# SAFRAN: An interpretable, rule-based link prediction method outperforming embedding models

arXiv: https://arxiv.org/abs/2109.08002 · HTML: https://mlsanity.com/paper/2109.08002/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 12 of 12)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [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)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction](https://mlsanity.com/paper/1911.09419/) (2019)
- [Knowledge Graph Embedding for Link Prediction: A Comparative Analysis](https://mlsanity.com/paper/2002.00819/) (2020)
- [Interaction Embeddings for Prediction and Explanation in Knowledge Graphs](https://mlsanity.com/paper/1903.04750/) (2019)
- [Reinforced Anytime Bottom Up Rule Learning for Knowledge Graph Completion](https://mlsanity.com/paper/2004.04412/) (2020)
- [Towards Learning Instantiated Logical Rules from Knowledge Graphs](https://mlsanity.com/paper/2003.06071/) (2020)
- [Building Rule Hierarchies for Efficient Logical Rule Learning from Knowledge Graphs](https://mlsanity.com/paper/2006.16171/) (2020)

## Built on by (most cited first, 15 of 15)

- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Sem@K: Is my knowledge graph embedding model semantic-aware?](https://mlsanity.com/paper/2301.05601/) (2023)
- [Knowledge Graph Embeddings in the Biomedical Domain: Are They Useful? A Look at Link Prediction, Rule Learning, and Downstream Polypharmacy Tasks](https://mlsanity.com/paper/2305.19979/) (2023)
- [Enhancing Multi-Hop Knowledge Graph Reasoning through Reward Shaping Techniques](https://mlsanity.com/paper/2403.05801/) (2024)
- [Comprehensible Artificial Intelligence on Knowledge Graphs: A survey](https://mlsanity.com/paper/2404.03499/) (2024)
- [Inductive Knowledge Graph Completion with GNNs and Rules: An Analysis](https://mlsanity.com/paper/2308.07942/) (2023)
- [Leveraging LLM-GNN Integration for Open-World Question Answering over Knowledge Graphs](https://mlsanity.com/paper/2604.13979/) (2026)
- [Neurosymbolic Methods for Rule Mining](https://mlsanity.com/paper/2408.05773/) (2024)
- [Simple Rule Injection for ComplEx Embeddings](https://mlsanity.com/paper/2308.03269/) (2023)
- [On the Aggregation of Rules for Knowledge Graph Completion](https://mlsanity.com/paper/2309.00306/) (2023)
- [Emulating the Human Mind: A Neural-symbolic Link Prediction Model with Fast and Slow Reasoning and Filtered Rules](https://mlsanity.com/paper/2310.13996/) (2023)
- [Improving rule mining via embedding-based link prediction](https://mlsanity.com/paper/2406.10144/) (2024)
- [PathE: Leveraging Entity-Agnostic Paths for Parameter-Efficient Knowledge Graph Embeddings](https://mlsanity.com/paper/2501.19095/) (2025)
- [Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets](https://mlsanity.com/paper/2508.06706/) (2025)
- [Cyberswarm: a novel swarm intelligence algorithm inspired by cyber community dynamics](https://mlsanity.com/paper/2512.14752/) (2025)

## Abstract (arXiv)

Neural embedding-based machine learning models have shown promise for predicting novel links in knowledge graphs. Unfortunately, their practical utility is diminished by their lack of interpretability. Recently, the fully interpretable, rule-based algorithm AnyBURL yielded highly competitive results on many general-purpose link prediction benchmarks. However, current approaches for aggregating predictions made by multiple rules are affected by redundancies. We improve upon AnyBURL by introducing the SAFRAN rule application framework, which uses a novel aggregation approach called Non-redundant Noisy-OR that detects and clusters redundant rules prior to aggregation. SAFRAN yields new state-of-the-art results for fully interpretable link prediction on the established general-purpose benchmarks FB15K-237, WN18RR and YAGO3-10. Furthermore, it exceeds the results of multiple established embedding-based algorithms on FB15K-237 and WN18RR and narrows the gap between rule-based and embedding-based algorithms on YAGO3-10.