mlsanityData to 7 Oct 2026

A Rotated Hyperbolic Wrapped Normal Distribution for Hierarchical Representation Learning

arXiv 2205.13371 ↗First posted 25 May 2022cs.LGcited by 10

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Abstract (arXiv)

We present a rotated hyperbolic wrapped normal distribution (RoWN), a simple yet effective alteration of a hyperbolic wrapped normal distribution (HWN). The HWN expands the domain of probabilistic modeling from Euclidean to hyperbolic space, where a tree can be embedded with arbitrary low distortion in theory. In this work, we analyze the geometric properties of the diagonal HWN, a standard choice of distribution in probabilistic modeling. The analysis shows that the distribution is inappropriate to represent the data points at the same hierarchy level through their angular distance with the same norm in the Poincar'e disk model. We then empirically verify the presence of limitations of HWN, and show how RoWN, the proposed distribution, can alleviate the limitations on various hierarchical datasets, including noisy synthetic binary tree, WordNet, and Atari 2600 Breakout. The code is available at https://github.com/ml-postech/RoWN.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 14 of its 39 references that are in the map. First posted on arXiv 25 May 2022.

Builds on

14 of 39 references.

References · 14

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2015Variational Inference with Normalizing Flowscited by 2,161
  3. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  4. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  5. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  6. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 261
  7. 2020Low-Dimensional Hyperbolic Knowledge Graph Embeddingscited by 195
  8. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  9. 2020Riemannian Continuous Normalizing Flowscited by 143
  10. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  11. 2014Word Representations via Gaussian Embeddingcited by 96
  12. 2020Latent Variable Modelling with Hyperbolic Normalizing Flowscited by 49
2 more
  1. 2020Knowledge Association with Hyperbolic Knowledge Graph Embeddingscited by 31
  2. 2017Hierarchical Embeddings for Hypernymy Detection and Directionalitycited by 19

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Cited by year

Citing papers per year: 2022: 1; 2023: 4; 2024: 2; 2025: 3.

10 papers.

  1. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  2. 2022Hyperbolic VAE via Latent Gaussian Distributionscited by 14
  3. 2023Geometric Relational Embeddings: A Surveycited by 8
  4. 2025Wrapped Gaussian on the manifold of Symmetric Positive Definite Matricescited by 5
  5. 2023Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learningcited by 3
  6. 2024Hyperbolic Metric Learning for Visual Outlier Detectioncited by 3
  7. 2025A group-theoretic framework for machine learning in hyperbolic spacescited by 2
  8. 2023HLoOP -- Hyperbolic 2-space Local Outlier Probabilitiescited by 0
  9. 2024Hyperboloid GPLVM for Discovering Continuous Hierarchies via Nonparametric Estimationcited by 0
  10. 2025HyperST: Hierarchical Hyperbolic Learning for Spatial Transcriptomics Predictioncited by 0