# On Multi-Relational Link Prediction with Bilinear Models

arXiv: https://arxiv.org/abs/1709.04808 · HTML: https://mlsanity.com/paper/1709.04808/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2017.

## Built on by (most cited first, 17 of 17)

- [Link Prediction with Attention Applied on Multiple Knowledge Graph Embedding Models](https://mlsanity.com/paper/2302.06229/) (2023)
- [Searching to Sparsify Tensor Decomposition for N-ary Relational Data](https://mlsanity.com/paper/2104.10625/) (2021)
- [Poisoning Knowledge Graph Embeddings via Relation Inference Patterns](https://mlsanity.com/paper/2111.06345/) (2021)
- [Bilinear Scoring Function Search for Knowledge Graph Learning](https://mlsanity.com/paper/2107.00184/) (2021)
- [HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations](https://mlsanity.com/paper/2108.05774/) (2021)
- [Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction](https://mlsanity.com/paper/2408.08226/) (2024)
- [Efficient Relation-aware Scoring Function Search for Knowledge Graph Embedding](https://mlsanity.com/paper/2104.10880/) (2021)
- [KGTuner: Efficient Hyper-parameter Search for Knowledge Graph Learning](https://mlsanity.com/paper/2205.02460/) (2022)
- [Re-thinking Knowledge Graph Completion Evaluation from an Information Retrieval Perspective](https://mlsanity.com/paper/2205.04105/) (2022)
- [Geometric Algebra based Embeddings for Static and Temporal Knowledge Graph Completion](https://mlsanity.com/paper/2202.09464/) (2022)
- [Joint Pre-training and Local Re-training: Transferable Representation Learning on Multi-source Knowledge Graphs](https://mlsanity.com/paper/2306.02679/) (2023)
- [Capturing Knowledge Graphs and Rules with Octagon Embeddings](https://mlsanity.com/paper/2401.16270/) (2024)
- [Gene-Metabolite Association Prediction with Interactive Knowledge Transfer Enhanced Graph for Metabolite Production](https://mlsanity.com/paper/2410.18475/) (2024)
- [On the Theoretical Limitations of Embedding-based Link Prediction](https://mlsanity.com/paper/2506.22271/) (2025)
- [Quadratic GCN for Graph Classification](https://mlsanity.com/paper/2104.06750/) (2021)
- [Principled Representation Learning for Entity Alignment](https://mlsanity.com/paper/2110.10871/) (2021)
- [On the Effectiveness of Knowledge Graph Embeddings: a Rule Mining Approach](https://mlsanity.com/paper/2206.00983/) (2022)

## Abstract (arXiv)

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can provide good prediction performance. The main goal of this paper is to explore the expressiveness of and the connections between various bilinear models proposed in the literature. In particular, a substantial number of models can be represented as bilinear models with certain additional constraints enforced on the embeddings. We explore whether or not these constraints lead to universal models, which can in principle represent every set of relations, and whether or not there are subsumption relationships between various models. We report results of an independent experimental study that evaluates recent bilinear models in a common experimental setup. Finally, we provide evidence that relation-level ensembles of multiple bilinear models can achieve state-of-the art prediction performance.