Research map / Architectures and efficiency / CNN design
Steerable rotation-equivariant CNNs
Designs steerable filters for rotation, scale, and Euclidean equivariance in convolutional networks.
40 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · 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.
9 papers in 2023–24 and 6 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 6.6% to 5.9%.
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
- 2016 · Exploiting Cyclic Symmetry in Convolutional Neural Networks (ICML 2016 · 155 citations)
- 2017 · Harmonic Networks: Deep Translation and Rotation Equivariance (CVPR 2017 · 594 citations)
- 2018 · Learning Steerable Filters for Rotation Equivariant CNNs (CVPR 2018 · 309 citations)
- 2019 · General E(2)-Equivariant Steerable CNNs (NeurIPS 2019 · 93 citations)
- 2020 · Scale-Equivariant Steerable Networks (ICLR 2020 · 69 citations)
- 2021 · PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNs (AAAI 2021 · 17 citations)
- 2022 · Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs (ICLR 2022 · 6 citations)
- 2023 · Scaling Spherical CNNs (ICML 2023 · 6 citations)
- 2024 · Making Vision Transformers Truly Shift-Equivariant (CVPR 2024 · 9 citations)
- 2025 · Rotation-Equivariant Self-Supervised Method in Image Denoising (CVPR 2025 · 5 citations)
- 2026 · REViT: Roto-reflection Equivariant Convolutional Vision Transformer (ICML 2026 · 0 citations)
Earliest papers here
- Exploiting Cyclic Symmetry in Convolutional Neural Networks (ICML 2016 · 155 citations)
- Harmonic Networks: Deep Translation and Rotation Equivariance (CVPR 2017 · 594 citations)
- Warped Convolutions: Efficient Invariance to Spatial Transformations (ICML 2017 · 23 citations)
What has been tried
33 papers here report 309 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 8%, hurt 24%, 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 |
|---|---|---|---|---|
| Add A-token | CIFAR-10 circular shifts · Top-1 accuracy | 93.66 ± .19 -> 93.39 ± .13 | Hurt | Making Vision Transformers Truly Shift-Equivariant (CVPR 2024 · 9 citations) |
| Use Fconv rather than the CNN convolution baseline | Gaussian25 average · PSNR | 30.56 -> 30.65 | Helped | Rotation-Equivariant Self-Supervised Method in Image Denoising (CVPR 2025 · 5 citations) |
| increase bandlimit from L=0 to L=1 | SO(2)-DDMNIST · accuracy | 0.469 -> 0.894 | Helped | A Probabilistic Approach to Learning the Degree of Equivariance in Steerable CNNs (ICML 2024 · 1 citation) |
| Use the weighted Cayley-table parameters in the kernel head | Not specified · Not specified | Helped | Clifford-Steerable Convolutional Neural Networks (ICML 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 5 papers of this approach from 2024–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- CNN · 2 of 5 papers
- E2-CNN · 2 of 5 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 15 papers; from OpenAlex and the papers' affiliations).
- Qualcomm · 2 papers
- University of Amsterdam · 2 papers
Use it
Download BibTeX of 28 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Group symmetry equivariant networks (55 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).