In plain words: Entities are stored as quaternions—numbers with three imaginary parts—and relations act as rotations in four-dimensional space, so all parts of an entity interact directly. It beat the previous best complex-number approach on four standard tests of filling in missing facts.
Abstract · Quaternion Knowledge Graph Embeddings
In this work, we move beyond the traditional complex-valued representations, introducing more expressive hypercomplex representations to model entities and relations for knowledge graph embeddings. More specifically, quaternion embeddings, hypercomplex-valued embeddings with three imaginary components, are utilized to represent entities. Relations are modelled as rotations in the quaternion space. The advantages of the proposed approach are: (1) Latent inter-dependencies (between all components) are aptly captured with Hamilton product, encouraging a more compact interaction between entities and relations; (2) Quaternions enable expressive rotation in four-dimensional space and have more degree of freedom than rotation in complex plane; (3) The proposed framework is a generalization of ComplEx on hypercomplex space while offering better geometrical interpretations, concurrently satisfying the key desiderata of relational representation learning (i.e., modeling symmetry, anti-symmetry and inversion). Experimental results demonstrate that our method achieves state-of-the-art performance on four well-established knowledge graph completion benchmarks.
Shuai Zhang, Yi Tay, Lina Yao, Qi Liu
arXiv:1904.10281 · cs.LG, cs.CL, stat.ML · submitted Apr 23, 2019 · updated Oct 31, 2019
abstract · pdf · html · Accepted by NeurIPS 2019
[1] https://en.wikipedia.org/wiki/Nash_embedding_theorems