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.

翻译：随着深层学习技术的迅速发展,最近的各种工作都试图应用图形神经网络(GNNs)解决NP硬性问题,如Boolean可满足性(SAT),这表明了弥合机器学习与象征性推理之间的差距的潜力;然而,文献中并未很好地调查GNNs预测的解决办法的质量。在本文中,我们从理论和实践角度研究了GNNs学习解决最大可满足性问题的能力。我们建立了两种GNN模式,从基准中学习MaxSAT案例的解决方案,并表明GNNs具有通过实验性评估解决MaxSAT问题的吸引力。我们还根据算法调整理论,从理论上解释了GNNs首次学会在一定程度上解决MaxSAT问题的效果。