  Modern neural networks obtain information about the problem and calculate the
output solely from the input values. We argue that it is not always optimal,
and the network's performance can be significantly improved by augmenting it
with a query mechanism that allows the network at run time to make several
solution trials and get feedback on the loss value on each trial. To
demonstrate the capabilities of the query mechanism, we formulate an
unsupervised (not depending on labels) loss function for Boolean Satisfiability
Problem (SAT) and theoretically show that it allows the network to extract rich
information about the problem. We then propose a neural SAT solver with a query
mechanism called QuerySAT and show that it outperforms the neural baseline on a
wide range of SAT tasks.
