Research map / Point clouds / Point cloud classification
Equivariant point cloud networks
Build rotation-equivariant and invariant architectures for point clouds.
84 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2017–2026) · an approach in Point cloud classification, keyword cluster “adversarial · convolution · invariant”
State History Benchmarks Tried Checklist Preprints Who Export
Where it stands
Quiet None of the tracked benchmarks has a report from 2025–26.
28 papers in 2023–24 and 27 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 12.1% to 10.4%.
No longer reported by papers here: ModelNet40 SO(3)/SO(3) (accuracy, last in 2024).
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 · Deep Sets (NeurIPS 2017 · 438 citations)
- 2018 · Deep Parametric Continuous Convolutional Neural Networks (CVPR 2018 · 358 citations)
- 2019 · On the Continuity of Rotation Representations in Neural Networks (CVPR 2019 · 1,198 citations)
- 2020 · SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks (NeurIPS 2020 · 258 citations)
- 2021 · UV-Net: Learning From Boundary Representations (CVPR 2021 · 115 citations)
- 2022 · On the Effectiveness of Persistent Homology (NeurIPS 2022 · 13 citations)
- 2023 · Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants With No False Negatives and No False Positives (CVPR 2023 · 14 citations)
- 2024 · HIMap: HybrId Representation Learning for End-to-end Vectorized HD Map Construction (CVPR 2024 · 29 citations)
- 2025 · Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance (AAAI 2025 · 4 citations)
- 2026 · Change Point Localization and Inference in Dynamic Multilayer Networks (ICLR 2026 · 0 citations)
Earliest papers here
- Deep Sets (NeurIPS 2017 · 438 citations)
- Deep Parametric Continuous Convolutional Neural Networks (CVPR 2018 · 358 citations)
- LDMNet: Low Dimensional Manifold Regularized Neural Networks (CVPR 2018 · 37 citations)
Benchmark records
The best number each year that beat every earlier one, among papers of this approach reporting their own method. Numbers are extracted by AI from each paper's text; check the paper before citing.
ModelNet40 SO(3)/SO(3) · accuracy (higher is better)
4 papers, 2021–2024 · not reported since 2024
| Year | Best so far | Set by |
|---|---|---|
| 2021 | 89.3 | A Functional Approach to Rotation Equivariant Non-Linearities for Tensor Field Networks. (CVPR 2021 · 31 citations) |
| 2023 | 90 | Equivariance with Learned Canonicalization Functions (ICML 2023 · 3 citations) |
| 2024 | 91.5 | Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis (CVPR 2024 · 7 citations) |
What has been tried
67 papers here report 627 measured changes (a component added, removed or swapped, compared with a baseline): helped 70%, no clear effect 5%, hurt 21%, 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 point-level representation with hybrid representation and element-level masked attention | nuScenes val, easy · mAP | 68.5 -> 70.6 | Helped | HIMap: HybrId Representation Learning for End-to-end Vectorized HD Map Construction (CVPR 2024 · 29 citations) |
| add fusion of invariant- and equivariant-branch outputs | ModelNet40 z/SO(3) · accuracy (%) | 89.1 -> 90.4 | Helped | Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis (CVPR 2024 · 7 citations) |
| Add the super-part encoder | PartNet Table · PA | 61.04 -> 64.83 | Helped | Generative 3D Part Assembly via Part-Whole-Hierarchy Message Passing (CVPR 2024 · 5 citations) |
| Use position-orientation feature maps instead of position-only feature maps | rMD17, ten molecules · energy and force MAE | Aspirin E 4.7 -> 1.7; Aspirin F 16.3 -> 5.8; Azobenzene E 3.2 -> 0.7; Azobenzene F 12.2 -> 2.3 | Helped | Fast, Expressive $\mathrm{SE}(n)$ Equivariant Networks through Weight-Sharing in Position-Orientation Space (ICLR 2024 · 5 citations) |
| use one prediction block instead of three | CMU Walking · MSE (×10−2) | 4.8 -> 5.6 | Hurt | Pose-Transformed Equivariant Network for 3D Point Trajectory Prediction (CVPR 2024 · 2 citations) |
| increase the number of basis functions from 1 to 3 | Synthetic data · FNR | 0.38 ± 0.41 -> 0.13 ± 0.22 | Helped | Conjugate Bayesian Two-step Change Point Detection for Hawkes Process (NeurIPS 2024 · 2 citations) |
| Initialize PW matching with Fiedler-W instead of other tested strategies | Randomly perturbed 2D/3D shapes · Matching convergence | Helped | An in depth look at the Procrustes-Wasserstein distance: properties and barycenters (ICML 2025 · 1 citation) | |
| Use shared transport maps with local modulation rather than full per-edge maps | CC classification · accuracy | 0.955 ± 0.009 -> 0.970 ± 0.010 | Helped | Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework (NeurIPS 2025 · 1 citation) |
| Keep the front-view at original scale | OpenLane-V2 subset_A · DET_t | 46.8 -> 53.8 | Helped | TopoPoint: Enhance Topology Reasoning via Endpoint Detection in Autonomous Driving (NeurIPS 2025 · 1 citation) |
| Add edge masking during training | NS-PwC resolution generalization · relative test error | Helped | RIGNO: A Graph-based Framework For Robust And Accurate Operator Learning For PDEs On Arbitrary Domains (NeurIPS 2025 · 1 citation) | |
| use reference rotation alignment rather than randomly rotated training fields | QM9 · molecule neutrality (%) | 82.6 -> 91.5 | Helped | E(3)-equivariant models cannot learn chirality: Field-based molecular generation (ICLR 2025 · 1 citation) |
| learn the directions instead of keeping them fixed | MNIST · accuracy | 77.61 ± 7.98 -> 81.29 ± 3.39 | Helped | Differentiable Euler Characteristic Transforms for Shape Classification (ICLR 2024 · 1 citation) |
What reviewers will expect
Datasets and baselines named in the 22 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Datasets
- QM9 · 4 of 22 papers
- MNIST · 2 of 22 papers
- ShapeNet · 2 of 22 papers
- ModelNet40 · 2 of 22 papers
Baselines
- PointNet · 4 of 22 papers
- DGCNN · 3 of 22 papers
- MeshGraphNet · 2 of 22 papers
- UPT · 2 of 22 papers
- DimeNet++ · 2 of 22 papers
- EDM · 2 of 22 papers
- SchNet · 2 of 22 papers
- PaiNN · 2 of 22 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 55 papers; from OpenAlex and the papers' affiliations).
- University of Amsterdam · 3 papers
- Nanyang Technological University · 2 papers
- Technische Universität München · 2 papers
- NVIDIA · 2 papers
- University of Montreal · 2 papers
- Nanjing University · 2 papers
- University of Pennsylvania · 2 papers
- University of California, Berkeley · 2 papers
- ETHZ - ETH Zurich · 2 papers
- Inria · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Local feature aggregation networks (158 papers)
- Efficient point sampling architectures (45 papers)
- Adversarial point cloud attacks (37 papers)
Elsewhere in the topic
- Point-language and open-vocabulary 3D (107 papers)
- Scene flow and dynamic point clouds (89 papers)
- Self-supervised point cloud pretraining (73 papers)
- LiDAR point cloud compression and completion (60 papers)
- Point cloud detection and tracking (56 papers)
- Masked point autoencoders (22 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).