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Graph Convolutional Neural Networks via Scattering

arXiv 1804.00099 ↗First posted 31 Mar 2018cs.IT cs.LG eess.SPcited by 46

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Abstract (arXiv)

We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations and stable to graph manipulations. Numerical results demonstrate competitive performance on relevant datasets.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Mar 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 13; 2023: 9; 2024: 5; 2025: 6; 2026: 1.

46 papers.

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  1. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  2. 2022Unlearning Graph Classifiers with Limited Data Resourcescited by 31
  3. 2022Skeleton-Parted Graph Scattering Networks for 3D Human Motion Predictioncited by 29
  4. 2022Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem?cited by 25
  5. 2021Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNscited by 18
  6. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  7. 2022Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networkscited by 18
  8. 2022Geometric Scattering on Measure Spacescited by 17
  9. 2023Approximately Equivariant Graph Networkscited by 16
  10. 2021Parametric Scattering Networkscited by 15
  11. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  12. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
34 more
  1. 2021Space-Time Graph Neural Networkscited by 10
  2. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
  3. 2022The Manifold Scattering Transform for High-Dimensional Point Cloud Datacited by 9
  4. 2022Learnable Filters for Geometric Scattering Modulescited by 9
  5. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  6. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  7. 2021Convolutional Filtering and Neural Networks with Non Commutative Algebrascited by 8
  8. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  9. 2021Molecular Graph Generation via Geometric Scatteringcited by 7
  10. 2022Stability of Aggregation Graph Neural Networkscited by 7
  11. 2021Graph Neural Networks With Lifting-based Adaptive Graph Waveletscited by 6
  12. 2021On the Stability of Low Pass Graph Filter With a Large Number of Edge Rewirescited by 5
  13. 2024A General Graph Spectral Wavelet Convolution via Chebyshev Order Decompositioncited by 4
  14. 2022Graph Neural Network Based Node Deployment for Throughput Enhancementcited by 3
  15. 2023BLIS-Net: Classifying and Analyzing Signals on Graphscited by 3
  16. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  17. 2023Graph Scattering beyond Wavelet Shacklescited by 2
  18. 2023Manifold Filter-Combine Networkscited by 2
  19. 2023Directed Scattering for Knowledge Graph-based Cellular Signaling Analysiscited by 2
  20. 2023On the Trade-Off between Stability and Representational Capacity in Graph Neural Networkscited by 2
  21. 2025HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Datacited by 2
  22. 2023Multiscale Hodge Scattering Networks for Data Analysiscited by 1
  23. 2024Energy Propagation in Scattering Convolution Networks Can Be Arbitrarily Slowcited by 1
  24. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  25. 2022From CNNs to Shift-Invariant Twin Models Based on Complex Waveletscited by 0
  26. 2023ViDa: Visualizing DNA hybridization trajectories with biophysics-informed deep graph embeddingscited by 0
  27. 2024A short review on the maximum clique problem algorithms with classical, AI, and quantum methodscited by 0
  28. 2024Convergence of Manifold Filter-Combine Networkscited by 0
  29. 2024ProtScape: A molecular structure and energy-aware representation for protein conformation generationcited by 0
  30. 2025Digital implementations of deep feature extractors are intrinsically informativecited by 0
  31. 2025InfoGain Wavelets: Furthering the Design of Graph Diffusion Waveletscited by 0
  32. 2025Scattering Networks on Noncommutative Finite Groupscited by 0
  33. 2025ARM-Explainer -- Explaining and improving graph neural network predictions for the maximum clique problem using node features and association rule miningcited by 0
  34. 2026Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?cited by 0