# A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising

arXiv: https://arxiv.org/abs/2309.08385 · HTML: https://mlsanity.com/paper/2309.08385/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Graph Embedding on Biomedical Networks: Methods, Applications, and Evaluations](https://mlsanity.com/paper/1906.05017/) (2019)
- [Untrained Graph Neural Networks for Denoising](https://mlsanity.com/paper/2109.11700/) (2021)
- [Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks](https://mlsanity.com/paper/2106.04292/) (2021)

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

- [Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Nets](https://mlsanity.com/paper/2606.09051/) (2026)

## Abstract (arXiv)

Hypergraph Neural networks (HyperGNNs) and hypergraph signal denoising (HyperGSD) are two fundamental topics in higher-order network modeling. Understanding the connection between these two domains is particularly useful for designing novel HyperGNNs from a HyperGSD perspective, and vice versa. In particular, the tensor-hypergraph convolutional network (T-HGCN) has emerged as a powerful architecture for preserving higher-order interactions on hypergraphs, and this work shows an equivalence relation between a HyperGSD problem and the T-HGCN. Inspired by this intriguing result, we further design a tensor-hypergraph iterative network (T-HGIN) based on the HyperGSD problem, which takes advantage of a multi-step updating scheme in every single layer. Numerical experiments are conducted to show the promising applications of the proposed T-HGIN approach.