Revisiting GNNs for Boolean Satisfiability

Jan Hula, Mikolas Janota, David Mojžíšek

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Keywords: graph neural networks, satisfiability, curriculum, SAT

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TL;DR: We introduce several enhancements for Graph Neural Networks that are trained to predict solutions of combinatorial problems.

Abstract: We introduce a number of enhancements for the training and inference procedure of Graph Neural Networks that are trained to predict solutions of combinatorial problems. We motivate these enhancements by pointing to possible connections to two approximation algorithms studied in the domain of Boolean Satisfiability: Belief Propagation and Semidefinite Programming Relaxations. The first significant enhancement is a curriculum training procedure, which incrementally increases the problem complexity in the training set together with increasing the number of message passing iterations of the Graph Neural Network. We show that the curriculum, together with several other optimizations, reduces training time by more than an order of magnitude compared to the baseline without the curriculum. Furthermore, we apply decimation and initial embedding sampling, which significantly increases the percentage of solved problems.

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Submission Number: 4009