Sharing Parameter by Conjugation for Knowledge Graph Embeddings in Complex Space

TL;DR

This work addresses the memory and training-time demands of complex-valued knowledge graph embeddings by introducing conjugate-parameter sharing, which halves the relation-embedding parameter count without sacrificing accuracy. The method, instantiated as Complεx and 5★ε, preserves the expressive transformations of ComplEx and 5★E while reducing computation in regularization and memory usage. Across five benchmark datasets, the conjugate models achieve comparable or superior accuracy and demonstrate substantial training-time savings (notably ~31% on average for 5★E) with easy applicability to other complex-valued KGEs. The results suggest a practical path to scalable KG completion with reduced environmental footprint and preserved modeling power.

Abstract

A Knowledge Graph (KG) is the directed graphical representation of entities and relations in the real world. KG can be applied in diverse Natural Language Processing (NLP) tasks where knowledge is required. The need to scale up and complete KG automatically yields Knowledge Graph Embedding (KGE), a shallow machine learning model that is suffering from memory and training time consumption issues. To mitigate the computational load, we propose a parameter-sharing method, i.e., using conjugate parameters for complex numbers employed in KGE models. Our method improves memory efficiency by 2x in relation embedding while achieving comparable performance to the state-of-the-art non-conjugate models, with faster, or at least comparable, training time. We demonstrated the generalizability of our method on two best-performing KGE models $5^{\bigstar}\mathrm{E}$ and $\mathrm{ComplEx}$ on five benchmark datasets.

Figures (1)

• Figure 1: Transformed entities illustrated in 3D