mlsanityData to 14 Oct 2026

Normed Spaces for Graph Embedding

arXiv 2312.01502 ↗First posted 3 Dec 2023cs.LG cs.SIcited by 2

Not on the map. Why?

Abstract (arXiv)

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight, we highlight normed spaces as a more flexible and computationally efficient alternative to several popular Riemannian manifolds for learning graph embeddings. Normed space embeddings significantly outperform several popular manifolds on a large range of synthetic and real-world graph reconstruction benchmark datasets while requiring significantly fewer computational resources. We also empirically verify the superiority of normed space embeddings on growing families of graphs associated with negative, zero, and positive curvature, further reinforcing the flexibility of normed spaces in capturing diverse graph structures as graph sizes increase. Lastly, we demonstrate the utility of normed space embeddings on two applied graph embedding tasks, namely, link prediction and recommender systems. Our work highlights the potential of normed spaces for geometric graph representation learning, raises new research questions, and offers a valuable tool for experimental mathematics in the field of finite metric space embeddings. We make our code and data publically available.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 35 of its 68 references that are in the map. First posted on arXiv 3 Dec 2023.

Builds on

35 of 68 references.

References · 35

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2016node2vec: Scalable Feature Learning for Networkscited by 1,918
  4. 2014DeepWalk: Online Learning of Social Representationscited by 1,547
  5. 2016Variational Graph Auto-Encoderscited by 1,382
  6. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  7. 2019Hyperbolic Graph Convolutional Neural Networkscited by 402
  8. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  9. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 206
  10. 2020Low-Dimensional Hyperbolic Knowledge Graph Embeddingscited by 195
  11. 2018Riemannian Adaptive Optimization Methodscited by 194
  12. 2016A Riemannian Network for SPD Matrix Learningcited by 162
23 more
  1. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 162
  2. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 156
  3. 2020Geoopt: Riemannian Optimization in PyTorchcited by 114
  4. 2019Constant Curvature Graph Convolutional Networkscited by 108
  5. 2020DeepSphere: a graph-based spherical CNNcited by 66
  6. 2018Explorations in Homeomorphic Variational Auto-Encodingcited by 65
  7. 2020From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clusteringcited by 65
  8. 2016Building Deep Networks on Grassmann Manifoldscited by 58
  9. 2017Neural Embeddings of Graphs in Hyperbolic Spacecited by 58
  10. 2019Spherical Text Embeddingcited by 49
  11. 2018HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systemscited by 47
  12. 2017TorusE: Knowledge Graph Embedding on a Lie Groupcited by 36
  13. 2020Computationally Tractable Riemannian Manifolds for Graph Embeddingscited by 29
  14. 2021Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approachcited by 23
  15. 2022Heterogeneous manifolds for curvature-aware graph embeddingcited by 23
  16. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  17. 2016Learning an Invariant Hilbert Space for Domain Adaptationcited by 17
  18. 2020Ultrahyperbolic Representation Learningcited by 17
  19. 2019A Degeneracy Framework for Scalable Graph Autoencoderscited by 12
  20. 2023Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matricescited by 10
  21. 2019Fine-Grained Entity Typing in Hyperbolic Spacecited by 9
  22. 2022Weisfeiler and Leman Go Walking: Random Walk Kernels Revisitedcited by 9
  23. 2018Change Detection in Graph Streams by Learning Graph Embeddings on Constant-Curvature Manifoldscited by 8

Built on by

Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025No Metric to Rule Them All: Toward Principled Evaluations of Graph-Learning Datasetscited by 16
  2. 2025Siegel Neural Networkscited by 1