mlsanityData to 7 Oct 2026

Geometric deep learning: going beyond Euclidean data

arXiv 1611.08097 ↗First posted 24 Nov 2016cs.CVcited by 1,042

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Abstract (arXiv)

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.

Key facts. Cited by 1,042 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Nov 2016.

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Citing papers per year: 2021: 237; 2022: 222; 2023: 182; 2024: 135; 2025: 162; 2026: 104.

1,042 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2021Perceiver: General Perception with Iterative Attentioncited by 1,089
  3. 2023Graph of Thoughts: Solving Elaborate Problems with Large Language Modelscited by 873
  4. 2021How Attentive are Graph Attention Networks?cited by 818
  5. 2021Rethinking Graph Transformers with Spectral Attentioncited by 468
  6. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  7. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  8. 2021Weisfeiler and Lehman Go Cellular: CW Networkscited by 218
  9. 2023NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classificationcited by 207
  10. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  11. 2022Graph neural networks for materials science and chemistrycited by 181
  12. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
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  1. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  2. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  3. 2021Deep Parametric Continuous Convolutional Neural Networkscited by 161
  4. 2021Equivariant Subgraph Aggregation Networkscited by 154
  5. 2021GraphiT: Encoding Graph Structure in Transformerscited by 146
  6. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  7. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  8. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 124
  9. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  10. 2021Geometric Deep Learning on Molecular Representationscited by 113
  11. 2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
  12. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
  13. 2022Neural Collapse: A Review on Modelling Principles and Generalizationcited by 95
  14. 2021Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networkscited by 93
  15. 2021Graph Neural Networks in Network Neurosciencecited by 91
  16. 2022Clifford Neural Layers for PDE Modelingcited by 91
  17. 2023DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusioncited by 85
  18. 2021Space-Time-Separable Graph Convolutional Network for Pose Forecastingcited by 84
  19. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  20. 2021Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyondcited by 81
  21. 2021Driving-Signal Aware Full-Body Avatarscited by 81
  22. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  23. 2021H3D-Net: Few-Shot High-Fidelity 3D Head Reconstructioncited by 81
  24. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 77
  25. 2021DIG: A Turnkey Library for Diving into Graph Deep Learning Researchcited by 76
  26. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 76
  27. 2021Neural Production Systems: Learning Rule-Governed Visual Dynamicscited by 75
  28. 2021Self-Supervised Graph Neural Networks for Improved Electroencephalographic Seizure Analysiscited by 75
  29. 2021FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learningcited by 68
  30. 2021Deep Regression on Manifolds: A 3D Rotation Case Studycited by 67
  31. 2021Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Futurecited by 67
  32. 2021Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Spacecited by 67
  33. 2022Neural Conservation Laws: A Divergence-Free Perspectivecited by 67
  34. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  35. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  36. 2022Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observationscited by 64
  37. 2024Demystifying Chains, Trees, and Graphs of Thoughtscited by 63
  38. 2021On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Featurescited by 62

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