Graph neural network improves phase prediction in SAT solvers

A new graph neural network model can predict the phase assignments that modern SAT solvers rely on, improving solving rates over a leading competitive solver in benchmark tests. The model, called Neural Multi-scale Graph Convolutional Network (NeuroMGCN), was developed by Wenjing Chang and Changhan Wang and described in a regular paper published on 25 October 2026 in the International Journal of Data Science and Analytics. The Boolean Satisfiability problem, or SAT, was the first problem proven to be NP-complete, and it is widely applied in fields such as artificial intelligence and program verification.

Contemporary SAT solvers are built around the Conflict-Driven Clause Learning algorithm, whose performance depends heavily on key heuristic strategies such as variable branching and phase assignment. With advancements in deep learning, graph neural networks have increasingly been utilized for phase prediction tasks in SAT solving to boost efficiency. NeuroMGCN combines two architectural ideas: multi-scale attention mechanisms and dynamic relation-aware graph convolution.

According to the authors, this combination allows the network to effectively capture complex dependencies among variables in SAT formulas, improving the accuracy of backbone variable prediction. The model is trained with a pretraining and fine-tuning strategy, in which it first learns general representations and is then adapted to specific solving tasks. The study reports two kinds of results.

In the phase prediction task itself, NeuroMGCN outperformed the NeuroBack baseline on backbone variable classification in terms of accuracy, precision, recall and F1 score. In end-to-end solver tests, NeuroMGCN-guided solving raised the solving rate by 4.1 percent over the Kissat solver in the main track tests of the SATCOMP-2023 competition and by 5.2 percent in the main track tests of SATCOMP-2024. The model was trained and evaluated on multiple real-world datasets.

The authors present the work as evidence of the potential of graph neural networks in SAT phase prediction, offering new insights for developing efficient and intelligent SAT solving frameworks.

Subject of Research: Multi-scale graph neural network approach for phase prediction in SAT solvers

Article Title: Multi-scale graph neural network approach for phase prediction in SAT solvers

Article References: Chang, W., & Wang, C. (2026). Multi-scale graph neural network approach for phase prediction in SAT solvers. International Journal of Data Science and Analytics, 22(1), Article 359. https://doi.org/10.1007/s41060-026-01291-7

Image Credits: AI Generated

DOI: 10.1007/s41060-026-01291-7

Keywords: Multi-scale, graph, neural, network, approach, phase, prediction, solvers, scientific research