This paper presents a unified framework for learning representations of entities and relations in knowledge bases (KBs) using neural-embedding approaches. The authors show that existing models like NTN and TransE can be generalized under this framework, where entities are represented as low-dimensional vectors and relations are modeled as bilinear or linear mapping functions. They evaluate various embedding models on the link prediction task and find that a simple bilinear formulation achieves state-of-the-art results (73.2% top-10 accuracy on Freebase). Additionally, they introduce a novel approach to extract logical rules from the learned embeddings, demonstrating that these embeddings are effective at capturing compositional semantics of relations. The proposed method outperforms a state-of-the-art rule mining system, AMIE, in mining Horn rules involving compositional reasoning. The paper also discusses the impact of different design choices on model performance and provides insights into the effectiveness of bilinear and additive interactions in relation to entity and relation representations.This paper presents a unified framework for learning representations of entities and relations in knowledge bases (KBs) using neural-embedding approaches. The authors show that existing models like NTN and TransE can be generalized under this framework, where entities are represented as low-dimensional vectors and relations are modeled as bilinear or linear mapping functions. They evaluate various embedding models on the link prediction task and find that a simple bilinear formulation achieves state-of-the-art results (73.2% top-10 accuracy on Freebase). Additionally, they introduce a novel approach to extract logical rules from the learned embeddings, demonstrating that these embeddings are effective at capturing compositional semantics of relations. The proposed method outperforms a state-of-the-art rule mining system, AMIE, in mining Horn rules involving compositional reasoning. The paper also discusses the impact of different design choices on model performance and provides insights into the effectiveness of bilinear and additive interactions in relation to entity and relation representations.