Mixed Multi-relational Representation Learning for Low-Dimensional Knowledge Graph Embedding

Hyperbolic embeddings have recently received attention in machine learning because of their better ability to handle hierarchical data than Euclidean embeddings. Moreover, Hyperbolic models are also being developed for multi-relational knowledge graphs which contain multiple hierarchical relationships and have achieved promising results, such as MuRP, HyperKG, and ROTH. However, not all data is hierarchical. We also found that most of the geometry models were trained to attain good results on high-dimensional embeddings and low-dimensional embeddings are often of little interest. Besides, neural networks and graph networks models have had an impressive performance. However, they also require a relatively high-dimensional embedding to achieve good results, making them limited to use in large-scale knowledge graphs. To address these issues, in this paper, we introduce a new model named MuREL (Multi-Relational Euclidean Lorentzian), which learns a mixed embedding between two spaces, Euclidean and Lorentzian. They are not only suitable for a variety of data types but also work well on low-dimensional embeddings. Experiments on standard benchmark datasets from the task of link prediction show that our model outperforms existing Euclidean and Hyperbolic models, especially at lower dimensionality.