# Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

arXiv: https://arxiv.org/abs/1904.02688 · HTML: https://mlsanity.com/paper/1904.02688/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [On the Hardness of Probabilistic Neurosymbolic Learning](https://mlsanity.com/paper/2406.04472/) (2024)
- [Probabilistic Graph Reasoning for Natural Proof Generation](https://mlsanity.com/paper/2107.02418/) (2021)
- [Graph Pruning for Enumeration of Minimal Unsatisfiable Subsets](https://mlsanity.com/paper/2402.15524/) (2024)
- [Graph Neural Networks for Propositional Model Counting](https://mlsanity.com/paper/2205.04423/) (2022)
- [Current and Future Challenges in Knowledge Representation and Reasoning](https://mlsanity.com/paper/2308.04161/) (2023)
- [A Novel Neural-symbolic System under Statistical Relational Learning](https://mlsanity.com/paper/2309.08931/) (2023)
- [Scalable Algorithms for Approximate DNF Model Counting](https://mlsanity.com/paper/2601.10511/) (2026)
- [Parallel Noising in Neural Markov Logic Networks](https://mlsanity.com/paper/2607.19126/) (2026)

## Abstract (arXiv)

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.