mlsanityData to 7 Oct 2026

FSPool: Learning Set Representations with Featurewise Sort Pooling

arXiv 1906.02795 ↗First posted 6 Jun 2019cs.LG cs.AI stat.MLcited by 53

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Abstract (arXiv)

Traditional set prediction models can struggle with simple datasets due to an issue we call the responsibility problem. We introduce a pooling method for sets of feature vectors based on sorting features across elements of the set. This can be used to construct a permutation-equivariant auto-encoder that avoids this responsibility problem. On a toy dataset of polygons and a set version of MNIST, we show that such an auto-encoder produces considerably better reconstructions and representations. Replacing the pooling function in existing set encoders with FSPool improves accuracy and convergence speed on a variety of datasets.

Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jun 2019.

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Citing papers per year: 2021: 17; 2022: 6; 2023: 8; 2024: 8; 2025: 11; 2026: 3.

53 papers.

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  1. 2021Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentationcited by 88
  2. 2021SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Datacited by 78
  3. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  4. 2022Low Dimensional Invariant Embeddings for Universal Geometric Learningcited by 38
  5. 2021Top-N: Equivariant set and graph generation without exchangeabilitycited by 36
  6. 2023Neural Injective Functions for Multisets, Measures and Graphs via a Finite Witness Theoremcited by 33
  7. 2021Neural Auction: End-to-End Learning of Auction Mechanisms for E-Commerce Advertisingcited by 31
  8. 2021The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collidercited by 28
  9. 2023Object-centric architectures enable efficient causal representation learningcited by 21
  10. 2021Multiset-Equivariant Set Prediction with Approximate Implicit Differentiationcited by 17
  11. 2021multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoningcited by 15
  12. 2022Lorentz group equivariant autoencoderscited by 15
38 more
  1. 2021Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distancecited by 10
  2. 2023Complete Neural Networks for Complete Euclidean Graphscited by 10
  3. 2024PolyOculus: Simultaneous Multi-view Image-based Novel View Synthesiscited by 10
  4. 2024On permutation-invariant neural networkscited by 10
  5. 2025ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Planscited by 10
  6. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  7. 2021Multimodal Fusion Refiner Networkscited by 8
  8. 2025Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 8
  9. 2021Contextualized Scene Imagination for Generative Commonsense Reasoningcited by 7
  10. 2023Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networkscited by 7
  11. 2021Mini-Batch Consistent Slot Set Encoder for Scalable Set Encodingcited by 6
  12. 2021Set-to-Sequence Methods in Machine Learning: a Reviewcited by 6
  13. 2022Conditional Permutation Invariant Flowscited by 6
  14. 2023Polynomial Width is Sufficient for Set Representation with High-dimensional Featurescited by 6
  15. 2024On the H"older Stability of Multiset and Graph Neural Networkscited by 6
  16. 2025Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matchingcited by 6
  17. 2021USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problemscited by 5
  18. 2021Set Representation Learning with Generalized Sliced-Wasserstein Embeddingscited by 4
  19. 2022Scalable Set Encoding with Universal Mini-Batch Consistency and Unbiased Full Set Gradient Approximationcited by 4
  20. 2023Permutation-Invariant Set Autoencoders with Fixed-Size Embeddings for Multi-Agent Learningcited by 4
  21. 2023The Responsibility Problem in Neural Networks with Unordered Targetscited by 4
  22. 2024Generalization Bounds via Meta-Learned Model Representations: PAC-Bayes and Sample Compression Hypernetworkscited by 3
  23. 2025Advances in Set Function Learning: A Survey of Techniques and Applicationscited by 3
  24. 2025Mechanistic Independence: A Principle for Identifiable Disentangled Representationscited by 3
  25. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  26. 2023Equivariant vs. Invariant Layers: A Comparison of Backbone and Pooling for Point Cloud Classificationcited by 2
  27. 2025CheMixHub: Datasets and Benchmarks for Chemical Mixture Property Predictioncited by 2
  28. 2021Investigating transformers in the decomposition of polygonal shapes as point collectionscited by 1
  29. 2021The CAT SET on the MAT: Cross Attention for Set Matching in Bipartite Hypergraphscited by 1
  30. 2024Linear optimal transport subspaces for point set classificationcited by 1
  31. 2022GausSetExpander: A Simple Approach for Entity Set Expansioncited by 0
  32. 2022Effective and Interpretable Information Aggregation with Capacity Networkscited by 0
  33. 2024Approximating invariant functions with the sorting trick is theoretically justifiedcited by 0
  34. 2024Fourier Sliced-Wasserstein Embedding for Multisets and Measurescited by 0
  35. 2025Permutation-Invariant Transformer Neural Architectures for Set-Based Indoor Localization Using Learned RSSI Embeddingscited by 0
  36. 2025Wasserstein Hypergraph Neural Networkcited by 0
  37. 2025EMPEROR: Efficient Moment-Preserving Representation of Distributionscited by 0
  38. 2025Convolutional Set Transformercited by 0

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