  Graphs are the most ubiquitous data structures for representing relational
datasets and performing inferences in them. They model, however, only pairwise
relations between nodes and are not designed for encoding the higher-order
relations. This drawback is mitigated by hypergraphs, in which an edge can
connect an arbitrary number of nodes. Most hypergraph learning approaches
convert the hypergraph structure to that of a graph and then deploy existing
geometric deep learning methods. This transformation leads to information loss,
and sub-optimal exploitation of the hypergraph's expressive power. We present
HyperMSG, a novel hypergraph learning framework that uses a modular two-level
neural message passing strategy to accurately and efficiently propagate
information within each hyperedge and across the hyperedges. HyperMSG adapts to
the data and task by learning an attention weight associated with each node's
degree centrality. Such a mechanism quantifies both local and global importance
of a node, capturing the structural properties of a hypergraph. HyperMSG is
inductive, allowing inference on previously unseen nodes. Further, it is robust
and outperforms state-of-the-art hypergraph learning methods on a wide range of
tasks and datasets. Finally, we demonstrate the effectiveness of HyperMSG in
learning multimodal relations through detailed experimentation on a challenging
multimedia dataset.
