Research map / Architectures and efficiency / CNN design
Group convolution theory
Develops theory and efficient designs of group-equivariant convolutional networks on homogeneous spaces.
19 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.
2 papers in 2023–24 and 5 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 1.5% to 4.9%.
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 · Group Equivariant Convolutional Networks (ICML 2016 · 552 citations)
- 2017 · Deep Learning on Lie Groups for Skeleton-Based Action Recognition (CVPR 2017 · 290 citations)
- 2019 · A General Theory of Equivariant CNNs on Homogeneous Spaces (NeurIPS 2019 · 35 citations)
- 2020 · Attentive Group Equivariant Convolutional Networks (ICML 2020 · 38 citations)
- 2021 · Efficient Equivariant Network (NeurIPS 2021 · 8 citations)
- 2022 · Learning Partial Equivariances From Data (NeurIPS 2022 · 3 citations)
- 2023 · A General Framework for Robust G-Invariance in G-Equivariant Networks (NeurIPS 2023 · 1 citation)
- 2024 · The Selective $G$-Bispectrum and its Inversion: Applications to $G$-Invariant Networks (NeurIPS 2024 · 0 citations)
- 2025 · On the VC dimension of deep group convolutional neural networks (NeurIPS 2025 · 0 citations)
- 2026 · $\texttt{bispectrum}$: Selective $G$-Bispectra Made Practical (NeurIPS 2026)
Earliest papers here
- Group Equivariant Convolutional Networks (ICML 2016 · 552 citations)
- Deep Learning on Lie Groups for Skeleton-Based Action Recognition (CVPR 2017 · 290 citations)
- A General Theory of Equivariant CNNs on Homogeneous Spaces (NeurIPS 2019 · 35 citations)
What has been tried
15 papers here report 162 measured changes (a component added, removed or swapped, compared with a baseline): helped 66%, no clear effect 6%, hurt 25%, mixed 3%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Replace original model parameters with the full idealized ρ-set model | S5 · cross-entropy loss | Helped | Towards a Unified and Verified Understanding of Group-Operation Networks (ICLR 2025 · 0 citations) | |
| add equivariant anti-aliasing to R=2 subgroup downsampling | Rotated MNIST, SO(2) · Acc_orbit | 0.8106 -> 0.8358 | Helped | Group Downsampling with Equivariant Anti-aliasing (ICLR 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 5 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- STL-10 · 2 of 5 papers
- CIFAR-10 · 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 7 papers; from OpenAlex and the papers' affiliations).
- University of California, Santa Barbara · 3 papers
- UCLouvain · 2 papers
Use it
Download BibTeX of 19 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Group symmetry equivariant networks (55 papers)
- Steerable rotation-equivariant CNNs (40 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).