# Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets

arXiv: https://arxiv.org/abs/2508.06706 · HTML: https://mlsanity.com/paper/2508.06706/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 8 Aug 2025.

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

- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Semantic Probabilistic Layers for Neuro-Symbolic Learning](https://mlsanity.com/paper/2206.00426/) (2022)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Coherent Hierarchical Multi-Label Classification Networks](https://mlsanity.com/paper/2010.10151/) (2020)
- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [NLProlog: Reasoning with Weak Unification for Question Answering in Natural Language](https://mlsanity.com/paper/1906.06187/) (2019)
- [Reinforced Anytime Bottom Up Rule Learning for Knowledge Graph Completion](https://mlsanity.com/paper/2004.04412/) (2020)
- [SAFRAN: An interpretable, rule-based link prediction method outperforming embedding models](https://mlsanity.com/paper/2109.08002/) (2021)
- [SLASH: Embracing Probabilistic Circuits into Neural Answer Set Programming](https://mlsanity.com/paper/2110.03395/) (2021)
- [Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules](https://mlsanity.com/paper/2409.16238/) (2024)

## Abstract (arXiv)

Rule-based methods for knowledge graph completion provide explainable results, but often require tens of thousands of rules to achieve competitive performance. Although individual predictions may use only a few rules, reasoning over an entire dataset requires these massive rule sets, hampering system-level understanding. We address this by learning a probability distribution over sets of rules that work together using probabilistic circuits. Our approach achieves a 70-96% reduction in the number of rules needed to reach peak baseline performance. Using an equivalent minimal number of rules, we outperform the baseline by up to 31×. When comparing our minimal rule sets against baseline's full rule sets, we preserve 91% of peak baseline performance. Empirical validation on 8 benchmark datasets shows that our reduced rule sets exhibit higher utilization---fewer rules are wasted, and each prediction requires fewer rules. We show that our framework is grounded in well-known semantics of Nilsson's probabilistic logic and does not require independence assumptions. We provide exact probabilistic inference as well as an efficient lower bound and evaluate both.