mlsanityData to 14 Oct 2026

Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs

arXiv 1811.01900 ↗First posted 5 Nov 2018cs.LG stat.MLcited by 98

Not on the map. Why?

Abstract (arXiv)

We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with k-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.

Key facts. Cited by 98 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Nov 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 24; 2022: 23; 2023: 12; 2024: 17; 2025: 12; 2026: 10.

98 papers.

Sort:

By area:

  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  3. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  4. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 168
  5. 2021You are AllSet: A Multiset Function Framework for Hypergraph Neural Networkscited by 127
  6. 2022Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modelingcited by 127
  7. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 122
  8. 2021Graph-based Semi-supervised Learning: A Comprehensive Reviewcited by 79
  9. 2021NodePiece: Compositional and Parameter-Efficient Representations of Large Knowledge Graphscited by 72
  10. 2021Reconstruction for Powerful Graph Representationscited by 65
  11. 2021Universal Approximation of Functions on Setscited by 62
  12. 2022Theory of Graph Neural Networks: Representation and Learningcited by 61
38 more
  1. 2023On the Connection Between MPNN and Graph Transformercited by 61
  2. 2022Equivariant Hypergraph Diffusion Neural Operatorscited by 47
  3. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  4. 2022Likelihood-Free Parameter Estimation with Neural Bayes Estimatorscited by 32
  5. 2022Graph Neural Networks with Adaptive Readoutscited by 29
  6. 2023The Expressive Power of Graph Neural Networks: A Surveycited by 27
  7. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 26
  8. 2021A New Perspective on the Effects of Spectrum in Graph Neural Networkscited by 24
  9. 2025Learning Efficient Positional Encodings with Graph Neural Networkscited by 24
  10. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  11. 2024Amortized Probabilistic Conditioning for Optimization, Simulation and Inferencecited by 23
  12. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  13. 2021The Power of the Weisfeiler-Leman Algorithm for Machine Learning with Graphscited by 19
  14. 2022Going Deeper into Permutation-Sensitive Graph Neural Networkscited by 15
  15. 2021Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Taskscited by 13
  16. 2022Learnable Commutative Monoids for Graph Neural Networkscited by 13
  17. 2021Adaptive Neural Message Passing for Inductive Learning on Hypergraphscited by 10
  18. 2022Exponential Separations in Symmetric Neural Networkscited by 10
  19. 2023Universal Representation of Permutation-Invariant Functions on Vectors and Tensorscited by 10
  20. 2024On permutation-invariant neural networkscited by 10
  21. 2021SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddingscited by 9
  22. 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environmentscited by 8
  23. 2022Graph Ordering Attention Networkscited by 8
  24. 2024A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Predictioncited by 8
  25. 2022Conditional set generation using Seq2seq modelscited by 7
  26. 2022SS-GNN: A Simple-Structured Graph Neural Network for Affinity Predictioncited by 7
  27. 2022Invariance-Aware Randomized Smoothing Certificatescited by 7
  28. 2023A Unified Framework for Discovering Discrete Symmetriescited by 7
  29. 2023Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networkscited by 7
  30. 2024Baking Symmetry into GFlowNetscited by 7
  31. 2024Conditional diffusions for amortized neural posterior estimationcited by 7
  32. 2021Stochastic Aggregation in Graph Neural Networkscited by 6
  33. 2021Mini-Batch Consistent Slot Set Encoder for Scalable Set Encodingcited by 6
  34. 2021Set-to-Sequence Methods in Machine Learning: a Reviewcited by 6
  35. 2023Polynomial Width is Sufficient for Set Representation with High-dimensional Featurescited by 6
  36. 2024Recurrent Aggregators in Neural Algorithmic Reasoningcited by 6
  37. 2022What Functions Can Graph Neural Networks Generate?cited by 5
  38. 2022Equilibrium Aggregation: Encoding Sets via Optimizationcited by 5

50 most cited of 98 All 98 (JSON)