  There have been recent efforts for incorporating Graph Neural Network models
for learning full-stack 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 how the search strategy
in the learned models actually works. On the other hand, by fixing the search
strategy (e.g. greedy search), we would effectively deprive the neural models
of learning better strategies than those given. In this paper, we propose a
generic neural framework for learning CSP solvers 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 CSP 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
state-of-the-art baselines.
