Embedding knowledge graphs into continuous vector spaces has recently attracted increasing interest. Most existing methods perform the embedding task using only fact triples. Logical rules, although containing rich background information, have not been well studied in this task. This paper proposes a novel method of jointly embedding knowledge graphs and logical rules. The key idea is to represent and model triples and rules in a unified framework. Specifically, triples are represented as atomic formulae and modeled by the translation assumption, while rules represented as complex formulae and modeled by t-norm fuzzy logics. Embedding then amounts to minimizing a global loss over both atomic and complex formulae. In this manner, we learn embeddings compatible not only with triples but also with rules, which will certainly be more predictive for knowledge acquisition and inference. We evaluate our method with link prediction and triple classification tasks. Experimental results show that joint embedding brings significant and consistent improvements over stateof-the-art methods. Particularly, it enhances the prediction of new facts which cannot even be directly inferred by pure logical inference, demonstrating the capability of our method to learn more predictive embeddings.

This paper considers the problem of embedding Knowledge Graphs (KGs) consisting of entities and relations into lowdimensional vector spaces. Most of the existing methods perform this task based solely on observed facts. The only requirement is that the learned embeddings should be compatible within each individual fact. In this paper, aiming at further discovering the intrinsic geometric structure of the embedding space, we propose Semantically Smooth Embedding (SSE). The key idea of SSE is to take full advantage of additional semantic information and enforce the embedding space to be semantically smooth, i.e., entities belonging to the same semantic category will lie close to each other in the embedding space. Two manifold learning algorithms Laplacian Eigenmaps and Locally Linear Embedding are used to model the smoothness assumption. Both are formulated as geometrically based regularization terms to constrain the embedding task. We empirically evaluate SSE in two benchmark tasks of link prediction and triple classification, and achieve significant and consistent improvements over state-of-the-art methods. Furthermore, SSE is a general framework. The smoothness assumption can be imposed to a wide variety of embedding models, and it can also be constructed using other information besides entities' semantic categories.

Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Combining such an embedding model with logic rules has recently attracted increasing attention. Most previous attempts made a one-time injection of logic rules, ignoring the interactive nature between embedding learning and logical inference. And they focused only on hard rules, which always hold with no exception and usually require extensive manual effort to create or validate. In this paper, we propose Rule-Guided Embedding (RUGE), a novel paradigm of KG embedding with iterative guidance from soft rules. RUGE enables an embedding model to learn simultaneously from 1) labeled triples that have been directly observed in a given KG, 2) unlabeled triples whose labels are going to be predicted iteratively, and 3) soft rules with various confidence levels extracted automatically from the KG. In the learning process, RUGE iteratively queries rules to obtain soft labels for unlabeled triples, and integrates such newly labeled triples to update the embedding model. Through this iterative procedure, knowledge embodied in logic rules may be better transferred into the learned embeddings. We evaluate RUGE in link prediction on Freebase and YAGO. Experimental results show that: 1) with rule knowledge injected iteratively, RUGE achieves significant and consistent improvements over state-of-the-art baselines; and 2) despite their uncertainties, automatically extracted soft rules are highly beneficial to KG embedding, even those with moderate confidence levels. The code and data used for this paper can be obtained from https://github.com/iieir-km/RUGE.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-theart results with different few-shot sizes. The source code is available at https://github. com/JiaweiSheng/FAAN.