Equivariant Entity-Relationship Networks

Equivariant Entity-Relationship Networks

The relational model is a ubiquitous representation of big-data, in part due to its extensive use in databases. In this paper, we propose the Equivariant Entity-Relationship Network (EERN), which is a Multilayer Perceptron equivariant to the symmetry transformations of the Entity-Relationship model.To this end, we identify the most expressive family of linear maps that are exactly equivariant to entity relationship symmetries, and further show that they subsume recently introduced equivariant maps for sets, exchangeable tensors, and graphs. The proposed feed-forward layer has linear complexity in the data and can be used for both inductive and transductive reasoning about relational databases, including database embedding, and the prediction of missing records. This provides a principled theoretical foundation for the application of deep learning to one of the most abundant forms of data. Empirically, EERN outperforms different variants of coupled matrix tensor factorization in both synthetic and real-data experiments.

等变实体关系网络

关系模型是大数据的普遍表示，部分原因是它在数据库中的广泛使用。在本文中，我们提出了等价实体关系网络（EERN），它是实体关系模型对称变换的多层感知器等价变量。.. 为此，我们确定了最有表现力的线性图族，它们与实体关系对称性完全等价，并进一步表明它们包含了最近引入的等距图集，可交换张量和图。所提出的前馈层在数据中具有线性复杂度，并且可以用于关系数据库的归纳和转导推理，包括数据库嵌入和丢失记录的预测。这为将深度学习应用于最丰富的数据形式之一提供了有原则的理论基础。从经验上讲，在合成和实际数据实验中，ERN都优于耦合矩阵张量分解的不同变体。 （阅读更多）