Equivariant Entity-Relationship Networks

TL;DR

The paper introduces Equivariant Entity-Relationship Networks (EERN), a neural network model that respects the symmetries of relational data, enabling effective reasoning and embedding in database applications.

Contribution

It develops the most expressive equivariant linear maps for entity-relationship data, unifying and extending previous equivariant map frameworks, with practical feed-forward layers for relational reasoning.

Findings

EERN outperforms coupled matrix tensor factorization methods on synthetic data.

EERN demonstrates superior performance on real-world relational datasets.

The model provides a theoretical foundation for deep learning on relational data.

Abstract

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.