mlsanityData to 7 Oct 2026

The GeometricKernels Package: Heat and Mat'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs

arXiv 2407.08086 ↗First posted 10 Jul 2024cs.LG stat.CO stat.MLcited by 10

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Abstract (arXiv)

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In settings that involve structured data defined on graphs, meshes, manifolds, or other related spaces, defining kernels with good uncertainty-quantification behavior, and computing their value numerically, is less straightforward than in the Euclidean setting. To address this difficulty, we present GeometricKernels, a Python software package which implements the geometric analogs of classical Euclidean squared exponential - also known as heat - and Mat'ern kernels, which are widely-used in settings where uncertainty is of key interest. As a byproduct, we obtain the ability to compute Fourier-feature-type expansions, which are widely used in their own right, on a wide set of geometric spaces. Our implementation supports automatic differentiation in every major current framework simultaneously via a backend-agnostic design. In this companion paper to the package and its documentation, we outline the capabilities of the package and present an illustrated example of its interface. We also include a brief overview of the theory the package is built upon and provide some historic context in the appendix.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 32 of its 73 references that are in the map. First posted on arXiv 10 Jul 2024.

Builds on

32 of 73 references.

References · 32

  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
  2. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 603
  3. 2019A Survey on Graph Kernelscited by 148
  4. 2016GPflow: A Gaussian process library using TensorFlowcited by 139
  5. 2020Efficiently Sampling Functions from Gaussian Process Posteriorscited by 125
  6. 2014Hilbert Space Methods for Reduced-Rank Gaussian Process Regressioncited by 88
  7. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  8. 2020Mat'ern Gaussian Processes on Graphscited by 65
  9. 2020Graph Kernels: State-of-the-Art and Future Challengescited by 63
  10. 2020Pathwise Conditioning of Gaussian Processescited by 63
  11. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
  12. 2020Sparse Gaussian Processes with Spherical Harmonic Featurescited by 43
20 more
  1. 2016The Multiscale Laplacian Graph Kernelcited by 31
  2. 2020Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programmingcited by 28
  3. 2022Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces I: the compact casecited by 25
  4. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  5. 2021Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernelscited by 19
  6. 2023Hodge-Compositional Edge Gaussian Processescited by 16
  7. 2021The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still runningcited by 15
  8. 2023Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spacescited by 15
  9. 2023Gaussian Processes on Cellular Complexescited by 15
  10. 2020Graph Based Gaussian Processes on Restricted Domainscited by 10
  11. 2018Gaussian Process Landmarking on Manifoldscited by 9
  12. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 9
  13. 2023Intrinsic Gaussian Vector Fields on Manifoldscited by 8
  14. 2022Isotropic Gaussian Processes on Finite Spaces of Graphscited by 7
  15. 2023Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metricscited by 6
  16. 2023Posterior Contraction Rates for Mat'ern Gaussian Processes on Riemannian Manifoldscited by 6
  17. 2023Implicit Gaussian process representation of vector fields over arbitrary latent manifoldscited by 6
  18. 2023Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approachcited by 6
  19. 2023Implicit Manifold Gaussian Process Regressioncited by 4
  20. 2024Scalable Bayesian inference for heat kernel Gaussian processes on manifoldscited by 4

Built on by

Cited by year (2026 to 7 Oct)

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

10 papers.

  1. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  2. 2025Mesh-Informed Neural Operator : A Transformer Generative Approachcited by 11
  3. 2024Deep Random Features for Scalable Interpolation of Spatiotemporal Datacited by 6
  4. 2026Kernel-Gradient Drifting Modelscited by 6
  5. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 5
  6. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  7. 2025IIKL: Isometric Immersion Kernel Learning with Riemannian Manifold for Geometric Preservationcited by 0
  8. 2026Heat and Mat'ern Kernels on Matchingscited by 0
  9. 2026Do Deep Ensembles Actually Capture Uncertainty in Graph Neural Networks?cited by 0
  10. 2026A General Kernel Framework for Non-CND Distance Measures Using |D|-Dimensional Sparse Landmark Embeddingscited by 0