# Attn-JGNN: Attention Enhanced Join-Graph Neural Networks

arXiv: https://arxiv.org/abs/2510.15583 · HTML: https://mlsanity.com/paper/2510.15583/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [A General Survey on Attention Mechanisms in Deep Learning](https://mlsanity.com/paper/2203.14263/) (2022)
- [Quantitative Verification of Neural Networks And its Security Applications](https://mlsanity.com/paper/1906.10395/) (2019)
- [Belief Propagation Neural Networks](https://mlsanity.com/paper/2007.00295/) (2020)
- [Goal-Aware Neural SAT Solver](https://mlsanity.com/paper/2106.07162/) (2021)
- [A Scalable Approximate Model Counter](https://mlsanity.com/paper/1306.5726/) (2013)
- [NSNet: A General Neural Probabilistic Framework for Satisfiability Problems](https://mlsanity.com/paper/2211.03880/) (2022)
- [PDP: A General Neural Framework for Learning Constraint Satisfaction Solvers](https://mlsanity.com/paper/1903.01969/) (2019)
- [ADDMC: Weighted Model Counting with Algebraic Decision Diagrams](https://mlsanity.com/paper/1907.05000/) (2019)
- [Learning Branching Heuristics for Propositional Model Counting](https://mlsanity.com/paper/2007.03204/) (2020)
- [DPMC: Weighted Model Counting by Dynamic Programming on Project-Join Trees](https://mlsanity.com/paper/2008.08748/) (2020)
- [Rounding Meets Approximate Model Counting](https://mlsanity.com/paper/2305.09247/) (2023)
- [Discovering the Representation Bottleneck of Graph Neural Networks](https://mlsanity.com/paper/2205.07266/) (2022)
- [Fast Converging Anytime Model Counting](https://mlsanity.com/paper/2212.09390/) (2022)
- [Graph Neural Networks for Propositional Model Counting](https://mlsanity.com/paper/2205.04423/) (2022)

## Abstract (arXiv)

We propose an Attention Enhanced Join-Graph Neural Networks(Attn-JGNN) model for solving #SAT problems, which significantly improves the solving accuracy. Inspired by the Iterative Join Graph Propagation (IJGP) algorithm, Attn-JGNN uses tree decomposition to encode the CNF formula into a join-graph, then performs iterative message passing on the join-graph, and finally approximates the model number by learning partition functions. In order to further improve the accuracy of the solution, we apply the attention mechanism in and between clusters of the join-graphs, which makes Attn-JGNN pay more attention to the key variables and clusters in probabilistic inference, and reduces the redundant calculation. Finally, our experiments show that our Attn-JGNN model achieves better results than other neural network methods.