Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion

TL;DR

This paper introduces CoNHD, a novel hypergraph neural network that models edge-specific node features for edge-dependent node classification, overcoming limitations of previous methods and addressing oversmoothing.

Contribution

CoNHD reformulates hypergraph interactions as a diffusion process over co-representations, enabling edge-specific feature modeling and improved ENC performance.

Findings

Achieves state-of-the-art results on ENC benchmarks.

Effectively models edge-specific features without oversmoothing.

Demonstrates robustness across multiple downstream tasks.

Abstract

Hypergraphs are widely being employed to represent complex higher-order relations in real-world applications. Most existing research on hypergraph learning focuses on node-level or edge-level tasks. A practically relevant and more challenging task, edge-dependent node classification (ENC), is still under-explored. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node features unique to each hyperedge. The state-of-the-art ENC solution, WHATsNet, only outputs single node and edge representations, leading to the limitations of \textbf{entangled edge-specific features} and \textbf{non-adaptive representation sizes} when applied to ENC. Additionally, WHATsNet suffers from the common \textbf{oversmoothing issue} in most HGNNs. To address these limitations, we propose \textbf{CoNHD}, a novel HGNN architecture specifically designed to model edge-specific features for ENC. Instead of learning separate representations for nodes and edges, CoNHD reformulates within-edge and within-node interactions as a hypergraph diffusion process over node-edge co-representations. We develop a neural implementation of the proposed diffusion process, leveraging equivariant networks as diffusion operators to effectively learn the diffusion dynamics from data. Extensive experiments demonstrate that CoNHD achieves the best performance across all benchmark ENC datasets and several downstream tasks without sacrificing efficiency. Our implementation is available at https://github.com/zhengyijia/CoNHD.