PDP: A General Neural Framework for Learning SAT Solvers

Saeed Amizadeh, Sergiy Matusevych, Markus Weimer

Keywords: Neural SAT solvers, Graph Neural Networks, Neural Message Passing, Unsupervised Learning, Neural Decimation

TL;DR: We propose a general neural message passing framework for SAT solving based on the idea of propagation, decimation and prediction (PDP).

Abstract: There have been recent efforts for incorporating Graph Neural Network models for learning fully neural solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power of these neural embedding models, it is not clear to what extent they actually learn a search strategy vs. statistical biases in the training data. On the other hand, by fixing the search strategy (e.g. greedy search), one would effectively deprive the neural models of learning better strategies than those given. In this paper, we propose a generic neural framework for learning SAT solvers (and in general any CSP solver) that can be described in terms of probabilistic inference and yet learn search strategies beyond greedy search. Our framework is based on the idea of propagation, decimation and prediction (and hence the name PDP) in graphical models, and can be trained directly toward solving SAT in a fully unsupervised manner via energy minimization, as shown in the paper. Our experimental results demonstrate the effectiveness of our framework for SAT solving compared to both neural and the industrial baselines.