Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting
This addresses scalability issues in probabilistic inference for AI and logic domains, but it is incremental as it builds on existing approximate methods with neural enhancements.
The paper tackles the problem of weighted DNF counting, which is computationally hard, by proposing a neural model counting approach that combines approximate model counting with deep learning to accurately approximate model counts in linear time for bounded-width instances, showing good generalization to large-scale instances in experiments.
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.