Graph Neural Networks for Propositional Model Counting

TL;DR

This paper introduces a GNN-based architecture for approximate propositional model counting (#SAT), demonstrating effective scaling, competitive performance, and good generalization across different problem distributions.

Contribution

It presents a novel GNN framework for #SAT that extends belief propagation with self-attention, enabling scalable and adaptable approximate counting.

Findings

Model trained on small formulas scales to larger problems effectively.

Achieves performance comparable or superior to state-of-the-art approximate solvers.

Can be fine-tuned for different formula distributions, improving generalization.

Abstract

Graph Neural Networks (GNNs) have been recently leveraged to solve several logical reasoning tasks. Nevertheless, counting problems such as propositional model counting (#SAT) are still mostly approached with traditional solvers. Here we tackle this gap by presenting an architecture based on the GNN framework for belief propagation (BP) of Kuch et al., extended with self-attentive GNN and trained to approximately solve the #SAT problem. We ran a thorough experimental investigation, showing that our model, trained on a small set of random Boolean formulae, is able to scale effectively to much larger problem sizes, with comparable or better performances of state of the art approximate solvers. Moreover, we show that it can be efficiently fine-tuned to provide good generalization results on different formulae distributions, such as those coming from SAT-encoded combinatorial problems.