mlsanityData to 14 Oct 2026

Gaussian Processes on Cellular Complexes

arXiv 2311.01198 ↗First posted 2 Nov 2023cs.LG stat.MLcited by 15

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Abstract (arXiv)

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Mat'ern kernel and one that additionally mixes information of different cell types.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Builds on 19 of its 32 references that are in the map. First posted on arXiv 2 Nov 2023.

Builds on

19 of 32 references.

References · 19

  1. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 313
  2. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  3. 2019Topological Signal Processing over Simplicial Complexescited by 96
  4. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  5. 2020Cell Complex Neural Networkscited by 67
  6. 2020Mat'ern Gaussian Processes on Graphscited by 66
  7. 2018Structured Neural Summarizationcited by 54
  8. 2021Signal Processing on Cell Complexescited by 31
  9. 2023Generalized Simplicial Attention Neural Networkscited by 27
  10. 2020Evolutionary dynamics of higher-order interactions in social networkscited by 26
  11. 2020Gaussian Processes on Graphs via Spectral Kernel Learningcited by 24
  12. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
7 more
  1. 2023Hodge-Compositional Edge Gaussian Processescited by 16
  2. 2021The topological Dirac equation of networks and simplicial complexescited by 11
  3. 2021Adaptive Gaussian Processes on Graphs via Spectral Graph Waveletscited by 11
  4. 2021Non-separable Spatio-temporal Graph Kernels via SPDEscited by 11
  5. 2023Dirac signal processing of higher-order topological signalscited by 9
  6. 2023Intrinsic Gaussian Vector Fields on Manifoldscited by 8
  7. 2021Gaussian Processes on Hypergraphscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 8; 2025: 6; 2026: 1.

15 papers.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 66
  2. 2024E(n) Equivariant Topological Neural Networkscited by 22
  3. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  4. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  5. 2024The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphscited by 11
  6. 2025Topological Schr"odinger Bridge Matchingcited by 4
  7. 2024Graph Classification Gaussian Processes via Hodgelet Spectral Featurescited by 3
  8. 2025Simplicial Gaussian Models: Representation and Inferencecited by 2
  9. 2024Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learningcited by 1
  10. 2025Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representationscited by 1
  11. 2026Measuring Structure in Graph Benchmark Datasets Using Graph Invariantscited by 1
  12. 2024CW-CNN & CW-AN: Convolutional Networks and Attention Networks for CW-Complexescited by 0
3 more
  1. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  2. 2025Families of Optimal Transport Kernels for Cell Complexescited by 0
  3. 2025Colored Markov Random Fields for Probabilistic Topological Modelingcited by 0