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Many natural optimization problems are NP-hard, which implies that they areprobably hard to solve exactly in the worst-case. However, it suffices to getreasonably good solutions for all (or even most) instances in practice. Thispaper presents a new algorithm for computing approximate solutions in${\Theta(N})$ for the Maximum Exact 3-Satisfiability (MAX-E-$3$-SAT) problem byusing deep learning methodology. This methodology allows us to create alearning algorithm able to fix Boolean variables by using local informationobtained by the Survey Propagation algorithm. By performing an accurateanalysis, on random CNF instances of the MAX-E-$3$-SAT with several Booleanvariables, we show that this new algorithm, avoiding any decimation strategy,can build assignments better than a random one, even if the convergence of themessages is not found. Although this algorithm is not competitive withstate-of-the-art Maximum Satisfiability (MAX-SAT) solvers, it can solvesubstantially larger and more complicated problems than it ever saw duringtraining.

Learning from Survey Propagation: a Neural Network for MAX-E-$3$-SAT