mlsanityData to 7 Oct 2026

Manifold structure in graph embeddings

arXiv 2006.05168 ↗First posted 9 Jun 2020stat.ML cs.LGcited by 17

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Abstract (arXiv)

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is often available. In spectral embedding, this dimension may be very high. However, this paper shows that existing random graph models, including graphon and other latent position models, predict the data should live near a much lower-dimensional set. One may therefore circumvent the curse of dimensionality by employing methods which exploit hidden manifold structure.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jun 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 3; 2023: 3; 2024: 1; 2025: 3; 2026: 2.

17 papers.

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  1. 2021Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approachcited by 23
  2. 2024Hardness of Learning Neural Networks under the Manifold Hypothesiscited by 18
  3. 2021Spectral embedding for dynamic networks with stability guaranteescited by 13
  4. 2021Matrix factorisation and the interpretation of geodesic distancecited by 6
  5. 2023Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networkscited by 5
  6. 2023Frameless Graph Knowledge Distillationcited by 2
  7. 2022Implications of sparsity and high triangle density for graph representation learningcited by 1
  8. 2025SALMAN: Stability Analysis of Language Models Through the Maps Between Graph-based Manifoldscited by 1
  9. 2021Hermitian Symmetric Spaces for Graph Embeddingscited by 0
  10. 2021Latent structure blockmodels for Bayesian spectral graph clusteringcited by 0
  11. 2022Spectral embedding and the latent geometry of multipartite networkscited by 0
  12. 2022Graph-theoretical approach to robust 3D normal extraction of LiDAR datacited by 0
5 more
  1. 2023Semisupervised regression in latent structure networks on unknown manifoldscited by 0
  2. 2025Signal Recovery from Random Dot-Product Graphs Under Local Differential Privacycited by 0
  3. 2025Self-Reinforced Graph Contrastive Learningcited by 0
  4. 2026Uncovering Locally Low-dimensional Structure in Networks by Locally Optimal Spectral Embeddingcited by 0
  5. 2026Learning Submanifolds for Subsequent Inference on Random Dot Product Graphs, Part 1: Theorycited by 0