Equivariant Entity-Relationship Networks
This provides a principled theoretical foundation for deep learning on relational data, a common big-data form, but is incremental as it builds on existing equivariant methods.
The paper tackles the problem of applying deep learning to relational databases by proposing the Equivariant Entity-Relationship Network (EERN), a method equivariant to entity-relationship symmetries, which outperforms coupled matrix tensor factorization variants in synthetic and real-data experiments.
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.