mlsanityData to 7 Oct 2026

Position: Topological Deep Learning is the New Frontier for Relational Learning

arXiv 2402.08871 ↗First posted 14 Feb 2024cs.LG stat.MLcited by 65

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Abstract (arXiv)

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Key facts. Cited by 65 papers in the map (data through 7 Oct 2026). Builds on 147 of its 250 references that are in the map. First posted on arXiv 14 Feb 2024.

Builds on

147 of 250 references.

References · 147

  1. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  2. 2017Graph Attention Networkscited by 8,854
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  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
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  12. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
38 more
  1. 2020A Generalization of Transformer Networks to Graphscited by 653
  2. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
  3. 2019Graph Transformer Networkscited by 520
  4. 2022DiGress: Discrete Denoising diffusion for graph generationcited by 503
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  6. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  7. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
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  15. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  16. 2019Topology-Preserving Deep Image Segmentationcited by 198
  17. 2023MeshDiffusion: Score-based Generative 3D Mesh Modelingcited by 198
  18. 2022Graph neural networks for materials science and chemistrycited by 181
  19. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  20. 2023Representational Strengths and Limitations of Transformerscited by 132
  21. 2020Networks beyond pairwise interactions: structure and dynamicscited by 127
  22. 2021UniGNN: a Unified Framework for Graph and Hypergraph Neural Networkscited by 127
  23. 2019Topological Autoencoderscited by 124
  24. 2021CF-GNNExplainer: Counterfactual Explanations for Graph Neural Networkscited by 118
  25. 2019Ripser: efficient computation of Vietoris-Rips persistence barcodescited by 115
  26. 2017Deep Learning with Topological Signaturescited by 113
  27. 2020Topology of deep neural networkscited by 111
  28. 2023Intrinsic Dimension Estimation for Robust Detection of AI-Generated Textscited by 111
  29. 2022Transformer for Graphs: An Overview from Architecture Perspectivecited by 107
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  31. 2020Simplicial Neural Networkscited by 105
  32. 2023Graph Foundation Models: Concepts, Opportunities and Challengescited by 101
  33. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
  34. 2019Topological Signal Processing over Simplicial Complexescited by 94
  35. 2020A Systematic Survey on Deep Generative Models for Graph Generationcited by 94
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  37. 2022Topological Deep Learning: Going Beyond Graph Datacited by 92
  38. 2021Topological Graph Neural Networkscited by 86

50 most cited of 147 All 147 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 15; 2025: 20; 2026: 30.

65 papers.

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  1. 2024TopoBench: A Framework for Benchmarking Topological Deep Learningcited by 24
  2. 2024A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guidecited by 22
  3. 2024MANTRA: The Manifold Triangulations Assemblagecited by 12
  4. 2025Copresheaf Topological Neural Networks: A Generalized Deep Learning Frameworkcited by 11
  5. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  6. 2025HOG-Diff: Higher-Order Guided Diffusion for Graph Generationcited by 6
  7. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  8. 2025The Flood Complex: Large-Scale Persistent Homology on Millions of Pointscited by 5
  9. 2026Topological Flow Matchingcited by 5
  10. 2024Demystifying Higher-Order Graph Neural Networkscited by 4
  11. 2024Bayesian Sheaf Neural Networkscited by 4
  12. 2024Topology meets Machine Learning: An Introduction using the Euler Characteristic Transformcited by 4
38 more
  1. 2025Manifold Topological Deep Learning for Biomedical Datacited by 4
  2. 2025Topological Schr"odinger Bridge Matchingcited by 4
  3. 2024Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learningcited by 3
  4. 2024ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domaincited by 3
  5. 2024Graph Classification Gaussian Processes via Hodgelet Spectral Featurescited by 3
  6. 2024Rapid and Precise Topological Comparison with Merge Tree Neural Networkscited by 2
  7. 2024Point Cloud Synthesis Using Inner Product Transformscited by 2
  8. 2024Topological Data Analysis Applications in Natural Language Processing: A Surveycited by 2
  9. 2025Continuous Simplicial Neural Networkscited by 2
  10. 2025Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passingcited by 2
  11. 2025LEAP: Local ECT-Based Learnable Positional Encodings for Graphscited by 2
  12. 2025MonSTeR: a Unified Model for Motion, Scene, Text Retrievalcited by 2
  13. 2025On topological descriptors for graph productscited by 2
  14. 2026The Logical Expressiveness of Topological Neural Networkscited by 2
  15. 2026Topological Neural Operatorscited by 2
  16. 2025Towards Scalable Topological Regularizerscited by 1
  17. 2025Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representationscited by 1
  18. 2025Graph Persistence goes Spectralcited by 1
  19. 2025Unreduced Persistence Diagrams for Topological Machine Learningcited by 1
  20. 2025On the Sheafification of Higher-Order Message Passingcited by 1
  21. 2025Bayesian Topological Convolutional Neural Netscited by 1
  22. 2026Multi-dimensional Persistent Sheaf Laplacians for Image Analysiscited by 1
  23. 2026TopoOR: A Unified Topological Scene Representation for the Operating Roomcited by 1
  24. 2026A Persistent Homology Design Space for 3D Point Cloud Deep Learningcited by 1
  25. 2026Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learningcited by 1
  26. 2026Topology-Preserving Neural Operator Learning via Hodge Decompositioncited by 1
  27. 2024TopOC: Topological Deep Learning for Ovarian and Breast Cancer Diagnosiscited by 0
  28. 2025A Quotient Homology Theory of Representation in Neural Networkscited by 0
  29. 2025Beyond holography: the entropic quantum gravity foundations of image processingcited by 0
  30. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  31. 2025Persistence Spheres: Bi-continuous Representations of Persistence Diagramscited by 0
  32. 2026Persistent Sheaf Laplacian Analysis of Protein Stability and Solubility Changes upon Mutationcited by 0
  33. 2026CCMamba: Topologically-Informed Selective State-Space Networks on Combinatorial Complexes for Higher-Order Graph Learningcited by 0
  34. 2026Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cellscited by 0
  35. 2026Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networkscited by 0
  36. 2026Topological Neural Tangent Kernelcited by 0
  37. 2026Geometry-Aware Simplicial Message Passingcited by 0
  38. 2026No Triangulation Without Representation: Generalization in Topological Deep Learningcited by 0

50 most cited of 65 All 65 (JSON)