# Complex and Holographic Embeddings of Knowledge Graphs: A Comparison

arXiv: https://arxiv.org/abs/1707.01475 · HTML: https://mlsanity.com/paper/1707.01475/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2017.

## Built on by (most cited first, 5 of 5)

- [Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding](https://mlsanity.com/paper/2110.03789/) (2021)
- [Out-of-Vocabulary Entities in Link Prediction](https://mlsanity.com/paper/2105.12524/) (2021)
- [CoNO: Complex Neural Operator for Continous Dynamical Physical Systems](https://mlsanity.com/paper/2406.02597/) (2024)
- [Kronecker Decomposition for Knowledge Graph Embeddings](https://mlsanity.com/paper/2205.06560/) (2022)
- [Adapting Pre-trained Language Models for Quantum Natural Language Processing](https://mlsanity.com/paper/2302.13812/) (2023)

## Abstract (arXiv)

Embeddings of knowledge graphs have received significant attention due to their excellent performance for tasks like link prediction and entity resolution. In this short paper, we are providing a comparison of two state-of-the-art knowledge graph embeddings for which their equivalence has recently been established, i.e., ComplEx and HolE [Nickel, Rosasco, and Poggio, 2016; Trouillon et al., 2016; Hayashi and Shimbo, 2017]. First, we briefly review both models and discuss how their scoring functions are equivalent. We then analyze the discrepancy of results reported in the original articles, and show experimentally that they are likely due to the use of different loss functions. In further experiments, we evaluate the ability of both models to embed symmetric and antisymmetric patterns. Finally, we discuss advantages and disadvantages of both models and under which conditions one would be preferable to the other.