Hyperbolic Dot Products: Geometry-Aware Similarity for Non-Euclidean Embeddings Article Swipe
Revista, Zen
,
IA, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17823370
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17823370
The ubiquitous Euclidean dot product serves as a fundamental measure of similarity in numerous machine learning applications, ranging from recommender systems to natural language processing. However, an increasing volume of complex, hierarchical, and graph-structured data exhibits intrinsic non-Euclidean geometries, rendering Euclidean embeddings and their associated similarity metrics suboptimal. Hyperbolic spaces, with their inherent negative curvature, naturally accommodate such data structures, offering superior embedding quality for phenomena like tree-like hierarchies and scale-free networks. This paper introduces and rigorously defines the concept of hyperbolic dot products as a geometry-aware similarity measure specifically tailored for non-Euclidean embeddings. We explore its mathematical foundations within the Poincaré disk model, illustrating how it naturally extends the notion of angular similarity to hyperbolic manifolds while respecting their unique curvature properties. Unlike traditional hyperbolic distance metrics, which focus on dissimilarity, the hyperbolic dot product offers a direct analogue to the projection-based similarity inherent in its Euclidean counterpart. We delve into its theoretical properties, contrasting it with both Euclidean dot product and hyperbolic distance, and discuss its potential to enhance performance in tasks requiring nuanced similarity assessment, such as semantic search, link prediction, and anomaly detection within hyperbolic latent spaces. This work provides a crucial step towards developing a comprehensive toolkit for effective data analysis and machine learning in the increasingly prevalent non-Euclidean data paradigm.
Related Topics
Concepts
Euclidean geometry
Similarity (geometry)
Dot product
Euclidean distance
Mathematics
Product (mathematics)
Hyperbolic space
Hyperbolic geometry
Similarity measure
Measure (data warehouse)
Theoretical computer science
Embedding
Computer science
Hyperbolic manifold
Hyperbolic tree
Curvature
Artificial intelligence
Euclidean space
Pure mathematics
Algebra over a field
Entropy (arrow of time)
Semantic similarity
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17823370
- OA Status
- green
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W7108994825Canonical identifier for this work in OpenAlex
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https://doi.org/10.5281/zenodo.17823370Digital Object Identifier
- Title
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Hyperbolic Dot Products: Geometry-Aware Similarity for Non-Euclidean EmbeddingsWork title
- Type
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articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-12-05Full publication date if available
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Revista, Zen, IA, 10List of authors in order
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https://doi.org/10.5281/zenodo.17823370Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17823370Direct OA link when available
- Concepts
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Euclidean geometry, Similarity (geometry), Dot product, Euclidean distance, Mathematics, Product (mathematics), Hyperbolic space, Hyperbolic geometry, Similarity measure, Measure (data warehouse), Theoretical computer science, Embedding, Computer science, Hyperbolic manifold, Hyperbolic tree, Curvature, Artificial intelligence, Euclidean space, Pure mathematics, Algebra over a field, Entropy (arrow of time), Semantic similarityTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.properties. | 122 |
| abstract_inverted_index.recommender | 19 |
| abstract_inverted_index.structures, | 59 |
| abstract_inverted_index.suboptimal. | 47 |
| abstract_inverted_index.theoretical | 153 |
| abstract_inverted_index.traditional | 124 |
| abstract_inverted_index.counterpart. | 148 |
| abstract_inverted_index.illustrating | 104 |
| abstract_inverted_index.increasingly | 211 |
| abstract_inverted_index.mathematical | 97 |
| abstract_inverted_index.specifically | 89 |
| abstract_inverted_index.applications, | 16 |
| abstract_inverted_index.comprehensive | 200 |
| abstract_inverted_index.hierarchical, | 31 |
| abstract_inverted_index.non-Euclidean | 37, 92, 213 |
| abstract_inverted_index.dissimilarity, | 131 |
| abstract_inverted_index.geometry-aware | 86 |
| abstract_inverted_index.graph-structured | 33 |
| abstract_inverted_index.projection-based | 142 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.92055493 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |