Deep Models of Interactions Across Sets

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).