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Simplicial Neural Networks

arXiv 2010.03633 ↗First posted 7 Oct 2020cs.LG math.AT stat.MLcited by 105

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Abstract (arXiv)

We present simplicial neural networks (SNNs), a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes. These are natural multi-dimensional extensions of graphs that encode not only pairwise relationships but also higher-order interactions between vertices - allowing us to consider richer data, including vector fields and n-fold collaboration networks. We define an appropriate notion of convolution that we leverage to construct the desired convolutional neural networks. We test the SNNs on the task of imputing missing data on coauthorship complexes.

Key facts. Cited by 105 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 12; 2022: 11; 2023: 30; 2024: 17; 2025: 11; 2026: 24.

105 papers.

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  1. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  2. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  3. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  4. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  5. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  6. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  7. 2021Simplicial Convolutional Neural Networkscited by 40
  8. 2022Simplicial Attention Networkscited by 40
  9. 2022Cell Attention Networkscited by 34
  10. 2021Signal Processing on Cell Complexescited by 31
  11. 2023Generalized Simplicial Attention Neural Networkscited by 27
  12. 2023Convolutional Learning on Simplicial Complexescited by 26
38 more
  1. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  2. 2024E(n) Equivariant Topological Neural Networkscited by 22
  3. 2021BScNets: Block Simplicial Complex Neural Networkscited by 21
  4. 2022Simplicial Attention Neural Networkscited by 21
  5. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  6. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  7. 2022Simplicial Convolutional Filterscited by 18
  8. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  9. 2023Simplicial Representation Learning with Neural k-Formscited by 18
  10. 2024TopoTune : A Framework for Generalized Combinatorial Complex Neural Networkscited by 18
  11. 2021Simplicial Complex Representation Learningcited by 17
  12. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  13. 2022SGAT: Simplicial Graph Attention Networkcited by 16
  14. 2023Simplicial Hopfield networkscited by 16
  15. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  16. 2023Combinatorial Complexes: Bridging the Gap Between Cell Complexes and Hypergraphscited by 15
  17. 2023CIN++: Enhancing Topological Message Passingcited by 14
  18. 2021Signal processing on simplicial complexescited by 12
  19. 2023Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networkscited by 11
  20. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  21. 2023Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexescited by 10
  22. 2023Dirac signal processing of higher-order topological signalscited by 9
  23. 2021Data-Centric AI Requires Rethinking Data Notioncited by 8
  24. 2022Convolutional Filtering in Simplicial Complexescited by 8
  25. 2023Cycle Invariant Positional Encoding for Graph Representation Learningcited by 8
  26. 2024On the Theoretical Expressive Power and the Design Space of Higher-Order Graph Transformerscited by 8
  27. 2023ICML 2023 Topological Deep Learning Challenge : Design and Resultscited by 7
  28. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  29. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6
  30. 2023CAT-Walk: Inductive Hypergraph Learning via Set Walkscited by 6
  31. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  32. 2022Pooling Strategies for Simplicial Convolutional Networkscited by 5
  33. 2023Topological Point Cloud Clusteringcited by 5
  34. 2023Homological Neural Networks: A Sparse Architecture for Multivariate Complexitycited by 5
  35. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  36. 2023Homological Convolutional Neural Networkscited by 4
  37. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  38. 2024Bayesian Sheaf Neural Networkscited by 4

50 most cited of 105 All 105 (JSON)