mlsanityData to 14 Oct 2026

A Unified View on Graph Neural Networks as Graph Signal Denoising

arXiv 2010.01777 ↗First posted 5 Oct 2020cs.LG stat.MLcited by 110

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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.

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

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Citing papers per year: 2021: 14; 2022: 28; 2023: 35; 2024: 22; 2025: 10; 2026: 1.

110 papers.

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  1. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
  2. 2021Graph Condensation for Graph Neural Networkscited by 150
  3. 2023GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learnercited by 132
  4. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  5. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 87
  6. 2022Graph Rationalization with Environment-based Augmentationscited by 70
  7. 2021Learning from Counterfactual Links for Link Predictioncited by 69
  8. 2021Elastic Graph Neural Networkscited by 67
  9. 2022A Survey on Graph Representation Learning Methodscited by 66
  10. 2022Graph Data Augmentation for Graph Machine Learning: A Surveycited by 62
  11. 2021Graph Neural Networks Inspired by Classical Iterative Algorithmscited by 60
  12. 2022Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminatingcited by 57
38 more
  1. 2021Graph Trend Filtering Networks for Recommendationscited by 53
  2. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  3. 2021Single Node Injection Attack against Graph Neural Networkscited by 45
  4. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  5. 2022Linkless Link Prediction via Relational Distillationcited by 39
  6. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
  7. 2023Simple and Asymmetric Graph Contrastive Learning without Augmentationscited by 38
  8. 2023Fast Graph Condensation with Structure-based Neural Tangent Kernelcited by 36
  9. 2022FMP: Toward Fair Graph Message Passing against Topology Biascited by 35
  10. 2022MLPInit: Embarrassingly Simple GNN Training Acceleration with MLP Initializationcited by 31
  11. 2023Class-Imbalanced Graph Learning without Class Rebalancingcited by 29
  12. 2022Optimization-Induced Graph Implicit Nonlinear Diffusioncited by 28
  13. 2022Transformers from an Optimization Perspectivecited by 27
  14. 2023A Survey on Spectral Graph Neural Networkscited by 26
  15. 2022A Practical, Progressively-Expressive GNNcited by 20
  16. 2023Multimodal Data Integration for Oncology in the Era of Deep Neural Networks: A Reviewcited by 20
  17. 2021A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinationscited by 18
  18. 2022Graph Neural Networks for Multimodal Single-Cell Data Integrationcited by 18
  19. 2023From Hypergraph Energy Functions to Hypergraph Neural Networkscited by 18
  20. 2024Graph Data Condensation via Self-expressive Graph Structure Reconstructioncited by 18
  21. 2022Test-Time Training for Graph Neural Networkscited by 17
  22. 2023Robust Mid-Pass Filtering Graph Convolutional Networkscited by 17
  23. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  24. 2023LazyGNN: Large-Scale Graph Neural Networks via Lazy Propagationcited by 16
  25. 2021Adaptive Kernel Graph Neural Networkcited by 15
  26. 2023Towards Data-centric Graph Machine Learning: Review and Outlookcited by 15
  27. 2025Cross-Contrastive Clustering for Multimodal Attributed Graphs with Dual Graph Filteringcited by 14
  28. 2021Implicit vs Unfolded Graph Neural Networkscited by 13
  29. 2022ES-GNN: Generalizing Graph Neural Networks Beyond Homophily with Edge Splittingcited by 13
  30. 2023A Generalized Neural Diffusion Framework on Graphscited by 13
  31. 2022LPGNet: Link Private Graph Networks for Node Classificationcited by 12
  32. 2023Chasing Fairness in Graphs: A GNN Architecture Perspectivecited by 12
  33. 2024Joint Graph Rewiring and Feature Denoising via Spectral Resonancecited by 12
  34. 2022The Devil is in the Conflict: Disentangled Information Graph Neural Networks for Fraud Detectioncited by 11
  35. 2023ERASE: Error-Resilient Representation Learning on Graphs for Label Noise Tolerancecited by 11
  36. 2023Deep Statistical Solver for Distribution System State Estimationcited by 10
  37. 2021Does your graph need a confidence boost? Convergent boosted smoothing on graphs with tabular node featurescited by 9
  38. 2022Descent Steps of a Relation-Aware Energy Produce Heterogeneous Graph Neural Networkscited by 9

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