Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities and relations such that the bilinear form defined therein is a well-behaved scoring function. Despite of their successful performances, existing bilinear forms overlook the modeling of relation compositions, resulting in lacks of interpretability for reasoning on KG. To fulfill this gap, we propose a new model called DihEdral, named after dihedral symmetry group. This new model learns knowledge graph embeddings that can capture relation compositions by nature. Furthermore, our approach models the relation embeddings parametrized by discrete values, thereby decrease the solution space drastically. Our experiments show that DihEdral is able to capture all desired properties such as (skew-) symmetry, inversion and (non-) Abelian composition, and outperforms existing bilinear form based approach and is comparable to or better than deep learning models such as ConvE.

翻译：链接预测对于在下游任务中应用不完整知识图(KG)至关重要。作为一套有效的连接预测方法,嵌入方法试图学习两个实体和关系的低级别代表,以便了解其中定义的双线表是一个良好守法的评分功能。尽管其表现很成功,但现有的双线表忽视了关系构成的模型,导致无法解释关于KG的推理。为了弥补这一差距,我们提议了一个新模型,名为DihEdral,以对称组命名。这个新模型学习知识图嵌入方法,可以按自然来记录关系构成。此外,我们的方法模型模拟了嵌入离散值的双线表关系,从而极大地缩小了溶解空间。我们的实验表明,DihEdral能够捕捉到所有想要的属性,例如(skew-)对称、反转和(n-n-n-n-n-n-belian)构成,以及超越以双线形式为基础的现有方法,并且可以比CONUE等深学习模型更接近或更好。