# Complex Embeddings for Simple Link Prediction

arXiv: https://arxiv.org/abs/1606.06357 · HTML: https://mlsanity.com/paper/1606.06357/

## Key facts

- Cited by 902 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2016.

## Built on by (most cited first, 30 of 902)

- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Prediction](https://mlsanity.com/paper/2106.06935/) (2021)
- [Deep Bidirectional Language-Knowledge Graph Pretraining](https://mlsanity.com/paper/2210.09338/) (2022)
- [GNN-RAG: Graph Neural Retrieval for Large Language Model Reasoning](https://mlsanity.com/paper/2405.20139/) (2024)
- [Temporal Knowledge Graph Reasoning Based on Evolutional Representation Learning](https://mlsanity.com/paper/2104.10353/) (2021)
- [A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodal](https://mlsanity.com/paper/2212.05767/) (2022)
- [Graph Foundation Models: Concepts, Opportunities and Challenges](https://mlsanity.com/paper/2310.11829/) (2023)
- [Question Answering Over Temporal Knowledge Graphs](https://mlsanity.com/paper/2106.01515/) (2021)
- [SimKGC: Simple Contrastive Knowledge Graph Completion with Pre-trained Language Models](https://mlsanity.com/paper/2203.02167/) (2022)
- [Graph Neural Networks for Link Prediction with Subgraph Sketching](https://mlsanity.com/paper/2209.15486/) (2022)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)
- [Sequence-to-Sequence Knowledge Graph Completion and Question Answering](https://mlsanity.com/paper/2203.10321/) (2022)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Simple and Efficient Heterogeneous Graph Neural Network](https://mlsanity.com/paper/2207.02547/) (2022)
- [Knowledge Graphs: Opportunities and Challenges](https://mlsanity.com/paper/2303.13948/) (2023)
- [TimeTraveler: Reinforcement Learning for Temporal Knowledge Graph Forecasting](https://mlsanity.com/paper/2109.04101/) (2021)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [TransferNet: An Effective and Transparent Framework for Multi-hop Question Answering over Relation Graph](https://mlsanity.com/paper/2104.07302/) (2021)
- [TLogic: Temporal Logical Rules for Explainable Link Forecasting on Temporal Knowledge Graphs](https://mlsanity.com/paper/2112.08025/) (2021)
- [Complex Knowledge Base Question Answering: A Survey](https://mlsanity.com/paper/2108.06688/) (2021)
- [A*Net: A Scalable Path-based Reasoning Approach for Knowledge Graphs](https://mlsanity.com/paper/2206.04798/) (2022)
- [Making Large Language Models Perform Better in Knowledge Graph Completion](https://mlsanity.com/paper/2310.06671/) (2023)
- [RHO (ρ): Reducing Hallucination in Open-domain Dialogues with Knowledge Grounding](https://mlsanity.com/paper/2212.01588/) (2022)
- [Differentially Private Federated Knowledge Graphs Embedding](https://mlsanity.com/paper/2105.07615/) (2021)
- [From Discrimination to Generation: Knowledge Graph Completion with Generative Transformer](https://mlsanity.com/paper/2202.02113/) (2022)
- [TorchDrug: A Powerful and Flexible Machine Learning Platform for Drug Discovery](https://mlsanity.com/paper/2202.08320/) (2022)
- [TwHIN-BERT: A Socially-Enriched Pre-trained Language Model for Multilingual Tweet Representations at Twitter](https://mlsanity.com/paper/2209.07562/) (2022)
- [Hybrid Transformer with Multi-level Fusion for Multimodal Knowledge Graph Completion](https://mlsanity.com/paper/2205.02357/) (2022)

## Abstract (arXiv)

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.