# FSPool: Learning Set Representations with Featurewise Sort Pooling

arXiv: https://arxiv.org/abs/1906.02795 · HTML: https://mlsanity.com/paper/1906.02795/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2019.

## Built on by (most cited first, 30 of 53)

- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Data](https://mlsanity.com/paper/2103.15619/) (2021)
- [Equivariant Frames and the Impossibility of Continuous Canonicalization](https://mlsanity.com/paper/2402.16077/) (2024)
- [Low Dimensional Invariant Embeddings for Universal Geometric Learning](https://mlsanity.com/paper/2205.02956/) (2022)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [Neural Injective Functions for Multisets, Measures and Graphs via a Finite Witness Theorem](https://mlsanity.com/paper/2306.06529/) (2023)
- [Neural Auction: End-to-End Learning of Auction Mechanisms for E-Commerce Advertising](https://mlsanity.com/paper/2106.03593/) (2021)
- [The Dark Machines Anomaly Score Challenge: Benchmark Data and Model Independent Event Classification for the Large Hadron Collider](https://mlsanity.com/paper/2105.14027/) (2021)
- [Object-centric architectures enable efficient causal representation learning](https://mlsanity.com/paper/2310.19054/) (2023)
- [Multiset-Equivariant Set Prediction with Approximate Implicit Differentiation](https://mlsanity.com/paper/2111.12193/) (2021)
- [multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoning](https://mlsanity.com/paper/2106.01354/) (2021)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distance](https://mlsanity.com/paper/2111.12849/) (2021)
- [Complete Neural Networks for Complete Euclidean Graphs](https://mlsanity.com/paper/2301.13821/) (2023)
- [PolyOculus: Simultaneous Multi-view Image-based Novel View Synthesis](https://mlsanity.com/paper/2402.17986/) (2024)
- [On permutation-invariant neural networks](https://mlsanity.com/paper/2403.17410/) (2024)
- [ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Plans](https://mlsanity.com/paper/2502.07962/) (2025)
- [Multimodal Fusion Refiner Networks](https://mlsanity.com/paper/2104.03435/) (2021)
- [SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2112.05872/) (2021)
- [Fourier Sliced-Wasserstein Embedding for Multisets and Measures](https://mlsanity.com/paper/2504.02544/) (2025)
- [Contextualized Scene Imagination for Generative Commonsense Reasoning](https://mlsanity.com/paper/2112.06318/) (2021)
- [Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks](https://mlsanity.com/paper/2309.04452/) (2023)
- [Mini-Batch Consistent Slot Set Encoder for Scalable Set Encoding](https://mlsanity.com/paper/2103.01615/) (2021)
- [Set-to-Sequence Methods in Machine Learning: a Review](https://mlsanity.com/paper/2103.09656/) (2021)
- [Conditional Permutation Invariant Flows](https://mlsanity.com/paper/2206.09021/) (2022)
- [Polynomial Width is Sufficient for Set Representation with High-dimensional Features](https://mlsanity.com/paper/2307.04001/) (2023)
- [On the H"older Stability of Multiset and Graph Neural Networks](https://mlsanity.com/paper/2406.06984/) (2024)
- [Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching](https://mlsanity.com/paper/2506.07199/) (2025)
- [USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems](https://mlsanity.com/paper/2107.07508/) (2021)
- [Set Representation Learning with Generalized Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2103.03892/) (2021)

## 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.