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

## TL;DR

This paper introduces a neural network-based method for approximate weighted DNF counting that achieves linear-time performance for bounded-width formulas, demonstrating strong generalization on large instances.

## Contribution

It presents a novel neural model counting approach that combines deep learning with approximate model counting for weighted #DNF, achieving scalable and accurate results.

## Key findings

- Achieves linear-time approximation for bounded-width weighted #DNF
- Model generalizes well to large-scale instances
- Outperforms traditional methods in scalability and accuracy

## Abstract

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.