mlsanityData to 7 Oct 2026

Group Invariant Global Pooling

arXiv 2305.19207 ↗First posted 30 May 2023cs.LG cs.AI cs.CGcited by 1

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Abstract (arXiv)

Much work has been devoted to devising architectures that build group-equivariant representations, while invariance is often induced using simple global pooling mechanisms. Little work has been done on creating expressive layers that are invariant to given symmetries, despite the success of permutation invariant pooling in various molecular tasks. In this work, we present Group Invariant Global Pooling (GIGP), an invariant pooling layer that is provably sufficiently expressive to represent a large class of invariant functions. We validate GIGP on rotated MNIST and QM9, showing improvements for the latter while attaining identical results for the former. By making the pooling process group orbit-aware, this invariant aggregation method leads to improved performance, while performing well-principled group aggregation.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 26 of its 38 references that are in the map. First posted on arXiv 30 May 2023.

Builds on

26 of 38 references.

References · 26

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2017Deep Setscited by 1,394
  3. 2016Group Equivariant Convolutional Networkscited by 1,154
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  5. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,037
  6. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2019General E(2)-Equivariant Steerable CNNscited by 441
  9. 2016Steerable CNNscited by 298
  10. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  11. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  12. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
14 more
  1. 2022e3nn: Euclidean Neural Networkscited by 171
  2. 2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 143
  3. 2017Equivariance Through Parameter-Sharingcited by 139
  4. 2020MDP Homomorphic Networks: Group Symmetries in Reinforcement Learningcited by 133
  5. 2019Scale-Equivariant Steerable Networkscited by 110
  6. 2020Expressive Power of Invariant and Equivariant Graph Neural Networkscited by 100
  7. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  8. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  9. 2016TI-POOLING: transformation-invariant pooling for feature learning in Convolutional Neural Networkscited by 66
  10. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  11. 2022Relaxing Equivariance Constraints with Non-stationary Continuous Filterscited by 41
  12. 2017Deep Rotation Equivariant Networkcited by 16
  13. 2021Group Equivariant Subsamplingcited by 15
  14. 2020Breaking the Expressive Bottlenecks of Graph Neural Networkscited by 6

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Citing papers per year: 2026: 1.

1 paper.

  1. 2026Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networkscited by 0