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Pseudo-Riemannian Embedding Models for Multi-Relational Graph Representations

arXiv 2212.03720 ↗First posted 2 Dec 2022cs.SI cs.LG stat.MLcited by 0

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Abstract (arXiv)

In this paper we generalize single-relation pseudo-Riemannian graph embedding models to multi-relational networks, and show that the typical approach of encoding relations as manifold transformations translates from the Riemannian to the pseudo-Riemannian case. In addition we construct a view of relations as separate spacetime submanifolds of multi-time manifolds, and consider an interpolation between a pseudo-Riemannian embedding model and its Wick-rotated Riemannian counterpart. We validate these extensions in the task of link prediction, focusing on flat Lorentzian manifolds, and demonstrate their use in both knowledge graph completion and knowledge discovery in a biological domain.

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References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2014Embedding Entities and Relations for Learning and Inference in Knowledge Basescited by 932
  3. 2016Complex Embeddings for Simple Link Predictioncited by 902
  4. 2017Convolutional 2D Knowledge Graph Embeddingscited by 730
  5. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  6. 2019TuckER: Tensor Factorization for Knowledge Graph Completioncited by 290
  7. 2015A Review of Relational Machine Learning for Knowledge Graphscited by 265
  8. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  9. 2020Low-Dimensional Hyperbolic Knowledge Graph Embeddingscited by 195
  10. 2019Multi-relational Poincar'e Graph Embeddingscited by 126
  11. 2020The impossibility of low rank representations for triangle-rich complex networkscited by 32
  12. 2021Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approachcited by 23
8 more
  1. 2021Scientific Language Models for Biomedical Knowledge Base Completion: An Empirical Studycited by 23
  2. 2019Hyperbolic Disk Embeddings for Directed Acyclic Graphscited by 21
  3. 2019Memory-Efficient Adaptive Optimizationcited by 19
  4. 2020Ultrahyperbolic Representation Learningcited by 17
  5. 2018On Evaluating Embedding Models for Knowledge Base Completioncited by 10
  6. 2021Directed Graph Embeddings in Pseudo-Riemannian Manifoldscited by 9
  7. 2016Embedding Graphs in Lorentzian Spacetimecited by 8
  8. 2018Semi-Riemannian Manifold Optimizationcited by 4

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