We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability.   Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve problems that are substantially larger and more difficult than it ever saw during training by simply running for more iterations. Moreover, NeuroSAT generalizes to novel distributions; after training only on random SAT problems, at test time it can solve SAT problems encoding graph coloring, clique detection, dominating set, and vertex cover problems, all on a range of distributions over small random graphs.
We train a graph network to predict boolean satisfiability and show that it learns to search for solutions, and that the solutions it finds can be decoded from its activations. The paper describes a general neural network architecture for predicting satisfiability This paper presents the NeuroSAT architecture which uses a deep message passing neural net for predicting the satisfiability of CNF instances