Structure based SAT dataset for analysing GNN generalisation

2025-02-17

AI Summary

Prior work on SAT solving with graph neural networks (GNNs) focuses predominantly on CDCL solvers and lacks systematic analysis of GNN sensitivity to input graph structural properties—such as modularity and self-similarity—that critically influence generalization. Method: We introduce StructureSAT, the first benchmark explicitly coupling structural graph metrics with GNN generalization performance. It features a novel hierarchical partitioning paradigm for SAT problem families based on graph-theoretic properties. We conduct rigorous structural graph analysis and empirical GNN evaluations across diverse graph topologies. Contribution/Results: We identify implicit structural bias—specifically, over-reliance on modularity and self-similarity—as a key cause of generalization failure. We further release an extensible SAT graph generation toolkit and evaluation framework. This work establishes both theoretical grounding and empirical evidence for structure-aware GNN design in SAT solving.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Satisfiability (SAT) solvers based on techniques such as conflict driven clause learning (CDCL) have produced excellent performance on both synthetic and real world industrial problems. While these CDCL solvers only operate on a per-problem basis, graph neural network (GNN) based solvers bring new benefits to the field by allowing practitioners to exploit knowledge gained from solved problems to expedite solving of new SAT problems. However, one specific area that is often studied in the context of CDCL solvers, but largely overlooked in GNN solvers, is the relationship between graph theoretic measure of structure in SAT problems and the generalisation ability of GNN solvers. To bridge the gap between structural graph properties (e.g., modularity, self-similarity) and the generalisability (or lack thereof) of GNN based SAT solvers, we present StructureSAT: a curated dataset, along with code to further generate novel examples, containing a diverse set of SAT problems from well known problem domains. Furthermore, we utilise a novel splitting method that focuses on deconstructing the families into more detailed hierarchies based on their structural properties. With the new dataset, we aim to help explain problematic generalisation in existing GNN SAT solvers by exploiting knowledge of structural graph properties. We conclude with multiple future directions that can help researchers in GNN based SAT solving develop more effective and generalisable SAT solvers.

Problem

• Analyzing GNN generalization in SAT solvers
• Exploring structural graph properties impact
• Creating dataset to improve GNN solvers

Innovation

• StructureSAT dataset creation
• Novel hierarchical splitting method
• Exploiting structural graph properties