Tensorized Hypergraph Neural Networks

TL;DR

This work addresses the limitation of conventional HGNNs that rely on first-order connectivity by introducing THNN, a Tensorized Hypergraph Neural Network that performs high-order outer-product message passing over adjacency tensors. THNN achieves scalable high-order modeling through a partially symmetric CP decomposition of the weight tensor, enabling linear growth in parameters while capturing complex hyperedge interactions. The method is extended to non-uniform hypergraphs via Global Node and Multi-Uniform Processing strategies and validated on ModelNet40 and NTU with significant performance gains over strong baselines. The results demonstrate the practical value of high-order hypergraph representations for 3D object classification and illustrate a route toward broader non-uniform hypergraph applications, with connections to tensor fusion and polynomial regression techniques.

Abstract

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.

Figures (6)

• Figure 1: An example of adjacency tensor of a 3-uniform hypergraph. In this example, the adjacency tensor of hypergraph $\mathcal{G}$ is defined as the $3$-order tensor $\mathcal{A} \in\{0,1\}^{7 \times 7 \times 7}$ with the entry $\mathcal{A}_{v_{i},v_{j},v_{k}} = 1$ if $\left\{v_{i}, v_{j}, v_{k}\right\} \in \mathcal{E}$ and 0 otherwise.
• Figure 2: Illustration of concatenating 1 and high-order fusion zadeh2017tensor. Every circle corresponds to an element in a vector or tensor and $\circ$ indicates the outer product. We can concatenate a 1 to each vector, and then the outer product of vectors will introduce lower order dynamics.
• Figure 3: Illustration of THNN. THNN tries to pass the high-order interactions of neighbors in different hyperedges. The information of interactions is computed and processed via tensor operations.
• Figure 4: Inspired by zhen2022community, we can add a global node $v_g$ to a non-uniform hypergraph in order to make it uniform. The global node can be added many times in one hyperedge. Following this procedure, the hypergraph can well be represented as an adjacency tensor, allowing it to be directly processed in uniform-hypergraph form models.
• Figure 5: We can also process hypergraphs in layers and utilize distinct models to process sub-hypergraphs of different orders. The resultant embedding vectors of distinct layers are therefore concatenated and integrated through a fully-connected layer.