# Graph Neural Networks for Propositional Model Counting

arXiv: https://arxiv.org/abs/2205.04423 · HTML: https://mlsanity.com/paper/2205.04423/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 9 May 2022.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective](https://mlsanity.com/paper/2003.00330/) (2020)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting](https://mlsanity.com/paper/1904.02688/) (2019)

## Built on by (most cited first, 1 of 1)

- [Attn-JGNN: Attention Enhanced Join-Graph Neural Networks](https://mlsanity.com/paper/2510.15583/) (2025)

## Abstract (arXiv)

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.