mlsanityData to 14 Oct 2026

Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back

arXiv 2210.15058 ↗First posted 26 Oct 2022eess.SP cs.LGcited by 9

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Abstract (arXiv)

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 20 of its 34 references that are in the map. First posted on arXiv 26 Oct 2022.

Builds on

20 of 34 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  3. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  4. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 214
  5. 2019Topological Signal Processing over Simplicial Complexescited by 96
  6. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 95
  7. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 92
  8. 2020Sheaf Neural Networkscited by 84
  9. 2022Sheaf Neural Networks with Connection Laplacianscited by 65
  10. 2021Transferability Properties of Graph Neural Networkscited by 43
  11. 2020EdgeNets:Edge Varying Graph Neural Networkscited by 36
  12. 2022Cell Attention Networkscited by 35
8 more
  1. 2018The Vector Heat Methodcited by 31
  2. 2021Learning Decentralized Wireless Resource Allocations with Graph Neural Networkscited by 25
  3. 2020Algebraic Neural Networks: Stability to Deformationscited by 22
  4. 2022Simplicial Attention Neural Networkscited by 21
  5. 2013Spectral Convergence of the connection Laplacian from random samplescited by 19
  6. 2020Graph and graphon neural network stabilitycited by 15
  7. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 14
  8. 2021Stability of Neural Networks on Riemannian Manifoldscited by 7

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 2; 2026: 1.

9 papers.

  1. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 22
  2. 2024E(n) Equivariant Topological Neural Networkscited by 22
  3. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  4. 2024Bundle Neural Networks for message diffusion on graphscited by 14
  5. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  6. 2024An Intrinsic Vector Heat Networkcited by 1
  7. 2025On the Sheafification of Higher-Order Message Passingcited by 1
  8. 2025Topological Neural Networks over the Aircited by 0
  9. 2026Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answeringcited by 0