Modeling N-ary Relational Knowledge Bases with Tensor Decomposition

The binary relational knowledge base (KB, a.k.a. knowledge graph), representing real-world knowledge with binary relations and entities, has been an important research topic in artificial intelligence, while, considerable knowledge also involves beyond-binary relations. Recently, the area proposes to model n-ary relational KBs with both binary and beyond-binary relations included. However, most current models are extended from translational distance and neural network models in binary relational KBs, which suffer from weak expressiveness and high complexity, respectively. To overcome such issues, in this work, we propose a novel two-step modeling framework, GETD, generalizing the powerful tensor decomposition technique from binary relational KBs to the n-ary case. For n-ary relational KBs with single-arity relations, the GETD framework introduces Tucker decomposition and Tensor Ring decomposition for expressive and efficient modeling. Furthermore, the framework is technically extended for the representation of n-ary relational KBs with mixed-arity relations. The existing negative sampling technique is also generalized to the n-ary case for GETD. In addition, we theoretically prove that the GETD framework is fully expressive to completely represent any KBs. Empirical results on two representative datasets show that the proposed framework significantly outperforms the state-of-the-art methods, achieving 11–26% and 4–7% improvements on Hits@10 for the single-arity and the mixed-arity cases, respectively.