NeuroBack: Improving CDCL SAT Solving using Graph Neural Networks
This work addresses the practical improvement of SAT solving for fields like planning and verification, though it is incremental as it builds on existing GNN and CDCL methods.
The paper tackled the problem of enhancing Conflict-Driven Clause Learning (CDCL) SAT solvers using Graph Neural Networks (GNNs) by proposing NeuroBack, which predicts variable phases with a single offline model inference to avoid GPU reliance, resulting in solving up to 5.2% and 7.4% more problems on recent SAT competition sets.
Propositional satisfiability (SAT) is an NP-complete problem that impacts many research fields, such as planning, verification, and security. Mainstream modern SAT solvers are based on the Conflict-Driven Clause Learning (CDCL) algorithm. Recent work aimed to enhance CDCL SAT solvers using Graph Neural Networks (GNNs). However, so far this approach either has not made solving more effective, or required substantial GPU resources for frequent online model inferences. Aiming to make GNN improvements practical, this paper proposes an approach called NeuroBack, which builds on two insights: (1) predicting phases (i.e., values) of variables appearing in the majority (or even all) of the satisfying assignments are essential for CDCL SAT solving, and (2) it is sufficient to query the neural model only once for the predictions before the SAT solving starts. Once trained, the offline model inference allows NeuroBack to execute exclusively on the CPU, removing its reliance on GPU resources. To train NeuroBack, a new dataset called DataBack containing 120,286 data samples is created. NeuroBack is implemented as an enhancement to a state-of-the-art SAT solver called Kissat. As a result, it allowed Kissat to solve up to 5.2% and 7.4% more problems on two recent SAT competition problem sets, SATCOMP-2022 and SATCOMP-2023, respectively. NeuroBack therefore shows how machine learning can be harnessed to improve SAT solving in an effective and practical manner.