  We consider learning representations of entities and relations in KBs using
the neural-embedding approach. We show that most existing models, including NTN
(Socher et al., 2013) and TransE (Bordes et al., 2013b), can be generalized
under a unified learning framework, where entities are low-dimensional vectors
learned from a neural network and relations are bilinear and/or linear mapping
functions. Under this framework, we compare a variety of embedding models on
the link prediction task. We show that a simple bilinear formulation achieves
new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2%
vs. 54.7% by TransE on Freebase). Furthermore, we introduce a novel approach
that utilizes the learned relation embeddings to mine logical rules such as
"BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that
embeddings learned from the bilinear objective are particularly good at
capturing relational semantics and that the composition of relations is
characterized by matrix multiplication. More interestingly, we demonstrate that
our embedding-based rule extraction approach successfully outperforms a
state-of-the-art confidence-based rule mining approach in mining Horn rules
that involve compositional reasoning.
