Graph-Based Attention for Differentiable MaxSAT Solving

Sota Moriyama, Katsumi Inoue

Keywords: Maximum Satisfiability, Weighted Maximum Satisfiability, Graph Neural Network, Graph Attention, T-Norm, Neurosymbolic

TL;DR: We introduce SAT-based Graph Attention Networks (SGATs), a t-norm–based GNN architecture for differentiable (weighted) MaxSAT solving, and demonstrate that SGATs outperform existing state-of-the-art continuous approaches on standard benchmarks.

Abstract: The use of deep learning to solve fundamental AI problems such as Boolean Satisfiability (SAT) has been explored recently to develop robust and scalable reasoning systems. This work advances such neural-based reasoning approaches by developing a new Graph Neural Network (GNN) to differentiably solve (weighted) Maximum Satisfiability (MaxSAT). To this end, we propose SAT-based Graph Attention Networks (SGATs) as novel GNNs that are built on t-norm based attention and message passing mechanisms, and structurally designed to approximate greedy distributed local search. To demonstrate the effectiveness of our model, we develop a local search solver that uses SGATs to continuously solve any given MaxSAT problem. Experiments on (weighted) MaxSAT benchmark datasets demonstrate that SGATs significantly outperform existing neural-based architectures, and achieve state-of-the-art performance among continuous approaches, highlighting the strength of the proposed model.

Primary Area: Optimization (e.g., convex and non-convex, stochastic, robust)

Submission Number: 27018