Title: HyperQuery: A Framework for Higher Order Link Prediction. Abstract: Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life.  While graphs are a natural way to represent complex networks and are well studied, typical approaches to modeling group membership using graphs are lossy.  Hypergraphs are a more natural way to represent such ``higher order'' relationships, but efforts to apply machine learning techniques to hypergraph structured datasets have been limited thus far.  In this paper, we address the problem of link prediction in knowledge hypergraphs as well as regular hypergraphs and develop a novel, simple, and effective optimization architecture to solve this task. Additionally, we study how integrating data from node-level labels can improve the results of our system. Our self-supervised approach achieves significant improvement over state of the art results on several hyperedge prediction and knowledge hypergraph completeion benchmarks. 