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Cartan Networks: Group theoretical Hyperbolic Deep Learning

arXiv 2505.24353 ↗First posted 30 May 2025cs.LGcited by 0

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Abstract (arXiv)

Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally from their construction as symmetric spaces. This dual nature of Lie group and Riemannian manifold allows us to propose a new class of hyperbolic deep learning algorithms where group homomorphisms are interleaved with metric-preserving diffeomorphisms. The resulting algorithms, which we call Cartan networks, show promising results on various benchmark data sets and open the way to a novel class of hyperbolic deep learning architectures.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 50 references that are in the map. First posted on arXiv 30 May 2025.

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References · 24

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12 more
  1. 2020Geoopt: Riemannian Optimization in PyTorchcited by 114
  2. 2021Fully Hyperbolic Neural Networkscited by 108
  3. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 49
  4. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  5. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 47
  6. 2023A Unified Framework to Enforce, Discover, and Promote Symmetry in Machine Learningcited by 22
  7. 2019Scalable Hyperbolic Recommender Systemscited by 19
  8. 2023Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebrascited by 6
  9. 2025A group-theoretic framework for machine learning in hyperbolic spacescited by 3
  10. 2023Hyperbolic Convolutional Neural Networkscited by 2
  11. 2024On the Universal Statistical Consistency of Expansive Hyperbolic Deep Convolutional Neural Networkscited by 2
  12. 2025Clustering in hyperbolic ballscited by 1

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