Equivariant Hypergraph Neural Networks
This work addresses the problem of learning on hypergraphs with higher-order relations for researchers and practitioners in computer vision and machine learning, offering a novel framework that overcomes computational and expressiveness bottlenecks.
The paper tackles the limitations of existing hypergraph learning methods by introducing Equivariant Hypergraph Neural Networks (EHNN), which achieve maximal expressiveness for general hypergraph learning and demonstrate improved performance in tasks like synthetic k-edge identification, semi-supervised classification, and visual keypoint matching over strong baselines.
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.