mlsanityData to 7 Oct 2026

Equivariance Through Parameter-Sharing

arXiv 1702.08389 ↗First posted 27 Feb 2017stat.ML cs.NEcited by 139

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Abstract (arXiv)

We propose to study equivariance in deep neural networks through parameter symmetries. In particular, given a group G that acts discretely on the input and output of a standard neural network layer φW: ReM → ReN, we show that φW is equivariant with respect to G-action iff G explains the symmetries of the network parameters W. Inspired by this observation, we then propose two parameter-sharing schemes to induce the desirable symmetry on W. Our procedures for tying the parameters achieve G-equivariance and, under some conditions on the action of G, they guarantee sensitivity to all other permutation groups outside G.

Key facts. Cited by 139 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 30; 2022: 27; 2023: 29; 2024: 19; 2025: 21; 2026: 13.

139 papers.

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  1. 2022Pure Transformers are Powerful Graph Learnerscited by 188
  2. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  3. 2021Equivariant Subgraph Aggregation Networkscited by 154
  4. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  5. 2021Weisfeiler and Leman go Machine Learning: The Story so farcited by 121
  6. 2022Equivariance with Learned Canonicalization Functionscited by 106
  7. 2023Equivariant Architectures for Learning in Deep Weight Spacescited by 106
  8. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  9. 2021Provably Strict Generalisation Benefit for Equivariant Modelscited by 90
  10. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 85
  11. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  12. 2023Generalization on the Unseen, Logic Reasoning and Degree Curriculumcited by 73
38 more
  1. 2023Permutation Equivariant Neural Functionalscited by 69
  2. 2022Theory of Graph Neural Networks: Representation and Learningcited by 60
  3. 2023Graph Metanetworks for Processing Diverse Neural Architecturescited by 55
  4. 2023Neural Functional Transformerscited by 50
  5. 2023Approximation-Generalization Trade-offs under (Approximate) Group Equivariancecited by 45
  6. 2023Equivariant Deep Weight Space Alignmentcited by 34
  7. 2022Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditionscited by 33
  8. 2022Robust (Controlled) Table-to-Text Generation with Structure-Aware Equivariance Learningcited by 32
  9. 2025Symmetry in Neural Network Parameter Spacescited by 31
  10. 2021Provably Strict Generalisation Benefit for Invariance in Kernel Methodscited by 29
  11. 2021Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlatorscited by 28
  12. 2023Ultra-High-Resolution Detector Simulation with Intra-Event Aware GAN and Self-Supervised Relational Reasoningcited by 25
  13. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  14. 2024Universal Neural Functionalscited by 25
  15. 2022Equivariant Networks for Crystal Structurescited by 24
  16. 2023Symmetry Breaking and Equivariant Neural Networkscited by 24
  17. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  18. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 22
  19. 2022A Theory of PAC Learnability under Transformation Invariancescited by 21
  20. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
  21. 2021PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNscited by 19
  22. 2022Equivariance Discovery by Learned Parameter-Sharingcited by 18
  23. 2022Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networkscited by 18
  24. 2021Equivariant Networks for Pixelized Spherescited by 16
  25. 2023Making Vision Transformers Truly Shift-Equivariantcited by 16
  26. 2023Approximately Equivariant Graph Networkscited by 16
  27. 2023Truly Scale-Equivariant Deep Nets with Fourier Layerscited by 16
  28. 2021Deep Permutation Equivariant Structure from Motioncited by 15
  29. 2021Deep Learning for Two-Sided Matchingcited by 15
  30. 2023Expressive Sign Equivariant Networks for Spectral Geometric Learningcited by 15
  31. 2022Machine learning and invariant theorycited by 13
  32. 2025Probing Equivariance and Symmetry Breaking in Convolutional Networkscited by 12
  33. 2022Group invariant machine learning by fundamental domain projectionscited by 11
  34. 2023Flow Factorized Representation Learningcited by 11
  35. 2021Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamicscited by 10
  36. 2021Truly shift-equivariant convolutional neural networks with adaptive polyphase upsamplingcited by 10
  37. 2025Learning (Approximately) Equivariant Networks via Constrained Optimizationcited by 10
  38. 2021Training or Architecture? How to Incorporate Invariance in Neural Networkscited by 9

50 most cited of 139 All 139 (JSON)