mlsanityData to 14 Oct 2026

Learning Representations of Sets through Optimized Permutations

arXiv 1812.03928 ↗First posted 10 Dec 2018cs.LG cs.CV stat.MLcited by 15

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Abstract (arXiv)

Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoiding a bottleneck in traditional set models. We demonstrate our model's ability to learn permutations and set representations with either explicit or implicit supervision on four datasets, on which we achieve state-of-the-art results: number sorting, image mosaics, classification from image mosaics, and visual question answering.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Dec 2018.

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Citing papers per year: 2021: 2; 2022: 6; 2023: 1; 2024: 2; 2025: 2; 2026: 2.

15 papers.

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  1. 2022Equivariance with Learned Canonicalization Functionscited by 109
  2. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 43
  3. 2022GANzzle: Reframing jigsaw puzzle solving as a retrieval task using a generative mental imagecited by 10
  4. 2021Set-to-Sequence Methods in Machine Learning: a Reviewcited by 6
  5. 2023Positional Diffusion: Ordering Unordered Sets with Diffusion Probabilistic Modelscited by 5
  6. 2025Advances in Set Function Learning: A Survey of Techniques and Applicationscited by 3
  7. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  8. 2022Set Interdependence Transformer: Set-to-Sequence Neural Networks for Permutation Learning and Structure Predictioncited by 2
  9. 2022Towards Improving the Generation Quality of Autoregressive Slot VAEscited by 1
  10. 2021Set Twister for Single-hop Node Classificationcited by 0
  11. 2022GausSetExpander: A Simple Approach for Entity Set Expansioncited by 0
  12. 2022Effective and Interpretable Information Aggregation with Capacity Networkscited by 0
3 more
  1. 2024Approximating invariant functions with the sorting trick is theoretically justifiedcited by 0
  2. 2026Improving Set Function Approximation with Quasi-Arithmetic Neural Networkscited by 0
  3. 2026Distributionally Robust Set Representation Learning Under Inference-Time Element Corruptioncited by 0