# Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completion

arXiv: https://arxiv.org/abs/2109.09566 · HTML: https://mlsanity.com/paper/2109.09566/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## 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)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Go for a Walk and Arrive at the Answer: Reasoning Over Paths in Knowledge Bases using Reinforcement Learning](https://mlsanity.com/paper/1711.05851/) (2017)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (2018)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Learning Reasoning Strategies in End-to-End Differentiable Proving](https://mlsanity.com/paper/2007.06477/) (2020)
- [Learning Longer-term Dependencies in RNNs with Auxiliary Losses](https://mlsanity.com/paper/1803.00144/) (2018)

## Built on by (most cited first, 7 of 7)

- [Neurosymbolic AI for Reasoning over Knowledge Graphs: A Survey](https://mlsanity.com/paper/2302.07200/) (2023)
- [Large language models for artificial general intelligence (AGI): A survey of foundational principles and approaches](https://mlsanity.com/paper/2501.03151/) (2025)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [R5: Rule Discovery with Reinforced and Recurrent Relational Reasoning](https://mlsanity.com/paper/2205.06454/) (2022)
- [Neurosymbolic AI for Reasoning on Biomedical Knowledge Graphs](https://mlsanity.com/paper/2307.08411/) (2023)
- [MARS: A neurosymbolic approach for interpretable drug discovery](https://mlsanity.com/paper/2410.05289/) (2024)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)

## Abstract (arXiv)

Recent interest in Knowledge Base Completion (KBC) has led to a plethora of approaches based on reinforcement learning, inductive logic programming and graph embeddings. In particular, rule-based KBC has led to interpretable rules while being comparable in performance with graph embeddings. Even within rule-based KBC, there exist different approaches that lead to rules of varying quality and previous work has not always been precise in highlighting these differences. Another issue that plagues most rule-based KBC is the non-uniformity of relation paths: some relation sequences occur in very few paths while others appear very frequently. In this paper, we show that not all rule-based KBC models are the same and propose two distinct approaches that learn in one case: 1) a mixture of relations and the other 2) a mixture of paths. When implemented on top of neuro-symbolic AI, which learns rules by extending Boolean logic to real-valued logic, the latter model leads to superior KBC accuracy outperforming state-of-the-art rule-based KBC by 2-10% in terms of mean reciprocal rank. Furthermore, to address the non-uniformity of relation paths, we combine rule-based KBC with graph embeddings thus improving our results even further and achieving the best of both worlds.