Distance-Adaptive Quaternion Knowledge Graph Embedding with Bidirectional Rotation

TL;DR

This work addresses the gap between semantic-focused and distance-focused quaternion KGEs by introducing DaBR, which fuses semantic matching with geometric distance through bidirectional rotation and distance-adaptive translations. Head entities are right-rotated and tail entities are rotated in reverse using a normalized unit quaternion, while a distance embedding captures geometric proximity, with a joint score $oldsymbol{\phi}(h,r,t)=s(h,r,t)+\lambda d(h,r,t)$. The approach is supported by proofs showing it can handle symmetry, antisymmetry, inversion, and composition, and is validated on standard benchmarks where it achieves state-of-the-art or competitive results with fewer parameters than comparable models. The combination of semantics and geometry yields improved inter- and intra-cluster separability in embeddings and better handling of diverse relation types, indicating practical impact for knowledge graph completion tasks. Limitations include suboptimal H@1 performance on some datasets and inability to predict unseen entities, pointing to future work in generalization and entity expansion.

Abstract

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through semantic matching or geometric distance scoring functions. However, it appears that semantic matching diminishes the separability of entities, while the distance scoring function weakens the semantics of entities. To address this issue, we propose a novel quaternion knowledge graph embedding model. Our model combines semantic matching with entity's geometric distance to better measure the plausibility of triplets. Specifically, in the quaternion space, we perform a right rotation on head entity and a reverse rotation on tail entity to learn rich semantic features. Then, we utilize distance adaptive translations to learn geometric distance between entities. Furthermore, we provide mathematical proofs to demonstrate our model can handle complex logical relationships. Extensive experimental results and analyses show our model significantly outperforms previous models on well-known knowledge graph completion benchmark datasets. Our code is available at https://github.com/llqy123/DaBR.

Figures (6)

• Figure 1: The visualization embedding of QuatE and TransERR models after 100 epochs training. Points in the same color represent tail entities that have the same $(h_r, r_j )$ (query) context.
• Figure 2: The comparison of modeling entity semantics of QuatE, QuatRE and DaBR. These models learn the embeddings of knowledge graphs in quaternion spaces. $\otimes$ denotes the Hamilton product (Equation \ref{['equ:ham']}).
• Figure 3: MRR scores for QuatE, QuatRE and our DaBR models over 0 to 5200 training epochs.
• Figure 4: Visualization of the embeddings of tail entities using t-SNE. A point represents a tail entity. Points in the same color represent tail entities that have the same $(h_i, r_j )$ context.
• Figure 5: DaBR with distance-adaptation and without.