mlsanityData to 7 Oct 2026

Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections

arXiv 2211.10066 ↗First posted 18 Nov 2022cs.LG stat.ME stat.MLcited by 16

Not on the map. Why?

Abstract (arXiv)

It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few discrepancies to compare probability distributions defined over those spaces exist. Among the possible candidates, optimal transport distances are well defined on such Riemannian manifolds and enjoy strong theoretical properties, but suffer from high computational cost. On Euclidean spaces, sliced-Wasserstein distances, which leverage a closed-form of the Wasserstein distance in one dimension, are more computationally efficient, but are not readily available on hyperbolic spaces. In this work, we propose to derive novel hyperbolic sliced-Wasserstein discrepancies. These constructions use projections on the underlying geodesics either along horospheres or geodesics. We study and compare them on different tasks where hyperbolic representations are relevant, such as sampling or image classification.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 45 of its 88 references that are in the map. First posted on arXiv 18 Nov 2022.

Builds on

45 of 88 references.

References · 45

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33 more
  1. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 160
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  3. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
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  8. 2019Learning with minibatch Wasserstein : asymptotic and gradient propertiescited by 83
  9. 2020Statistical and Topological Properties of Sliced Probability Divergencescited by 83
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 4; 2025: 7; 2026: 4.

16 papers.

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  1. 2023Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signalscited by 19
  2. 2024Sliced Wasserstein with Random-Path Projecting Directionscited by 15
  3. 2025Lightspeed Geometric Dataset Distance via Sliced Optimal Transportcited by 10
  4. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  5. 2025Differentiable Generalized Sliced Wasserstein Planscited by 7
  6. 2024Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributionscited by 6
  7. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
  8. 2025Fast Estimation of Wasserstein Distances via Regression on Sliced Wasserstein Distancescited by 5
  9. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  10. 2025Distance-Based Tree-Sliced Wasserstein Distancecited by 4
  11. 2025Tree-Sliced Wasserstein Distance with Nonlinear Projectioncited by 3
  12. 2026HEEGNet: Hyperbolic Embeddings for EEGcited by 2
4 more
  1. 2025Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicingcited by 1
  2. 2026Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approachcited by 0
  3. 2026A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decodingcited by 0
  4. 20261-Lipschitz Neural Networks on Hadamard Manifoldscited by 0