mlsanityData to 7 Oct 2026

Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back

arXiv 2303.11323 ↗First posted 20 Mar 2023eess.SP cs.LGcited by 21

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Abstract (arXiv)

In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i.e. vector fields over the manifolds. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard convolutional filters in continuous time. We then introduce a discretization procedure, both in the space and time domains, to make TNNs implementable, showing that their discrete counterpart is a novel principled variant of the very recently introduced sheaf neural networks. We formally prove that this discretized architecture converges to the underlying continuous TNN. Finally, we numerically evaluate the effectiveness of the proposed architecture on various learning tasks, both on synthetic and real data.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 32 of its 68 references that are in the map. First posted on arXiv 20 Mar 2023.

Builds on

32 of 68 references.

References · 32

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
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  5. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  6. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  7. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  8. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  9. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  10. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  11. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
  12. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 117
20 more
  1. 2018Convolutional Neural Network Architectures for Signals Supported on Graphscited by 94
  2. 2019Topological Signal Processing over Simplicial Complexescited by 94
  3. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 90
  4. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  5. 2020Sheaf Neural Networkscited by 80
  6. 2020Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networkscited by 73
  7. 2022Sheaf Neural Networks with Connection Laplacianscited by 64
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  16. 2022Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Backcited by 9
  17. 2021Stability of Neural Networks on Riemannian Manifoldscited by 7
  18. 2018Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifoldscited by 6
  19. 2022Diffusion of Information on Networked Lattices by Gossipcited by 4
  20. 2020Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutionscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 5; 2025: 7; 2026: 7.

21 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  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 13
  5. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  6. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  7. 2025Cooperative Sheaf Neural Networkscited by 10
  8. 2023Implicit Gaussian process representation of vector fields over arbitrary latent manifoldscited by 6
  9. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  10. 2025Learning the Structure of Connection Graphscited by 3
  11. 2025VDW-GNNs: Vector diffusion wavelets for geometric graph neural networkscited by 1
  12. 2025Topological Neural Networks over the Aircited by 0
9 more
  1. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  2. 2025CoVariance Filters and Neural Networks over Hilbert Spacescited by 0
  3. 2026Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answeringcited by 0
  4. 2026Multi-Agent System Identification with Nonlinear Sheaf Diffusioncited by 0
  5. 2026Topological Signal Processing: An Application-Oriented Tutorialcited by 0
  6. 2026Learned, Relied Upon, or Necessary? Separating Checkpoint Dependence from Task-Level Value in Sheaf GNNscited by 0
  7. 2026Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Samplingcited by 0
  8. 2026Equivariant Cellular Sheaves for Molecular Electronic Structure: Bridging Sheaf Cohomology and E(3)-Equivariant Hamiltonian Learningcited by 0
  9. 2026Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphscited by 0