mlsanityData to 7 Oct 2026

Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks

arXiv 2304.10031 ↗First posted 20 Apr 2023cs.LGcited by 43

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Abstract (arXiv)

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature for relational systems has also led to a lack of unification in notation and language across message-passing Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying message-passing TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL for relational systems, and compare the recently published message-passing TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 54 of its 84 references that are in the map. First posted on arXiv 20 Apr 2023.

Builds on

54 of 84 references.

References · 54

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38 more
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Citing papers per year: 2023: 10; 2024: 17; 2025: 10; 2026: 6.

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  1. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  2. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  3. 2023Generalized Simplicial Attention Neural Networkscited by 27
  4. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  5. 2024TopoX: A Suite of Python Packages for Machine Learning on Topological Domainscited by 22
  6. 2024A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guidecited by 22
  7. 2024E(n) Equivariant Topological Neural Networkscited by 22
  8. 2025Human-Artificial Interaction in the Age of Agentic AI: A System-Theoretical Approachcited by 22
  9. 2024Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structurescited by 20
  10. 2023From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Modulecited by 19
  11. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  12. 2024TopoTune : A Framework for Generalized Combinatorial Complex Neural Networkscited by 18
31 more
  1. 2024Topological Neural Networks go Persistent, Equivariant, and Continuouscited by 15
  2. 2023CIN++: Enhancing Topological Message Passingcited by 14
  3. 2024Graph Neural Networks in Histopathology: Emerging Trends and Future Directionscited by 13
  4. 2024Attending to Topological Spaces: The Cellular Transformercited by 11
  5. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  6. 2024Heterogeneous Sheaf Neural Networkscited by 10
  7. 2023Topological Data Analysis for Neural Network Analysis: A Comprehensive Surveycited by 9
  8. 2023ICML 2023 Topological Deep Learning Challenge : Design and Resultscited by 7
  9. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  10. 2025Topological Dictionary Learningcited by 4
  11. 2024Deep Learning with Parametric Lensescited by 3
  12. 2023Zoo Guide to Network Embeddingcited by 2
  13. 2024Molecular topological deep learning for polymer property predictioncited by 2
  14. 2025On topological descriptors for graph productscited by 2
  15. 2023Topological Parallax: A Geometric Specification for Deep Perception Modelscited by 1
  16. 2023Algebraic Topological Networks via the Persistent Local Homology Sheafcited by 1
  17. 2026LLM as Graph Kernel: Rethinking Message Passing on Text-Rich Graphscited by 1
  18. 2023Topological Graph Signal Compressioncited by 0
  19. 2024Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactionscited by 0
  20. 2024Combinatorial Complex Score-based Diffusion Modelling through Stochastic Differential Equationscited by 0
  21. 2025Enhancing the Utility of Higher-Order Information in Relational Learningcited by 0
  22. 2025Quotient Complex Transformer (QCformer) for Perovskite Data Analysiscited by 0
  23. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  24. 2025A Remedy for Over-Squashing in Graph Learning via Forman-Ricci Curvature based Graph-to-Hypergraph Structural Liftingcited by 0
  25. 2025Dimensionality reduction and width of deep neural networks based on topological degree theorycited by 0
  26. 2025The Human Brain as a Combinatorial Complexcited by 0
  27. 2026CCMamba: Topologically-Informed Selective State-Space Networks on Combinatorial Complexes for Higher-Order Graph Learningcited by 0
  28. 2026TopoEdge: Topology-Grounded Agentic Framework for Edge Networking Code Generation and Repaircited by 0
  29. 2026Differentiable Lifting for Topological Neural Networkscited by 0
  30. 2026Higher-Order Morphology Priors for Quadruped Reinforcement Learning Under Actuator Degradationcited by 0
  31. 2026Batch Before You Lift: Scalable Topological Deep Learning on Large Graphscited by 0