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Revisiting Knowledge Base Embedding as Tensor Decomposition

We study the problem of knowledge base (KB) embedding, which is usually addressed through two frameworks---neural KB embedding and tensor decomposition. In this work, we theoretically analyze the neural embedding framework and subsequently connect it with tensor based embedding. Specifically, we show that in neural KB embedding the two commonly adopted optimization solutions---margin-based and negative sampling losses---are closely related to each other. We also reach the closed-form tensor that is implicitly approximated by popular neural KB approaches, revealing the underlying connection between neural and tensor based KB embedding models. Grounded in the theoretical results, we further present a tensor decomposition based framework KBTD to directly approximate the derived closed form tensor. Under this framework, the neural KB embedding models, such as NTN, TransE, Bilinear, and DISTMULT, are unified into a general tensor optimization architecture. Finally, we conduct experiments on the link prediction task in WordNet and Freebase, empirically demonstrating the effectiveness of the KBTD framework.

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