# Understanding Graph Neural Networks from Graph Signal Denoising Perspectives

arXiv: https://arxiv.org/abs/2006.04386 · HTML: https://mlsanity.com/paper/2006.04386/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [Graph Denoising with Framelet Regularizer](https://mlsanity.com/paper/2111.03264/) (2021)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Fairness-aware Message Passing for Graph Neural Networks](https://mlsanity.com/paper/2306.11132/) (2023)
- [From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisited](https://mlsanity.com/paper/2309.13599/) (2023)
- [What Has Been Enhanced in my Knowledge-Enhanced Language Model?](https://mlsanity.com/paper/2202.00964/) (2022)
- [Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspective](https://mlsanity.com/paper/2206.04471/) (2022)
- [Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing](https://mlsanity.com/paper/2308.03306/) (2023)
- [Quasi-Framelets: Robust Graph Neural Networks via Adaptive Framelet Convolution](https://mlsanity.com/paper/2201.04728/) (2022)
- [Large Graph Signal Denoising with Application to Differential Privacy](https://mlsanity.com/paper/2209.02043/) (2022)

## Abstract (arXiv)

Graph neural networks (GNNs) have attracted much attention because of their excellent performance on tasks such as node classification. However, there is inadequate understanding on how and why GNNs work, especially for node representation learning. This paper aims to provide a theoretical framework to understand GNNs, specifically, spectral graph convolutional networks and graph attention networks, from graph signal denoising perspectives. Our framework shows that GNNs are implicitly solving graph signal denoising problems: spectral graph convolutions work as denoising node features, while graph attentions work as denoising edge weights. We also show that a linear self-attention mechanism is able to compete with the state-of-the-art graph attention methods. Our theoretical results further lead to two new models, GSDN-F and GSDN-EF, which work effectively for graphs with noisy node features and/or noisy edges. We validate our theoretical findings and also the effectiveness of our new models by experiments on benchmark datasets. The source code is available at urlhttps://github.com/fuguoji/GSDN.