mlsanityData to 7 Oct 2026

Simplicial Convolutional Neural Networks

arXiv 2110.02585 ↗First posted 6 Oct 2021cs.LG eess.SPcited by 40

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Abstract (arXiv)

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks like graph signal reconstruction, graph or node classifications, and link prediction. However, these methods are only suitable for data defined on the nodes of a graph. In this paper, we propose a simplicial convolutional neural network (SCNN) architecture to learn from data defined on simplices, e.g., nodes, edges, triangles, etc. We study the SCNN permutation and orientation equivariance, complexity, and spectral analysis. Finally, we test the SCNN performance for imputing citations on a coauthorship complex.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 13 of its 18 references that are in the map. First posted on arXiv 6 Oct 2021.

Builds on

13 of 18 references.

References · 13

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  3. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  4. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  5. 2020Simplicial Neural Networkscited by 105
  6. 2019Topological Signal Processing over Simplicial Complexescited by 94
  7. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  8. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  9. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 73
  10. 2019HodgeNet: Graph Neural Networks for Edge Datacited by 39
  11. 2018Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Spacecited by 37
  12. 2020EdgeNets:Edge Varying Graph Neural Networkscited by 36
1 more
  1. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 12; 2024: 6; 2025: 7; 2026: 9.

40 papers.

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  1. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  2. 2022Simplicial Attention Networkscited by 40
  3. 2023Generalized Simplicial Attention Neural Networkscited by 27
  4. 2023Convolutional Learning on Simplicial Complexescited by 26
  5. 2022Simplicial Attention Neural Networkscited by 21
  6. 2022Simplicial Convolutional Filterscited by 18
  7. 2023Hodge-Compositional Edge Gaussian Processescited by 16
  8. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  9. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  10. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6
  11. 2023CAT-Walk: Inductive Hypergraph Learning via Set Walkscited by 6
  12. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
28 more
  1. 2022Pooling Strategies for Simplicial Convolutional Networkscited by 5
  2. 2023Homological Neural Networks: A Sparse Architecture for Multivariate Complexitycited by 5
  3. 2025HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representationscited by 5
  4. 2023Homological Convolutional Neural Networkscited by 4
  5. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  6. 2025Topological Schr"odinger Bridge Matchingcited by 4
  7. 2024Binarized Simplicial Convolutional Neural Networkscited by 3
  8. 2024Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learningcited by 3
  9. 2025Matched Topological Subspace Detectorcited by 3
  10. 2025Hypergraph Neural Sheaf Diffusion: A Symmetric Simplicial Set Framework for Higher-Order Learningcited by 3
  11. 2022Stable and Transferable Hyper-Graph Neural Networkscited by 2
  12. 2025Continuous Simplicial Neural Networkscited by 2
  13. 2024Graph Signal Adaptive Message Passingcited by 1
  14. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  15. 2023NervePool: A Simplicial Pooling Layercited by 0
  16. 2023Spectral Convergence of Complexon Shift Operatorscited by 0
  17. 2023Hodge-Aware Contrastive Learningcited by 0
  18. 2024Learning From Simplicial Data Based on Random Walks and 1D Convolutionscited by 0
  19. 2025Efficient Sparsification of Simplicial Complexes via Local Densities of Statescited by 0
  20. 2025Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networkscited by 0
  21. 2026From Classical to Topological Neural Networks Under Uncertaintycited by 0
  22. 2026No Triangulation Without Representation: Generalization in Topological Deep Learningcited by 0
  23. 2026Topological Kalman Filtering on Cell Complexescited by 0
  24. 2026Topological Signal Processing: An Application-Oriented Tutorialcited by 0
  25. 2026Periodic Topological Deep Learning for Polymer Design and Discoverycited by 0
  26. 2026Kernel Regression with Tensor Trains and Hadamard Overparameterizationcited by 0
  27. 2026Differentiable Lifting for Topological Neural Networkscited by 0
  28. 2026Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianccited by 0