Learning to Solve Weighted Maximum Satisfiability with a Co-Training Architecture

Wepropose SplitGNN, a graph neural network (GNN)-basedapproach that learns to solve weighted maximum satisfiabil ity (MaxSAT) problem. SplitGNN incorporates a co-trainingarchitecture consisting of supervised message passing mech anism and unsupervised solution boosting layer. A new graphrepresentation called edge-splitting factor graph is proposedto provide more structural information for learning, which isbased on spanning tree generation and edge classification. Toimprove the solutions on challenging and weighted instances,we implement a GPU-accelerated layer applying efficientscore calculation and relaxation-based optimization. Exper iments show that SplitGNN achieves 3* faster convergenceand better predictions compared with other GNN-based ar chitectures. More notably, SplitGNN successfully finds solu tions that outperform modern heuristic MaxSAT solvers onmuch larger and harder weighted MaxSAT benchmarks, anddemonstrates exceptional generalization abilities on diversestructural instances.