  Hypergraph neural networks (HGNN) have recently become attractive and
received significant attention due to their excellent performance in various
domains. However, most existing HGNNs rely on first-order approximations of
hypergraph connectivity patterns, which ignores important high-order
information. To address this issue, we propose a novel adjacency-tensor-based
\textbf{T}ensorized \textbf{H}ypergraph \textbf{N}eural \textbf{N}etwork
(THNN). THNN is a faithful hypergraph modeling framework through high-order
outer product feature message passing and is a natural tensor extension of the
adjacency-matrix-based graph neural networks. The proposed THNN is equivalent
to a high-order polynomial regression scheme, which enables THNN with the
ability to efficiently extract high-order information from uniform hypergraphs.
Moreover, in consideration of the exponential complexity of directly processing
high-order outer product features, we propose using a partially symmetric CP
decomposition approach to reduce model complexity to a linear degree.
Additionally, we propose two simple yet effective extensions of our method for
non-uniform hypergraphs commonly found in real-world applications. Results from
experiments on two widely used {hypergraph datasets for 3-D visual object
classification} show the model's promising performance.
