Embedding-based methods for knowledge base completion (KBC) learn
representations of entities and relations in a vector space, along with the
scoring function to estimate the likelihood of relations between entities. The
learnable class of scoring functions is designed to be expressive enough to
cover a variety of real-world relations, but this expressive comes at the cost
of an increased number of parameters. In particular, parameters in these
methods are superfluous for relations that are either symmetric or
antisymmetric. To mitigate this problem, we propose a new L1 regularizer for
Complex Embeddings, which is one of the state-of-the-art embedding-based
methods for KBC. This regularizer promotes symmetry or antisymmetry of the
scoring function on a relation-by-relation basis, in accordance with the
observed data. Our empirical evaluation shows that the proposed method
outperforms the original Complex Embeddings and other baseline methods on the
FB15k dataset.

该论文提出了一种新的 L1 规则器来强制符合观察数据的关系得分函数的对称性或反对称性，从而减少参数数量，实现 KBC 方面的更好性能。在 FB15k 数据集上，这种方法表现优于原始复杂嵌入及其他基准方法。

数据相关的学习对于对称性 / 反对称性关系知识库完成的影响

Data-dependent Learning of Symmetric/Antisymmetric Relations for  Knowledge Base Completion

In statistical relational learning, knowledge graph completion deals with
automatically understanding the structure of large knowledge graphs---labeled
directed graphs---and predicting missing relationships---labeled edges.
State-of-the-art embedding models propose different trade-offs between modeling
expressiveness, and time and space complexity. We reconcile both expressiveness
and complexity through the use of complex-valued embeddings and explore the
link between such complex-valued embeddings and unitary diagonalization. We
corroborate our approach theoretically and show that all real square
matrices---thus all possible relation/adjacency matrices---are the real part of
some unitarily diagonalizable matrix. This results opens the door to a lot of
other applications of square matrices factorization. Our approach based on
complex embeddings is arguably simple, as it only involves a Hermitian dot
product, the complex counterpart of the standard dot product between real
vectors, whereas other methods resort to more and more complicated composition
functions to increase their expressiveness. The proposed complex embeddings are
scalable to large data sets as it remains linear in both space and time, while
consistently outperforming alternative approaches on standard link prediction
benchmarks.

本文介绍了一种基于复杂嵌入的统计关系学习方法，在实现表达能力和时间 / 空间复杂度之间权衡的同时，探索了这种复杂嵌入和酉对角化之间的联系，提出的嵌入方法仅涉及共轭内积，具有良好的可扩展性和高准确率。

基于复杂张量分解的知识图谱补全

Knowledge Graph Completion via Complex Tensor Factorization

In statistical relational learning, the link prediction problem is key to
automatically understand the structure of large knowledge bases. As in previous
studies, we propose to solve this problem through latent factorization.
However, here we make use of complex valued embeddings. The composition of
complex embeddings can handle a large variety of binary relations, among them
symmetric and antisymmetric relations. Compared to state-of-the-art models such
as Neural Tensor Network and Holographic Embeddings, our approach based on
complex embeddings is arguably simpler, as it only uses the Hermitian dot
product, the complex counterpart of the standard dot product between real
vectors. Our approach is scalable to large datasets as it remains linear in
both space and time, while consistently outperforming alternative approaches on
standard link prediction benchmarks.

该研究基于复嵌入提出了一种解决大型知识库中链接预测问题的方法，相对于其他模型而言，这种方法更简单且可扩展性好，同时在标准链接预测测试中保持了更高的性能。