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Equivariant Hypergraph Diffusion Neural Operators

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arxiv 2207.06680 v3 pith:IDRDAC5Z submitted 2022-07-14 cs.LG cs.SI

Peihao Wang , Shenghao Yang , Yunyu Liu , Zhangyang Wang , Pan Li This is my paper · ORCID
classification cs.LGcs.SI
keywords ed-hnnhypergraphrelationshigher-orderneuraldatasetsdiffusionhypergraphs
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abstract

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%$\uparrow$ in prediction accuracy over four datasets therein.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hypergraph Neural Stochastic Diffusion: An SDE Framework for Uncertainty Estimation

    cs.LG 2026-07 conditional novelty 6.5 of 10

    HyperNSD models hypergraph node states as an incidence-aware SDE whose pathwise variability yields competitive uncertainty estimates for OOD and misclassification detection.

  2. Rethinking Addressing in Language Models via Contexualized Equivariant Positional Encoding

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    TAPE makes positional embeddings content-aware and equivariant, improving Transformer performance on arithmetic and long-context tasks and extending representational power to NC1-complete algorithms.

  3. From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

    cs.LG 2026-07 conditional novelty 5.0 of 10

    Hypergraph diffusion provably collapses node representations, and a reaction term that exactly cancels diffusion dissipation keeps a designed transverse energy level nonzero in Hypergraph Neural Reaction–Diffusion (HNRD).

  4. Wasserstein Hypergraph Neural Network

    cs.LG 2025-06 conditional novelty 5.0 of 10

    A hypergraph neural network with Sliced Wasserstein Pooling as its aggregator reports top node classification results on seven benchmark datasets.

  5. Hypergraph Diffusion for High-Order Recommender Systems

    cs.IR 2025-01 conditional novelty 4.0 of 10

    A wavelet-enhanced hypergraph diffusion model with two encoders and contrastive learning reports consistent, small ranking improvements over six baselines on three recommendation datasets.

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