mlsanityData to 14 Oct 2026

Signal Processing on Cell Complexes

arXiv 2110.05614 ↗First posted 11 Oct 2021cs.LG cs.SI eess.SPcited by 31

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Abstract (arXiv)

The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs with signals supported on the nodes, though the processing of signals on more general structures such as simplicial complexes has also been considered. In this paper, we give an introduction to signal processing on (abstract) regular cell complexes, which provide a unifying framework encompassing graphs, simplicial complexes, cubical complexes and various meshes as special cases. We discuss how appropriate Hodge Laplacians for these cell complexes can be derived. These Hodge Laplacians enable the construction of convolutional filters, which can be employed in linear filtering and non-linear filtering via neural networks defined on cell complexes.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 15 of its 37 references that are in the map. First posted on arXiv 11 Oct 2021.

Builds on

15 of 37 references.

References · 15

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  3. 2020Networks beyond pairwise interactions: structure and dynamicscited by 130
  4. 2020Simplicial Neural Networkscited by 110
  5. 2019Topological Signal Processing over Simplicial Complexescited by 96
  6. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 86
  7. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 82
  8. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  9. 2020Cell Complex Neural Networkscited by 67
  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. 2019Graph-based Semi-Supervised & Active Learning for Edge Flowscited by 25
3 more
  1. 2021Simplicial Complex Representation Learningcited by 17
  2. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
  3. 2020Signal processing on simplicial complexescited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 2; 2023: 11; 2024: 5; 2025: 7; 2026: 5.

31 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  3. 2023Convolutional Learning on Simplicial Complexescited by 27
  4. 2023Generalized Simplicial Attention Neural Networkscited by 27
  5. 2024E(n) Equivariant Topological Neural Networkscited by 22
  6. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  7. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  8. 2022Simplicial Convolutional Filterscited by 18
  9. 2023Gaussian Processes on Cellular Complexescited by 15
  10. 2022Causal Fourier Analysis on Directed Acyclic Graphs and Posetscited by 12
  11. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  12. 2023Dirac signal processing of higher-order topological signalscited by 9
19 more
  1. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 8
  2. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  3. 2023Representing Edge Flows on Graphs via Sparse Cell Complexescited by 5
  4. 2021Outlier Detection for Trajectories via Flow-embeddingscited by 4
  5. 2025Topological Dictionary Learningcited by 4
  6. 2025Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexescited by 2
  7. 2023Multiscale Hodge Scattering Networks for Data Analysiscited by 1
  8. 2026Stationarity and Spectral Characterization of Random Signals on Simplicial Complexescited by 1
  9. 2026TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selectioncited by 1
  10. 2023NervePool: A Simplicial Pooling Layercited by 0
  11. 2023Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformationcited by 0
  12. 2024Learning From Simplicial Data Based on Random Walks and 1D Convolutionscited by 0
  13. 2025Topological Neural Networks over the Aircited by 0
  14. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  15. 2025Faster Inference of Cell Complexes from Flows via Matrix Factorizationcited by 0
  16. 2025Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applicationscited by 0
  17. 2026Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answeringcited by 0
  18. 2026Topological Signal Processing: An Application-Oriented Tutorialcited by 0
  19. 2026Differentiable Lifting for Topological Neural Networkscited by 0