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.

翻译：超图神经网络（HGNN）近年来因其在各领域的优异性能而备受关注。然而，现有大多数HGNN依赖于超图连接模式的一阶近似，忽视了重要的高阶信息。为解决这一问题，我们提出了一种基于邻接张量的新型张量化超图神经网络（THNN）。THNN通过高阶外积特征消息传递实现了一种忠实的超图建模框架，是邻接矩阵图神经网络在张量上的自然扩展。所提出的THNN等价于高阶多项式回归方案，使其具备从均匀超图中高效提取高阶信息的能力。此外，针对直接处理高阶外积特征存在的指数级复杂度问题，我们提出采用部分对称CP分解方法将模型复杂度降至线性级别。同时，我们针对实际应用中常见的非均匀超图提出了两种简单有效的扩展方法。在两个广泛使用的三维视觉物体分类超图数据集上的实验结果表明，该模型具有出色的性能。