Deep Models of Interactions Across Sets

TL;DR

This paper introduces permutation equivariant deep models for interactions across sets, achieving state-of-the-art results in matrix completion, scalable to large datasets, and capable of generalizing to new objects and across domains.

Contribution

The paper proposes a novel permutation equivariant modeling scheme with provable expressiveness, enabling scalable, generalizable interaction modeling across multiple sets.

Findings

State-of-the-art performance on matrix completion benchmarks

Models require a number of parameters independent of object counts

Effective generalization to new objects and across different domains

Abstract

We use deep learning to model interactions across two or more sets of objects, such as user-movie ratings, protein-drug bindings, or ternary user-item-tag interactions. The canonical representation of such interactions is a matrix (or a higher-dimensional tensor) with an exchangeability property: the encoding's meaning is not changed by permuting rows or columns. We argue that models should hence be Permutation Equivariant (PE): constrained to make the same predictions across such permutations. We present a parameter-sharing scheme and prove that it could not be made any more expressive without violating PE. This scheme yields three benefits. First, we demonstrate state-of-the-art performance on multiple matrix completion benchmarks. Second, our models require a number of parameters independent of the numbers of objects, and thus scale well to large datasets. Third, models can be queried about new objects that were not available at training time, but for which interactions have since been observed. In experiments, our models achieved surprisingly good generalization performance on this matrix extrapolation task, both within domains (e.g., new users and new movies drawn from the same distribution used for training) and even across domains (e.g., predicting music ratings after training on movies).