# A Unified View on Graph Neural Networks as Graph Signal Denoising

arXiv: https://arxiv.org/abs/2010.01777 · HTML: https://mlsanity.com/paper/2010.01777/

## Key facts

- Cited by 110 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 30 of 110)

- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph Condensation for Graph Neural Networks](https://mlsanity.com/paper/2110.07580/) (2021)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion](https://mlsanity.com/paper/2301.09474/) (2023)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Learning from Counterfactual Links for Link Prediction](https://mlsanity.com/paper/2106.02172/) (2021)
- [Elastic Graph Neural Networks](https://mlsanity.com/paper/2107.06996/) (2021)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Single Node Injection Attack against Graph Neural Networks](https://mlsanity.com/paper/2108.13049/) (2021)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [Linkless Link Prediction via Relational Distillation](https://mlsanity.com/paper/2210.05801/) (2022)
- [Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models](https://mlsanity.com/paper/2309.11420/) (2023)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Fast Graph Condensation with Structure-based Neural Tangent Kernel](https://mlsanity.com/paper/2310.11046/) (2023)
- [FMP: Toward Fair Graph Message Passing against Topology Bias](https://mlsanity.com/paper/2202.04187/) (2022)
- [MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initialization](https://mlsanity.com/paper/2210.00102/) (2022)
- [Class-Imbalanced Graph Learning without Class Rebalancing](https://mlsanity.com/paper/2308.14181/) (2023)
- [Optimization-Induced Graph Implicit Nonlinear Diffusion](https://mlsanity.com/paper/2206.14418/) (2022)
- [Transformers from an Optimization Perspective](https://mlsanity.com/paper/2205.13891/) (2022)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [A Practical, Progressively-Expressive GNN](https://mlsanity.com/paper/2210.09521/) (2022)
- [Multimodal Data Integration for Oncology in the Era of Deep Neural Networks: A Review](https://mlsanity.com/paper/2303.06471/) (2023)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Graph Neural Networks for Multimodal Single-Cell Data Integration](https://mlsanity.com/paper/2203.01884/) (2022)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. A single GNN layer typically consists of a feature transformation and a feature aggregation operation. The former normally uses feed-forward networks to transform features, while the latter aggregates the transformed features over the graph. Numerous recent works have proposed GNN models with different designs in the aggregation operation. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models including GCN, GAT, PPNP, and APPNP can be regarded as (approximately) solving a graph denoising problem with a smoothness assumption. Such a unified view across GNNs not only provides a new perspective to understand a variety of aggregation operations but also enables us to develop a unified graph neural network framework UGNN. To demonstrate its promising potential, we instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes. Comprehensive experiments show the effectiveness of ADA-UGNN.