What relations are reliably embeddable in Euclidean space?
Not on the map. Why?
Abstract (arXiv)
We consider the problem of embedding a relation, represented as a directed graph, into Euclidean space. For three types of embeddings motivated by the recent literature on knowledge graphs, we obtain characterizations of which relations they are able to capture, as well as bounds on the minimal dimensionality and precision needed.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Mar 2019.
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Citing papers per year: 2021: 2; 2022: 0; 2023: 1; 2024: 1; 2025: 0; 2026: 2.
6 papers.
- 2021Exact Representation of Sparse Networks with Symmetric Nonnegative Embeddingscited by 3
- 2024Binder: Hierarchical Concept Representation through Order Embedding of Binary Vectorscited by 3
- 2021What is Learned in Knowledge Graph Embeddings?cited by 2
- 2023Towards Ordinal Data Sciencecited by 1
- 2026Relation Geometry in Semantic Space of Language Modelscited by 0
- 2026PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrievalcited by 0
- 2026PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrieval5 Sep 2026
- 2026Relation Geometry in Semantic Space of Language Models29 Jul 2026
- 2024Binder: Hierarchical Concept Representation through Order Embedding of Binary Vectors16 Apr 2024
- 2023Towards Ordinal Data Science13 Jul 2023
- 2021Exact Representation of Sparse Networks with Symmetric Nonnegative Embeddings4 Nov 2021
- 2021What is Learned in Knowledge Graph Embeddings?19 Oct 2021