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The Claim

The Poincaré embedding model, introduced by Maximilian Nickel and Douwe Kiela in 2017, demonstrated that hierarchical structures can be embedded with low distortion in hyperbolic space.

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The Short Version

The claim accurately identifies the authors, year, and core contribution of the Poincaré embeddings paper, and the broader research community consistently describes the work as demonstrating low-distortion hierarchical embedding in hyperbolic space. The original 2017 paper empirically showed that Poincaré ball embeddings significantly outperform Euclidean baselines on hierarchical datasets like WordNet. However, the paper provides empirical benchmarks rather than formal distortion guarantees, and later research shows distortion can increase for wider hierarchies.

Caveats

  • The original paper demonstrates low distortion empirically on specific benchmarks (e.g., WordNet) but does not provide formal worst-case distortion bounds or universal guarantees.
  • Later research (2023) shows that distortion can increase for wider hierarchies because the Poincaré embedding method relies on contrastive learning without partial-order awareness.
  • Subsequent models such as the Lorentz model (2018) were shown to improve upon Poincaré embeddings in low-dimensional settings, indicating the original method's low-distortion performance has important caveats.

The Receipts

  1. Poincaré Embeddings for Learning Hierarchical Representations

    arXiv

  2. Poincaré Embeddings for Learning Hierarchical Representations

    NeurIPS Proceedings

  3. Poincaré Embeddings for Learning Hierarchical Representations

    NeurIPS

  4. Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry

    PMLR Proceedings

  5. Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry

    arXiv

  6. Poincaré Embeddings for Learning Hierarchical Representations

    Facebook AI Research

  7. Highly Scalable and Provably Accurate Classification in Poincaré Balls

    University of Illinois Experts

  8. Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders

    NeurIPS

  9. models.poincare – Train and use Poincare embeddings — gensim

    Gensim Documentation

  10. Learning Contextual Hierarchical Structure of Medical Concepts with Poincaré Embeddings

    PubMed Central

+ 18 more sources — see the full list on Lenz

Filed Under

Douwe KielaMaximilian NickelPoincaré embedding model