Predicting Propositional Satisfiability via End-to-End Learning

Chris Cameron, Rex Chen, Jason Hartford, Kevin Leyton-Brown

Abstract: Strangely enough, it is possible to use machine learning mod- els to predict the satisfiability status of hard SAT problems with accuracy considerably higher than random guessing. Ex- isting methods have relied on extensive, manual feature engi- neering and computationally complex features (e.g., based on linear programming relaxations). We show for the first time that even better performance can be achieved by end-to-end learning methods — i.e., models that map directly from raw problem inputs to predictions and take only linear time to eval- uate. Our work leverages deep network models which capture a key invariance exhibited by SAT problems: satisfiability status is unaffected by reordering variables and clauses. We showed that end-to-end learning with deep networks can outperform previous work on random 3-SAT problems at the solubility phase transition, where: (1) exactly 50% of problems are satis- fiable; and (2) empirical runtimes of known solution methods scale exponentially with problem size (e.g., we achieved 84% prediction accuracy on 600-variable problems, which take hours to solve with state-of-the-art methods). We also showed that deep networks can generalize across problem sizes (e.g., a network trained only on 100-variable problems, which typ- ically take about 10 ms to solve, achieved 81% accuracy on 600-variable problems).