Papers › Poincaré Embeddings for Learning Hierarchical Representations

Poincaré Embeddings for Learning Hierarchical Representations

22 May 2017NeurIPS 2017 12arXiv:1705.08039archive 2025-07-28

Maximilian Nickel, Douwe Kiela

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

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FranxYao/PoincareProbe mentioned on GitHubpytorch report
HazyResearch/hgcn mentioned on GitHubpytorch report
drewwilimitis/hyperbolic-learning mentioned on GitHubpytorch report
drewwilimitis/poincare mentioned on GitHubpytorch report
nishnik/poincare_embeddings mentioned on GitHub report

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dist nishnik/poincare_embeddings/poincare.py community (archive-listed) ran · violated contract fingerprinted MIT (permissive) · 286b2d4f46b065fb · report
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transitive_closure TatsuyaShirakawa/poincare-embedding/scripts/create_wordnet_noun_hierarchy.py community (archive-listed) ran · our draft was wrong MIT (permissive) · f4913cfd2afb2564 · report
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Tasks

Graph EmbeddingRepresentation LearningRiemannian optimization

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Link Prediction WordNet Poincare Embeddings (dim=100) Accuracy 77.4 #2 of 7 Archive leaderboard report
Link Prediction WordNet Poincare Embeddings (dim=50) Accuracy 77.0 #3 of 7 Archive leaderboard report
Link Prediction WordNet Poincare Embeddings (dim=20) Accuracy 74.3 #4 of 7 Archive leaderboard report
Link Prediction WordNet Poincare Embeddings (dim=10) Accuracy 68.3 #5 of 7 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

Introduced by this paper: Poincaré Embeddings

Poincaré Embeddings

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