This paper generated a lot of discussion and ultimately all referees agreed that the main ideas of the paper are interesting and well-motivated, while providing new directions for the graph learning literature. There are a few concerns on presentation issues, but these can be addressed in a camera version. For these reasons, the consensus is to recommend accepting this paper. The paper makes extensive use of k-ary prediction tasks but ignores a large body of literature considering that topic. Thus, for the camera version, the authors are encouraged to consider the following papers and references therein, and augment the related work and baselines as appropriate: -- Zhang et al. Beyond link prediction: Predicting hyperlinks in adjacency space. AAAI 2018. -- Benson, Austin R. et al. Simplicial closure and higher-order link prediction. PNAS, 2018. -- Xu et al. "Hyperlink prediction in hypernetworks using latent social features" International Conference on Discovery Science, 2013. -- Zhang et al. Recovering metabolic networks using a novel hyperlink prediction method, arXiv:1610.06941 (2016). -- Patania et al. The shape of collaborations. EPJ Data Science 2017. -- Patil et al. Negative Sampling for Hyperlink Prediction in Networks. PAKDD 2020 -- Yoon et al. How Much and When Do We Need Higher-order Information in Hypergraphs? A Case Study on Hyperedge Prediction. WWW 2020.