mlsanityData to 14 Oct 2026

Multiset-Equivariant Set Prediction with Approximate Implicit Differentiation

arXiv 2111.12193 ↗First posted 23 Nov 2021cs.LG stat.MLcited by 17

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Abstract (arXiv)

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 44 of its 62 references that are in the map. First posted on arXiv 23 Nov 2021.

Builds on

44 of 62 references.

References · 44

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  4. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  5. 2020End-to-End Object Detection with Transformerscited by 7,414
  6. 2018How Powerful are Graph Neural Networks?cited by 4,393
  7. 2016Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotationscited by 2,656
  8. 2019A Survey on Bias and Fairness in Machine Learningcited by 1,917
  9. 2016CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoningcited by 1,457
  10. 2017Deep Setscited by 1,421
  11. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  12. 2020Object-Centric Learning with Slot Attentioncited by 876
32 more
  1. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  2. 2019Deep Equilibrium Modelscited by 615
  3. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 599
  4. 2019Meta-Learning with Implicit Gradientscited by 525
  5. 2019Differentiable Convex Optimization Layerscited by 465
  6. 2017Scene Graph Generation by Iterative Message Passingcited by 462
  7. 2018GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoderscited by 383
  8. 2019Multi-Object Representation Learning with Iterative Variational Inferencecited by 360
  9. 2017A simple neural network module for relational reasoningcited by 346
  10. 2015Order Matters: Sequence to sequence for setscited by 237
  11. 2018Learning Deep Generative Models of Graphscited by 229
  12. 2021Efficient and Modular Implicit Differentiationcited by 203
  13. 2020DeepSVG: A Hierarchical Generative Network for Vector Graphics Animationcited by 159
  14. 2019Does Object Recognition Work for Everyone?cited by 151
  15. 2020Multiscale Deep Equilibrium Modelscited by 151
  16. 2015End-to-end people detection in crowded scenescited by 140
  17. 2019Implicit Deep Learningcited by 124
  18. 2016On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimizationcited by 112
  19. 2020Implicit Graph Neural Networkscited by 100
  20. 2019On the Limitations of Representing Functions on Setscited by 90
  21. 2019End-to-End Neural Speaker Diarization with Permutation-Free Objectivescited by 88
  22. 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 86
  23. 2020Face Recognition: Too Bias, or Not Too Bias?cited by 82
  24. 2019Deep Set Prediction Networkscited by 71
  25. 2019FSPool: Learning Set Representations with Featurewise Sort Poolingcited by 53
  26. 2020Differentiating through the Fr'echet Meancited by 53
  27. 2021iDARTS: Differentiable Architecture Search with Stochastic Implicit Gradientscited by 51
  28. 2017End-to-End Learning for Structured Prediction Energy Networkscited by 33
  29. 2020Conditional Set Generation with Transformerscited by 32
  30. 2020Super-efficiency of automatic differentiation for functions defined as a minimumcited by 24
  31. 2020Set Prediction without Imposing Structure as Conditional Density Estimationcited by 12
  32. 2020Learn to Predict Sets Using Feed-Forward Neural Networkscited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 4; 2024: 6; 2025: 3; 2026: 1.

17 papers.

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  1. 2022Equivariance with Learned Canonicalization Functionscited by 109
  2. 2022Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiationcited by 46
  3. 2024A Canonicalization Perspective on Invariant and Equivariant Learningcited by 27
  4. 2023Symmetry Breaking and Equivariant Neural Networkscited by 25
  5. 2022Equivariant Networks for Crystal Structurescited by 24
  6. 2023TorchDEQ: A Library for Deep Equilibrium Modelscited by 21
  7. 2023Object-centric architectures enable efficient causal representation learningcited by 21
  8. 2023Unlocking Slot Attention by Changing Optimal Transport Costscited by 16
  9. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 16
  10. 2024PolyOculus: Simultaneous Multi-view Image-based Novel View Synthesiscited by 10
  11. 2024On permutation-invariant neural networkscited by 10
  12. 2024Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Modelscited by 8
5 more
  1. 2025When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approachcited by 3
  2. 2025Advances in Set Function Learning: A Survey of Techniques and Applicationscited by 3
  3. 2024Multiset Transformer: Advancing Representation Learning in Persistence Diagramscited by 2
  4. 2024Learning Set Functions with Implicit Differentiationcited by 1
  5. 2026GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generationcited by 0