# Learnable Hypergraph Laplacian for Hypergraph Learning

arXiv: https://arxiv.org/abs/2106.05701 · HTML: https://mlsanity.com/paper/2106.05701/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluations](https://mlsanity.com/paper/1906.05017/) (2019)
- [Structural Deep Embedding for Hyper-Networks](https://mlsanity.com/paper/1711.10146/) (2017)
- [Diversified Multiscale Graph Learning with Graph Self-Correction](https://mlsanity.com/paper/2103.09754/) (2021)

## Built on by (most cited first, 16 of 16)

- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [Preventing Over-Smoothing for Hypergraph Neural Networks](https://mlsanity.com/paper/2203.17159/) (2022)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [GraphTTA: Test Time Adaptation on Graph Neural Networks](https://mlsanity.com/paper/2208.09126/) (2022)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings](https://mlsanity.com/paper/2212.14077/) (2022)
- [DVHGNN: Multi-Scale Dilated Vision HGNN for Efficient Vision Recognition](https://mlsanity.com/paper/2503.14867/) (2025)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learning](https://mlsanity.com/paper/2505.05702/) (2025)
- [A Simple Hypergraph Kernel Convolution based on Discounted Markov Diffusion Process](https://mlsanity.com/paper/2210.16884/) (2022)
- [Explaining Hypergraph Neural Networks: From Local Explanations to Global Concepts](https://mlsanity.com/paper/2410.07764/) (2024)
- [Attention-based graph neural networks: a survey](https://mlsanity.com/paper/2605.08679/) (2026)
- [Spectral Convergence of Complexon Shift Operators](https://mlsanity.com/paper/2309.07169/) (2023)
- [Wasserstein Hypergraph Neural Network](https://mlsanity.com/paper/2506.09682/) (2025)

## Abstract (arXiv)

HyperGraph Convolutional Neural Networks (HGCNNs) have demonstrated their potential in modeling high-order relations preserved in graph structured data. However, most existing convolution filters are localized and determined by the pre-defined initial hypergraph topology, neglecting to explore implicit and long-ange relations in real-world data. In this paper, we propose the first learning-based method tailored for constructing adaptive hypergraph structure, termed HypERgrAph Laplacian aDaptor (HERALD), which serves as a generic plug-in-play module for improving the representational power of HGCNNs. Specifically, HERALD adaptively optimizes the adjacency relationship between hypernodes and hyperedges in an end-to-end manner and thus the task-aware hypergraph is learned. Furthermore, HERALD employs the self-attention mechanism to capture the non-local paired-nodes relation. Extensive experiments on various popular hypergraph datasets for node classification and graph classification tasks demonstrate that our approach obtains consistent and considerable performance enhancement, proving its effectiveness and generalization ability.