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Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

arXiv 1606.09375 ↗First posted 30 Jun 2016cs.LG stat.MLcited by 2,085

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Abstract (arXiv)

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

Key facts. Cited by 2,085 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jun 2016.

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Citing papers per year: 2020: 1; 2021: 477; 2022: 441; 2023: 381; 2024: 375; 2025: 249; 2026: 161.

2,085 papers.

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  1. 2021E(n) Equivariant Graph Neural Networkscited by 951
  2. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  3. 2022Message Passing Neural PDE Solverscited by 368
  4. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  5. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 326
  6. 2021Channel-wise Topology Refinement Graph Convolution for Skeleton-Based Action Recognitioncited by 317
  7. 2021Graph Neural Network-Based Anomaly Detection in Multivariate Time Seriescited by 300
  8. 2021Spectral Temporal Graph Neural Network for Multivariate Time-series Forecastingcited by 298
  9. 2024A Survey on Vision-Language-Action Models for Embodied AIcited by 274
  10. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  11. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  12. 2021GRAND: Graph Neural Diffusioncited by 258
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  1. 2022Long Range Graph Benchmarkcited by 258
  2. 2023A Survey on Oversmoothing in Graph Neural Networkscited by 246
  3. 2023One for All: Towards Training One Graph Model for All Classification Taskscited by 239
  4. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  5. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  6. 2023Language is All a Graph Needscited by 219
  7. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  8. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  9. 2021Large-Scale Chemical Language Representations Capture Molecular Structure and Propertiescited by 203
  10. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  11. 2022Representing Long-Range Context for Graph Neural Networks with Global Attentioncited by 193
  12. 2022Rethinking Graph Neural Networks for Anomaly Detectioncited by 185
  13. 2022Vision GNN: An Image is Worth Graph of Nodescited by 185
  14. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  15. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
  16. 2022Graph neural networks for materials science and chemistrycited by 181
  17. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  18. 2024LLaGA: Large Language and Graph Assistantcited by 177
  19. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  20. 2021Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learningcited by 175
  21. 2021Training Graph Neural Networks with 1000 Layerscited by 169
  22. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  23. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  24. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  25. 2023Exphormer: Sparse Transformers for Graphscited by 166
  26. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  27. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  28. 2021Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillationcited by 151
  29. 2021Graph Condensation for Graph Neural Networkscited by 150
  30. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  31. 2021Graph Learning: A Surveycited by 140
  32. 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
  33. 2022NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphscited by 137
  34. 2021Nested Graph Neural Networkscited by 136
  35. 2021Real-time Deep Dynamic Characterscited by 133
  36. 2024Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spacescited by 132
  37. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  38. 2022ROLAND: Graph Learning Framework for Dynamic Graphscited by 131

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