# Stability and Generalization of Hypergraph Collaborative Networks

arXiv: https://arxiv.org/abs/2308.02347 · HTML: https://mlsanity.com/paper/2308.02347/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Builds on (most cited first, 13 of 13)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [Adversarial Attacks and Defenses in Images, Graphs and Text: A Review](https://mlsanity.com/paper/1909.08072/) (2019)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Stability and Generalization of Graph Convolutional Neural Networks](https://mlsanity.com/paper/1905.01004/) (2019)
- [RGCNN: Regularized Graph CNN for Point Cloud Segmentation](https://mlsanity.com/paper/1806.02952/) (2018)
- [Deformable Shape Completion with Graph Convolutional Autoencoders](https://mlsanity.com/paper/1712.00268/) (2017)
- [Robust Spatial Filtering with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1703.00792/) (2017)

## Built on by (most cited first, 1 of 1)

- [Stability and Generalization of Quantum Neural Networks](https://mlsanity.com/paper/2501.12737/) (2025)

## Abstract (arXiv)

Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to exploit more complex relationships. In particular, the hypergraph collaborative networks yield superior results compared to other hypergraph neural networks for various semi-supervised learning tasks. The collaborative network can provide high quality vertex embeddings and hyperedge embeddings together by formulating them as a joint optimization problem and by using their consistency in reconstructing the given hypergraph. In this paper, we aim to establish the algorithmic stability of the core layer of the collaborative network and provide generalization guarantees. The analysis sheds light on the design of hypergraph filters in collaborative networks, for instance, how the data and hypergraph filters should be scaled to achieve uniform stability of the learning process. Some experimental results on real-world datasets are presented to illustrate the theory.