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arXiv · 2012.06344

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

Raffaele Marino
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Abstract

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

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Raffaele Marino. 2020-12-10. Learning from Survey Propagation: a Neural Network for MAX-E-$3$-SAT. https://doi.org/10.1088/2632-2153%2Fac0496

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