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

TL;DR

This paper introduces a deep learning-based algorithm for approximating solutions to MAX-E-3-SAT problems, leveraging survey propagation insights to fix variables efficiently without decimation, enabling solutions for larger instances.

Contribution

The paper presents a novel neural network approach that uses local survey propagation information to solve MAX-E-3-SAT approximately, capable of handling larger problems than training data.

Findings

The algorithm outperforms random assignment in solution quality.

It can solve larger and more complex problems than seen during training.

It operates effectively even without message convergence.

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.