Heuristic for a SAT Solver?cited by 10
2 more
  1. 2020NNgSAT: Neural Network guided SAT Attack on Logic Locked Complex Structurescited by 3
  2. 2019Graph Neural Reasoning May Fail in Certifying Boolean Unsatisfiabilitycited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 7; 2024: 3; 2025: 8; 2026: 5.

28 papers.

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  1. 2022Machine Learning Methods in Solving the Boolean Satisfiability Problemcited by 22
  2. 2022NSNet: A General Neural Probabilistic Framework for Satisfiability Problemscited by 18
  3. 2023G4SATBench: Benchmarking and Advancing SAT Solving with Graph Neural Networkscited by 18
  4. 2024LinSATNet: The Positive Linear Satisfiability Neural Networkscited by 16
  5. 2022SATformer: Transformer-Based UNSAT Core Learningcited by 14
  6. 2023HardSATGEN: Understanding the Difficulty of Hard SAT Formula Generation and A Strong Structure-Hardness-Aware Baselinecited by 12
  7. 2023Are Graph Neural Networks Optimal Approximation Algorithms?cited by 11
  8. 2025Self-Supervised Transformers as Iterative Solution Improvers for Constraint Satisfactioncited by 6
  9. 2021Generating Symbolic Reasoning Problems with Transformer GANscited by 5
  10. 2022Denoising Diffusion for Sampling SAT Solutionscited by 4
  11. 2025Geometric Algorithms for Neural Combinatorial Optimization with Constraintscited by 4
  12. 2023Addressing Variable Dependency in GNN-based SAT Solvingcited by 3
16 more
  1. 2025Neural Approaches to SAT Solving: Design Choices and Interpretabilitycited by 2
  2. 2026Learning to Decode in Parallel: Self-Coordinating Neural Network for Real-Time Quantum Error Correctioncited by 2
  3. 2026Benchmarking Graph Neural Networks in Solving Hard Constraint Satisfaction Problemscited by 2
  4. 2023Discrete Denoising Diffusion Approach to Integer Factorizationcited by 1
  5. 2024Learning Better Representations From Less Data For Propositional Satisfiabilitycited by 1
  6. 2025Structure based SAT dataset for analysing GNN generalisationcited by 1
  7. 2025HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problemscited by 1
  8. 2025MILP-SAT-GNN: Yet Another Neural SAT Solvercited by 1
  9. 2026On the Expressive Power of GNNs for Boolean Satisfiabilitycited by 1
  10. 2023Machine Learning for SAT: Restricted Heuristics and New Graph Representationscited by 0
  11. 2023Using deep learning to construct stochastic local search SAT solvers with performance boundscited by 0
  12. 2024A short review on the maximum clique problem algorithms with classical, AI, and quantum methodscited by 0
  13. 2025A Geometric Perspective on the Difficulties of Learning GNN-based SAT Solverscited by 0
  14. 2025Attn-JGNN: Attention Enhanced Join-Graph Neural Networkscited by 0
  15. 2026Target-Aware Data Augmentation for SAT Predictioncited by 0
  16. 2026Tiny Recursive Message Passingcited by 0