Quaternion Knowledge Graph Embedding

Complex-valued representations have demonstrated promising results on modeling relational data, i.e., knowledge graphs. This paper proposes a new knowledge graph embedding method. More concretely, we move beyond standard complex representations, adopting expressive hypercomplex representations for learning representations of entities and relations. Hypercomplex embeddings, or Quaternion embeddings (QuatE), are complex valued embeddings with three imaginary components. Different from standard complex (Hermitian) inner product, latent interdependencies (between all components) are aptly captured via the Hamilton product in Quaternion space, encouraging a more efficient and expressive representation learning process. Moreover, Quaternions are intuitively desirable for smooth and pure rotation in vector space, preventing noise from sheer/scaling operators. Finally, Quaternion inductive biases enjoy and satisfy the key desiderata of relational representation learning (i.e., modeling symmetry, anti-symmetry and inversion). Experimental results demonstrate that QuatE achieves state-of-the-art performance on four well-established knowledge graph completion benchmarks.