  Many problems in computer vision and machine learning can be cast as learning
on hypergraphs that represent higher-order relations. Recent approaches for
hypergraph learning extend graph neural networks based on message passing,
which is simple yet fundamentally limited in modeling long-range dependencies
and expressive power. On the other hand, tensor-based equivariant neural
networks enjoy maximal expressiveness, but their application has been limited
in hypergraphs due to heavy computation and strict assumptions on fixed-order
hyperedges. We resolve these problems and present Equivariant Hypergraph Neural
Network (EHNN), the first attempt to realize maximally expressive equivariant
layers for general hypergraph learning. We also present two practical
realizations of our framework based on hypernetworks (EHNN-MLP) and
self-attention (EHNN-Transformer), which are easy to implement and
theoretically more expressive than most message passing approaches. We
demonstrate their capability in a range of hypergraph learning problems,
including synthetic k-edge identification, semi-supervised classification, and
visual keypoint matching, and report improved performances over strong message
passing baselines. Our implementation is available at
https://github.com/jw9730/ehnn.
