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LanczosNet: Multi-Scale Deep Graph Convolutional Networks

arXiv 1901.01484 ↗First posted 6 Jan 2019cs.LG stat.MLcited by 73

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Abstract (arXiv)

We propose the Lanczos network (LanczosNet), which uses the Lanczos algorithm to construct low rank approximations of the graph Laplacian for graph convolution. Relying on the tridiagonal decomposition of the Lanczos algorithm, we not only efficiently exploit multi-scale information via fast approximated computation of matrix power but also design learnable spectral filters. Being fully differentiable, LanczosNet facilitates both graph kernel learning as well as learning node embeddings. We show the connection between our LanczosNet and graph based manifold learning methods, especially the diffusion maps. We benchmark our model against several recent deep graph networks on citation networks and QM8 quantum chemistry dataset. Experimental results show that our model achieves the state-of-the-art performance in most tasks. Code is released at: urlhttps://github.com/lrjconan/LanczosNetwork.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jan 2019.

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Citing papers per year: 2020: 1; 2021: 26; 2022: 14; 2023: 11; 2024: 14; 2025: 5; 2026: 2.

73 papers.

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  1. 2020Permutation Invariant Graph Generation via Score-Based Generative Modelingcited by 263
  2. 2021GRAND: Graph Neural Diffusioncited by 258
  3. 2021Large-Scale Chemical Language Representations Capture Molecular Structure and Propertiescited by 203
  4. 2022Graph neural networks for materials science and chemistrycited by 181
  5. 2021LaneRCNN: Distributed Representations for Graph-Centric Motion Forecastingcited by 112
  6. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  7. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  8. 2021Graph-MLP: Node Classification without Message Passing in Graphcited by 73
  9. 2021Local Augmentation for Graph Neural Networkscited by 52
  10. 2021How Framelets Enhance Graph Neural Networkscited by 46
  11. 2023Towards Understanding the Generalization of Graph Neural Networkscited by 41
  12. 2021p-Laplacian Based Graph Neural Networkscited by 39
38 more
  1. 2023A Survey on Spectral Graph Neural Networkscited by 26
  2. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  3. 2023PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detectioncited by 25
  4. 2022Graph Neural Networks for Moleculescited by 21
  5. 2022Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networkscited by 19
  6. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  7. 2024PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systemscited by 18
  8. 2024Spatio-Spectral Graph Neural Networkscited by 17
  9. 2025Beyond Message Passing: Neural Graph Pattern Machinecited by 17
  10. 2021Graph Attention Networks with Positional Embeddingscited by 16
  11. 2024FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preferencecited by 16
  12. 2021Towards Graph Self-Supervised Learning with Contrastive Adjusted Zoomingcited by 15
  13. 2022Skeleton-based Action Recognition via Temporal-Channel Aggregationcited by 13
  14. 2021Adaptive Gaussian Processes on Graphs via Spectral Graph Waveletscited by 11
  15. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  16. 2024Non-convolutional Graph Neural Networkscited by 11
  17. 2021Why Propagate Alone? Parallel Use of Labels and Features on Graphscited by 9
  18. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  19. 2021Graph Denoising with Framelet Regularizercited by 8
  20. 2025Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheavescited by 8
  21. 2021Enhance Information Propagation for Graph Neural Network by Heterogeneous Aggregationscited by 6
  22. 2021Graph Neural Networks With Lifting-based Adaptive Graph Waveletscited by 6
  23. 2023Bi-level Contrastive Learning for Knowledge-Enhanced Molecule Representationscited by 6
  24. 2024Spatio-spectral graph neural operator for solving computational mechanics problems on irregular domain and unstructured gridcited by 6
  25. 2021Learning Graph Representation by Aggregating Subgraphs via Mutual Information Maximizationcited by 5
  26. 2021Self-Supervised Dynamic Graph Representation Learning via Temporal Subgraph Contrastcited by 4
  27. 2022Incorporating Heterophily into Graph Neural Networks for Graph Classificationcited by 4
  28. 2024CKGConv: General Graph Convolution with Continuous Kernelscited by 4
  29. 2024Cross-Modal Learning for Chemistry Property Prediction: Large Language Models Meet Graph Machine Learningcited by 4
  30. 2021Multi-scale Graph Convolutional Networks with Self-Attentioncited by 3
  31. 2022Graph Neural Network Based Node Deployment for Throughput Enhancementcited by 3
  32. 2024Strong Transitivity Relations and Graph Neural Networkscited by 3
  33. 2024Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filteringcited by 3
  34. 2021Simple Graph Convolutional Networkscited by 2
  35. 2022Graph Neural Diffusion Networks for Semi-supervised Learningcited by 2
  36. 2022Live Stream Temporally Embedded 3D Human Body Pose and Shape Estimationcited by 2
  37. 2022Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernelcited by 2
  38. 2022How Powerful is Implicit Denoising in Graph Neural Networkscited by 2

50 most cited of 73 All 73 (JSON)