mlsanityData to 14 Oct 2026

Neural Networks on Symmetric Spaces of Noncompact Type

arXiv 2601.01097 ↗First posted 3 Jan 2026stat.ML cs.LGcited by 6

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Abstract (arXiv)

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of noncompact type. In this paper, we propose a novel approach for developing neural networks on such spaces. Our approach relies on a unified formulation of the distance from a point to a hyperplane on the considered spaces. We show that some existing formulations of the point-to-hyperplane distance can be recovered by our approach under specific settings. Furthermore, we derive a closed-form expression for the point-to-hyperplane distance in higher-rank symmetric spaces of noncompact type equipped with G-invariant Riemannian metrics. The derived distance then serves as a tool to design fully-connected (FC) layers and an attention mechanism for neural networks on the considered spaces. Our approach is validated on challenging benchmarks for image classification, electroencephalogram (EEG) signal classification, image generation, and natural language inference.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 43 of its 78 references that are in the map. First posted on arXiv 3 Jan 2026.

Builds on

43 of 78 references.

References · 43

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31 more
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  5. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 73
  6. 2019Riemannian batch normalization for SPD neural networkscited by 72
  7. 2020EEG-TCNet: An Accurate Temporal Convolutional Network for Embedded Motor-Imagery Brain-Machine Interfacescited by 63
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  27. 2023Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Spacecited by 11
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Hyperbolic Busemann Neural Networkscited by 5
  2. 2026Intrinsic Lorentz Neural Networkcited by 3
  3. 2026LAtte: Hyperbolic Lorentz Attention for Cross-Subject EEG Classificationcited by 0
  4. 2026ReManNet: A Riemannian Manifold Network for Monocular 3D Lane Detectioncited by 0
  5. 2026Batch Normalization for Neural Networks on Complex Domainscited by 0
  6. 2026The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspectivecited by 0