mlsanityData to 14 Oct 2026

Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders

arXiv 1901.06033 ↗First posted 17 Jan 2019stat.ML cs.LGcited by 112

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Abstract (arXiv)

The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. We therefore endow VAEs with a Poincar'e ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidean counterpart, and can qualitatively and quantitatively better recover hierarchical structures.

Key facts. Cited by 112 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Jan 2019.

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Citing papers per year: 2021: 21; 2022: 25; 2023: 22; 2024: 16; 2025: 18; 2026: 10.

112 papers.

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  1. 2022Riemannian Score-Based Generative Modellingcited by 219
  2. 2021Hyperbolic Deep Neural Networks: A Surveycited by 139
  3. 2021Fully Hyperbolic Neural Networkscited by 108
  4. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 73
  5. 2022Plug & Play Attacks: Towards Robust and Flexible Model Inversion Attackscited by 60
  6. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 57
  7. 2021Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphscited by 50
  8. 2021Probing BERT in Hyperbolic Spacescited by 50
  9. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 49
  10. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 47
  11. 2021Unsupervised Discovery of the Long-Tail in Instance Segmentation Using Hierarchical Self-Supervisioncited by 39
  12. 2021A Self-supervised Mixed-curvature Graph Neural Networkcited by 33
38 more
  1. 2022Self-Supervised Continual Graph Learning in Adaptive Riemannian Spacescited by 32
  2. 2021CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Datacited by 28
  3. 2021Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencodercited by 27
  4. 2022Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Casecited by 26
  5. 2022Hyperbolic Deep Reinforcement Learningcited by 25
  6. 2023Poincar'e ResNetcited by 25
  7. 2022A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learningcited by 24
  8. 2022A Geometric Perspective on Variational Autoencoderscited by 24
  9. 2022Hierarchical Sketch Induction for Paraphrase Generationcited by 22
  10. 2024Manifold Integrated Gradients: Riemannian Geometry for Feature Attributioncited by 21
  11. 2024Hyperbolic Geometric Latent Diffusion Model for Graph Generationcited by 20
  12. 2025Hyperbolic Deep Learning for Foundation Models: A Surveycited by 20
  13. 2023Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimizationcited by 18
  14. 2021Neural Distance Embeddings for Biological Sequencescited by 17
  15. 2023Manifold Learning by Mixture Models of VAEs for Inverse Problemscited by 17
  16. 2022Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projectionscited by 16
  17. 2024Learning Structured Representations with Hyperbolic Embeddingscited by 16
  18. 2021Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoderscited by 15
  19. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  20. 2022Hyperbolic VAE via Latent Gaussian Distributionscited by 14
  21. 2024HyperVQ: MLR-based Vector Quantization in Hyperbolic Spacecited by 13
  22. 2021On Incorporating Inductive Biases into VAEscited by 11
  23. 2023Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Spacecited by 11
  24. 2021Continuous normalizing flows on manifoldscited by 10
  25. 2022A Rotated Hyperbolic Wrapped Normal Distribution for Hierarchical Representation Learningcited by 10
  26. 2022Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifoldscited by 10
  27. 2023Tree Variational Autoencoderscited by 10
  28. 2022Curvature Graph Generative Adversarial Networkscited by 9
  29. 2023Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learningcited by 9
  30. 2021Highly Scalable and Provably Accurate Classification in Poincare Ballscited by 8
  31. 2021Adaptive Hierarchical Similarity Metric Learning with Noisy Labelscited by 8
  32. 2022Random Laplacian Features for Learning with Hyperbolic Spacecited by 8
  33. 2022Autoencoding Hyperbolic Representation for Adversarial Generationcited by 7
  34. 2022Hyperbolic Relevance Matching for Neural Keyphrase Extractioncited by 7
  35. 2023Hyperbolic Graph Diffusion Modelcited by 7
  36. 2023Riemannian Laplace Approximation with the Fisher Metriccited by 7
  37. 2023Attributable and Scalable Opinion Summarizationcited by 6
  38. 2023L3DMC: Lifelong Learning using Distillation via Mixed-Curvature Spacecited by 6

50 most cited of 112 All 112 (JSON)