Research map / Architectures and efficiency / CNN design
Group symmetry equivariant networks
Builds networks equivariant to Lie groups, diffeomorphisms, and gauge symmetries.
55 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in CNN design, keyword cluster “equivariant · equivariance · group”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
16 papers in 2023–24 and 22 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 11.7% to 21.6%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2017 · Equivariance Through Parameter-Sharing (ICML 2017 · 112 citations)
- 2018 · Group Equivariant Capsule Networks (NeurIPS 2018 · 93 citations)
- 2019 · Gauge Equivariant Convolutional Networks and the Icosahedral CNN (ICML 2019 · 165 citations)
- 2020 · Co-Attentive Equivariant Neural Networks: Focusing Equivariance On Transformations Co-Occurring in Data (ICLR 2020 · 14 citations)
- 2021 · LieTransformer: Equivariant Self-Attention for Lie Groups (ICML 2021 · 33 citations)
- 2022 · Enabling Equivariance for Arbitrary Lie Groups (CVPR 2022 · 12 citations)
- 2023 · The Lie Derivative for Measuring Learned Equivariance (ICLR 2023 · 6 citations)
- 2024 · Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Products (ICLR 2024 · 4 citations)
- 2025 · Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant (NeurIPS 2025 · 3 citations)
- 2026 · Normalization Equivariance for Arbitrary Backbones, with Application to Image Denoising (ICML 2026 · 0 citations)
Earliest papers here
- Equivariance Through Parameter-Sharing (ICML 2017 · 112 citations)
- Group Equivariant Capsule Networks (NeurIPS 2018 · 93 citations)
- Gauge Equivariant Convolutional Networks and the Icosahedral CNN (ICML 2019 · 165 citations)
What has been tried
35 papers here report 354 measured changes (a component added, removed or swapped, compared with a baseline): helped 62%, no clear effect 11%, hurt 23%, mixed 4%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use 8 scalar and 2 vector message representations rather than 16 scalars | Z+4g amplitude regression · MSE (× 10^-5) | 40 ± 4 -> 1.0 ± 0.1 | Helped | Lorentz Local Canonicalization: How to make any Network Lorentz-Equivariant (NeurIPS 2025 · 3 citations) |
| Increase the number of orientations from 4 to 16 | MNIST-rot · error (%) | 2.72 -> 1.16 | Helped | Continuous Rotation Group Equivariant Network Inspired by Neural Population Coding (AAAI 2024 · 2 citations) |
| add fine-tuning on canonicalized data | ACE OOD · test error (× E-04) | \num{29.19} ± \num{5.64} -> \textbf{\num{11.34} ± \num{2.92}} | Helped | Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups (ICLR 2025 · 1 citation) |
| Use equivariant layers only in the first half of ViT-H | ImageNet-1K · Top-1 accuracy | 84.6 -> 85.0 | Helped | Flopping for FLOPs: Leveraging Equivariance for Computational Efficiency (ICML 2025 · 0 citations) |
| Set GEConvNet kernel size to 0 | 2D Chern-number prediction · accuracy and robustness | Helped | Learning Chern Numbers of Multiband Topological Insulators with Gauge Equivariant Neural Networks (NeurIPS 2025 · 0 citations) | |
| Add entropy regularization | MNIST rotations · accuracy | 97.56 ± .07 -> 98.04 ± .11 | Helped | Learning symmetries via weight-sharing with doubly stochastic tensors (NeurIPS 2024 · 0 citations) |
| Use local adaptive rather than local constant polynomial coefficients | MedMNIST3D datasets except Adrenal · AUC | Organ 0.761 -> 0.977; Nodule 0.856 -> 0.916; Fracture 0.758 -> 0.803; Vessel 0.805 -> 0.968; Synapse 0.883 -> 0.984 | Helped | On the Fourier analysis in the SO(3) space : the EquiLoPO Network (ICLR 2025) |
What reviewers will expect
Datasets and baselines named in the 12 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- MNIST · 3 of 12 papers
- CIFAR10 · 2 of 12 papers
Baselines
- Data augmentation · 2 of 12 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 38 papers; from OpenAlex and the papers' affiliations).
- Chalmers University of Technology · 4 papers
- Peking University · 2 papers
- Massachusetts Institute of Technology · 2 papers
- Imperial College London · 2 papers
- Chalmers University · 2 papers
Use it
Download BibTeX of 38 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Steerable rotation-equivariant CNNs (40 papers)
- Group convolution theory (19 papers)
Elsewhere in the topic
- Filter design and trained-filter analysis (128 papers)
- Compact CNN architectures (114 papers)
- Efficient CNN scaling and dynamic inference (104 papers)
- Dense matching and estimation CNNs (93 papers)
- Invertible and wide-network analysis (65 papers)
- Theory of convolutional inductive bias (64 papers)
- Large and dynamic kernel design (62 papers)
- Biologically inspired CNN explanation (46 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).