# Knowledge Graph Embeddings in Geometric Algebras

arXiv: https://arxiv.org/abs/2010.00989 · HTML: https://mlsanity.com/paper/2010.00989/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Time-aware Graph Neural Networks for Entity Alignment between Temporal Knowledge Graphs](https://mlsanity.com/paper/2203.02150/) (2022)
- [Knowledge Graph Embedding: An Overview](https://mlsanity.com/paper/2309.12501/) (2023)
- [Multiple Run Ensemble Learning with Low-Dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2104.05003/) (2021)
- [Toward Practical Entity Alignment Method Design: Insights from New Highly Heterogeneous Knowledge Graph Datasets](https://mlsanity.com/paper/2304.03468/) (2023)
- [Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2202.09464/) (2022)
- [Embedding Knowledge Graphs in Degenerate Clifford Algebras](https://mlsanity.com/paper/2402.04870/) (2024)
- [Fully tensorial approach to hypercomplex-valued neural networks](https://mlsanity.com/paper/2407.00449/) (2024)
- [Prior Bilinear Based Models for Knowledge Graph Completion](https://mlsanity.com/paper/2309.13834/) (2023)

## Abstract (arXiv)

Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor Octonion) representations, all of which are subsumed into a geometric algebra. In this work,we introduce a novel geometric algebra-based KG embedding framework, GeomE, which uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.