mlsanityData to 7 Oct 2026

Simplicial Complex Representation Learning

arXiv 2103.04046 ↗First posted 6 Mar 2021cs.LG cs.CG cs.CVcited by 17

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Abstract (arXiv)

Simplicial complexes form an important class of topological spaces that are frequently used in many application areas such as computer-aided design, computer graphics, and simulation. Representation learning on graphs, which are just 1-d simplicial complexes, has witnessed a great attention in recent years. However, there has not been enough effort to extend representation learning to higher dimensional simplicial objects due to the additional complexity these objects hold, especially when it comes to entire-simplicial complex representation learning. In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved. Our method uses our novel geometric message passing schemes to learn an entire simplicial complex representation in an end-to-end fashion. We demonstrate the proposed model on publicly available mesh dataset. To the best of our knowledge, this work presents the first method for learning simplicial complex-level representation.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). Builds on 28 of its 45 references that are in the map. First posted on arXiv 6 Mar 2021.

Builds on

28 of 45 references.

References · 28

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Inductive Representation Learning on Large Graphscited by 6,284
  3. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
  4. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  5. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  6. 2014DeepWalk: Online Learning of Social Representationscited by 1,543
  7. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  8. 2017Representation Learning on Graphs: Methods and Applicationscited by 456
  9. 2014Deep metric learning using Triplet networkcited by 421
  10. 2017graph2vec: Learning Distributed Representations of Graphscited by 228
  11. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  12. 2017A Survey on Network Embeddingcited by 142
16 more
  1. 2020Simplicial Neural Networkscited by 105
  2. 2018Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplaciancited by 84
  3. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  4. 2020Cell Complex Neural Networkscited by 66
  5. 2018NetLSD: Hearing the Shape of a Graphcited by 51
  6. 2018REGAL: Representation Learning-based Graph Alignmentcited by 40
  7. 2020Deep Graph Mapper: Seeing Graphs through the Neural Lenscited by 22
  8. 2018A Simple Baseline Algorithm for Graph Classificationcited by 15
  9. 2019Simplex2Vec embeddings for community detection in simplicial complexescited by 13
  10. 2020k-simplex2vec: a simplicial extension of node2veccited by 13
  11. 2017Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homologycited by 8
  12. 2019Bayesian Topological Learning for Brain State Classificationcited by 7
  13. 2020Bayesian Topological Learning for Classifying the Structure of Biological Networkscited by 6
  14. 2017Effective learning is accompanied by high dimensional and efficient representations of neural activitycited by 4
  15. 2019Unsupervised Inductive Graph-Level Representation Learning via Graph-Graph Proximitycited by 2
  16. 2019Mesh Learning Using Persistent Homology on the Laplacian Eigenfunctionscited by 1

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Cited by year (2026 to 7 Oct)

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

17 papers.

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  1. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  2. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  3. 2023Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networkscited by 43
  4. 2021Signal Processing on Cell Complexescited by 31
  5. 2023Convolutional Learning on Simplicial Complexescited by 26
  6. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  7. 2023Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexescited by 15
  8. 2021Data-Centric AI Requires Rethinking Data Notioncited by 8
  9. 2023ICML 2023 Topological Deep Learning Challenge : Design and Resultscited by 7
  10. 2023Topo-MLP : A Simplicial Network Without Message Passingcited by 7
  11. 2022A Topological Deep Learning Framework for Neural Spike Decodingcited by 6
  12. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
5 more
  1. 2022Stable and Transferable Hyper-Graph Neural Networkscited by 2
  2. 2025Continuous Simplicial Neural Networkscited by 2
  3. 2026Weisfeiler and Lehman Go Categoricalcited by 1
  4. 2025Leveraging Personalized PageRank and Higher-Order Topological Structures for Heterophily Mitigation in Graph Neural Networkscited by 0
  5. 2026Differentiable Lifting for Topological Neural Networkscited by 0