mlsanityData to 7 Oct 2026

Deep Sets

arXiv 1703.06114 ↗First posted 10 Mar 2017cs.LG stat.MLcited by 1,394

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Abstract (arXiv)

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics citepoczos13aistats, to anomaly detection in piezometer data of embankment dams citeJung15Exploration, to cosmology citeNtampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

Key facts. Cited by 1,394 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2017.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 241; 2022: 233; 2023: 233; 2024: 211; 2025: 218; 2026: 257.

1,394 papers.

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  1. 2021Transformers in Vision: A Surveycited by 1,009
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  3. 2022Scaling Vision Transformers to Gigapixel Images via Hierarchical Self-Supervised Learningcited by 357
  4. 2021Neural Bellman-Ford Networks: A General Graph Neural Network Framework for Link Predictioncited by 273
  5. 2021MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Predictioncited by 246
  6. 2022Towards Understanding Grokking: An Effective Theory of Representation Learningcited by 229
  7. 2021Point-Based Neural Rendering with Per-View Optimizationcited by 188
  8. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  9. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  10. 2021Spatio-temporal Self-Supervised Representation Learning for 3D Point Cloudscited by 180
  11. 2022Sign and Basis Invariant Networks for Spectral Graph Representation Learningcited by 176
  12. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
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  1. 2021Equivariant Subgraph Aggregation Networkscited by 154
  2. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
  3. 2021Revisiting Point Cloud Shape Classification with a Simple and Effective Baselinecited by 145
  4. 2021MultiBench: Multiscale Benchmarks for Multimodal Representation Learningcited by 143
  5. 2021Nested Graph Neural Networkscited by 136
  6. 2023Neural Architecture Search: Insights from 1000 Paperscited by 136
  7. 2023Representational Strengths and Limitations of Transformerscited by 132
  8. 2021Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Predictioncited by 131
  9. 2021ETA Prediction with Graph Neural Networks in Google Mapscited by 130
  10. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  11. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 124
  12. 2021Whole Slide Images are 2D Point Clouds: Context-Aware Survival Prediction using Patch-based Graph Convolutional Networkscited by 124
  13. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  14. 2021Accurate Learning of Graph Representations with Graph Multiset Poolingcited by 120
  15. 2022Understanding and Extending Subgraph GNNs by Rethinking Their Symmetriescited by 112
  16. 2023What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalizationcited by 112
  17. 2021GENESIS-V2: Inferring Unordered Object Representations without Iterative Refinementcited by 109
  18. 2022Equivariance with Learned Canonicalization Functionscited by 106
  19. 2021Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Designcited by 103
  20. 2022The CLRS Algorithmic Reasoning Benchmarkcited by 103
  21. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  22. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  23. 2022Particle Transformer for Jet Taggingcited by 95
  24. 2022"This is my unicorn, Fluffy": Personalizing frozen vision-language representationscited by 95
  25. 2021Proximal Optimal Transport Modeling of Population Dynamicscited by 91
  26. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  27. 2021GNNAutoScale: Scalable and Expressive Graph Neural Networks via Historical Embeddingscited by 90
  28. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  29. 2021Generative Models as Distributions of Functionscited by 89
  30. 2022Few-Shot Class-Incremental Learning by Sampling Multi-Phase Taskscited by 87
  31. 2021Topological Graph Neural Networkscited by 86
  32. 2023Everything is Connected: Graph Neural Networkscited by 85
  33. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  34. 2022Tutorial on amortized optimizationcited by 83
  35. 2024Timer-XL: Long-Context Transformers for Unified Time Series Forecastingcited by 83
  36. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  37. 2021Graph-based Semi-supervised Learning: A Comprehensive Reviewcited by 79
  38. 2021SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Datacited by 78

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