MILP-SAT-GNN: Yet Another Neural SAT Solver
This work investigates the generalization capability and theoretical foundations of Graph Neural Networks (GNNs) for solving Boolean satisfiability (SAT) problems. Method: We model k-CNF formulas as weighted bipartite graphs and establish a reversible logical-to-graph mapping via mixed-integer linear programming encoding. To overcome expressivity limitations of standard GNNs on foldable formulas, we introduce Random Node Initialization (RNI); we further prove that, even without RNI, GNNs possess universal approximation power for unfoldable formulas. Contribution/Results: Theoretically, we establish clause-variable permutation invariance for the first time and characterize the completeness boundary of GNNs in SAT solving. Empirically, even simple GNN architectures achieve high accuracy and near-completeness in SAT classification under limited training data, demonstrating the feasibility and robustness of end-to-end neural SAT solving.