Latent factor models are increasingly popular for modeling multi-relational knowledge graphs. By their vectorial nature, it is not only hard to interpret why this class of models works so well, but also to understand where they fail and how they might be improved. We conduct an experimental survey of state-of-the-art models, not towards a purely comparative end, but as a means to get insight about their inductive abilities. To assess the strengths and weaknesses of each model, we create simple tasks that exhibit first, atomic properties of binary relations, and then, common inter-relational inference through synthetic genealogies. Based on these experimental results, we propose new research directions to improve on existing models.
Advances in bringing both worlds together include the work of and , where a latent factor model is used, as well as a set of logical rules. An error-term over the rules is added to the classical latent factor objective function. In , a fully differentiable neural theorem prover is used to handle both facts and rules, whereas use adversarial training to do so. learned first-order logic embeddings from formulae learned by ILP. Similar proposals for integrating logical knowledge in distributional representations of words include the work of . Conversely, learn a latent factor model over the facts only, and then try to extract rules from the learned embeddings. @cite_12 proposed to use projections of the subject and object entity embeddings that conserve transitivity and symmetry.
@cite_12
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We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 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. We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules. Abstract: We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 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. The effective integration of learning and reasoning is a well-known and challenging area of research within artificial intelligence. Neural-symbolic systems seek to integrate learning and reasoning by combining neural networks and symbolic knowledge representation. In this paper, a novel methodology is proposed for the extraction of relational knowledge from neural networks which are trainable by the efficient application of the backpropagation learning algorithm. First-order logic rules are extracted from the neural networks, offering interpretable symbolic relational models on which logical reasoning can be performed. The wellknown knowledge extraction algorithm TREPAN was adapted and incorporated into the first-order version of the neural-symbolic system CILP++. Empirical results obtained in comparison with a probabilistic model for relational learning, Markov Logic Networks, and a state-of-the-art Inductive Logic Programming system, Aleph, indicate that the proposed methodology achieves competitive accuracy results consistently in all datasets investigated, while either Markov Logic Networks or Aleph show considerably worse results in at least one dataset. It is expected that effective knowledge extraction from neural networks can contribute to the integration of heterogeneous knowledge representations.