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

2025/11/24 by Kaidi Wan, Minghao Liu, Wan, Kaidi +3
Computer Science · #Advanced Graph Neural Networks #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Graph Theory and Algorithms #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2511.19544

openalex publication_date 2025/11/24 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

Abstract

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

Citations

• GraSS: Combining Graph Neural Networks with Expert Knowledge for SAT Solver Selection
• torchmSAT: A GPU-Accelerated Approximation To The Maximum Satisfiability Problem
• Rethinking the Soft Conflict Pseudo Boolean Constraint on MaxSAT Local Search Solvers
• HardSATGEN: Understanding the Difficulty of Hard SAT Formula Generation and A Strong Structure-Hardness-Aware Baseline
• Augment with Care: Contrastive Learning for Combinatorial Problems
• Learning a SAT Solver from Single-Bit Supervision
• Attention Is All You Need
• Long Short-Term Memory
• “Neural” computation of decisions in optimization problems
• Depth-First Search and Linear Graph Algorithms

Related

• Can Graph Neural Networks Learn to Solve MaxSAT Problem?
• torchmSAT: A GPU-Accelerated Approximation To The Maximum Satisfiability Problem
• HyperSAT: Unsupervised Hypergraph Neural Networks for Weighted MaxSAT Problems
• Are Graph Neural Networks Optimal Approximation Algorithms?
• MILP-SAT-GNN: Yet Another Neural SAT Solver