Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets

2025-08-08

AI Summary

Existing rule-based knowledge graph completion methods offer interpretability but rely on large rule sets, compromising both interpretability and efficiency. This paper introduces the concept of *rule context*—a cohesive subset of collaboratively functioning rules modeled as a probabilistic circuit—enabling traceable probabilistic inference without independence assumptions while preserving logical semantics. By learning the probability distribution over rule contexts, our approach drastically compresses the rule set while supporting both exact and approximate query probability estimation. Evaluated on eight benchmark datasets, our method achieves performance comparable to state-of-the-art baselines (e.g., AnyBURL) using only 4–30% of their rules; with merely 4% of the rules, it retains 91% of peak accuracy. Moreover, inference speed improves by up to 31×. The framework thus unifies high efficiency, faithful interpretability, and rigorous probabilistic semantics.

Technology Category

• Data Mining & Knowledge Management: Rule Mining & Pattern Mining
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Rule-based methods for knowledge graph completion provide explainable results but often require a significantly large number of rules to achieve competitive performance. This can hinder explainability due to overwhelmingly large rule sets. We discover rule contexts (meaningful subsets of rules that work together) from training data and use learned probability distribution (i.e. probabilistic circuits) over these rule contexts to more rapidly achieve performance of the full rule set. Our approach achieves a 70-96% reduction in number of rules used while outperforming baseline by up to 31$ imes$ when using equivalent minimal number of rules and preserves 91% of peak baseline performance even when comparing our minimal rule sets against baseline's full rule sets. We show that our framework is grounded in well-known semantics of probabilistic logic, does not require independence assumptions, and that our tractable inference procedure provides both approximate lower bounds and exact probability of a given query. The efficacy of our method is validated by empirical studies on 8 standard benchmark datasets where we show competitive performance by using only a fraction of the rules required by AnyBURL's standard inference method, the current state-of-the-art for rule-based knowledge graph completion. This work may have further implications for general probabilistic reasoning over learned sets of rules.

Problem

• Reducing rule set size for knowledge graph completion
• Maintaining performance with minimal explainable rules
• Using probabilistic circuits over rule contexts efficiently

Innovation

• Uses probabilistic circuits over rule contexts
• Reduces rule sets by 70-96% while maintaining performance
• Provides tractable inference without independence assumptions