1) The document presents HINGE, a new method for embedding hyper-relational knowledge graphs that aims to better capture information from facts containing multiple relations and entities. 2) HINGE uses a CNN to learn representations from base triplets and their associated key-value pairs to characterize the plausibility of facts. 3) An evaluation on link prediction tasks shows HINGE outperforms baselines and demonstrates that the triplet structure encodes essential information, while other representations discard important information.