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With the rapid development of deep learning techniques, various recent workhas tried to apply graph neural networks (GNNs) to solve NP-hard problems suchas Boolean Satisfiability (SAT), which shows the potential in bridging the gapbetween machine learning and symbolic reasoning. However, the quality ofsolutions predicted by GNNs has not been well investigated in the literature.In this paper, we study the capability of GNNs in learning to solve MaximumSatisfiability (MaxSAT) problem, both from theoretical and practicalperspectives. We build two kinds of GNN models to learn the solution of MaxSATinstances from benchmarks, and show that GNNs have attractive potential tosolve MaxSAT problem through experimental evaluation. We also present atheoretical explanation of the effect that GNNs can learn to solve MaxSATproblem to some extent for the first time, based on the algorithmic alignmenttheory.

Can Graph Neural Networks Learn to Solve MaxSAT Problem?