Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets

arXiv:2508.06706v2 Announce Type: replace Abstract: 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 31imes. 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.

Source: arXiv cs.AI | 2026-08-11