Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods aim at re-representing symbolic relational data in Euclidean spaces. They offer better scalability, but can only numerically approximate relational structures and are less flexible in terms of reasoning tasks supported. This paper introduces a novel framework for relational representation learning that combines the best of both worlds. This framework, inspired by the auto-encoding principle, uses first-order logic as a data representation language, and the mapping between the original and latent representation is done by means of logic programs instead of neural networks. We show how learning can be cast as a constraint optimisation problem for which existing solvers can be used. The use of logic as a representation language makes the proposed framework more accurate (as the representation is exact, rather than approximate), more flexible, and more interpretable than deep learning methods. We experimentally show that these latent representations are indeed beneficial in relational learning tasks.
The most prominent paradigm in merging SRL and DL are (knowledge) graph embeddings @cite_22 @cite_11 . In contrast to s , these methods do not retain full relational data representation but approximate it by vectorisation. Several works @cite_20 @cite_19 impose logical constraints on embeddings but do not retain the relational representation.
@cite_19 @cite_22 @cite_20 @cite_11
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Methods based on representation learning currently hold the state-of-the-art in many natural language processing and knowledge base inference tasks. Yet, a major challenge is how to efficiently incorporate commonsense knowledge into such models. A recent approach regularizes relation and entity representations by propositionalization of first-order logic rules. However, propositionalization does not scale beyond domains with only few entities and rules. In this paper we present a highly efficient method for incorporating implication rules into distributed representations for automated knowledge base construction. We map entity-tuple embeddings into an approximately Boolean space and encourage a partial ordering over relation embeddings based on implication rules mined from WordNet. Surprisingly, we find that the strong restriction of the entity-tuple embedding space does not hurt the expressiveness of the model and even acts as a regularizer that improves generalization. By incorporating few commonsense rules, we achieve an increase of 2 percentage points mean average precision over a matrix factorization baseline, while observing a negligible increase in runtime. Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be “trained” on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive data sets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's knowledge vault project as an example of such combination. In adversarial training, a set of models learn together by pursuing competing goals, usually defined on single data instances. However, in relational learning and other non-i.i.d domains, goals can also be defined over sets of instances. For example, a link predictor for the is-a relation needs to be consistent with the transitivity property: if is-a(x_1, x_2) and is-a(x_2, x_3) hold, is-a(x_1, x_3) needs to hold as well. Here we use such assumptions for deriving an inconsistency loss, measuring the degree to which the model violates the assumptions on an adversarially-generated set of examples. The training objective is defined as a minimax problem, where an adversary finds the most offending adversarial examples by maximising the inconsistency loss, and the model is trained by jointly minimising a supervised loss and the inconsistency loss on the adversarial examples. This yields the first method that can use function-free Horn clauses (as in Datalog) to regularise any neural link predictor, with complexity independent of the domain size. We show that for several link prediction models, the optimisation problem faced by the adversary has efficient closed-form solutions. Experiments on link prediction benchmarks indicate that given suitable prior knowledge, our method can significantly improve neural link predictors on all relevant metrics.