Can Graph Neural Networks Learn to Solve MaxSAT Problem?

TL;DR

This paper investigates the ability of graph neural networks to solve the MaxSAT problem, demonstrating both theoretical insights and practical potential through experiments with GNN models.

Contribution

It provides the first theoretical explanation of GNNs' capacity to solve MaxSAT and evaluates their effectiveness on benchmark instances.

Findings

GNNs show promising results in solving MaxSAT.

Theoretical analysis supports GNNs' potential in MaxSAT solving.

Experimental evaluation confirms GNNs' practical applicability.

Abstract

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.