# Equivariant Multi-View Networks

arXiv: https://arxiv.org/abs/1904.00993 · HTML: https://mlsanity.com/paper/1904.00993/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2019.

## Built on by (most cited first, 30 of 45)

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [VARS: Video Assistant Referee System for Automated Soccer Decision Making from Multiple Views](https://mlsanity.com/paper/2304.04617/) (2023)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [Voint Cloud: Multi-View Point Cloud Representation for 3D Understanding](https://mlsanity.com/paper/2111.15363/) (2021)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [Recognizing Actions in Videos from Unseen Viewpoints](https://mlsanity.com/paper/2103.16516/) (2021)
- [Image to Sphere: Learning Equivariant Features for Efficient Pose Prediction](https://mlsanity.com/paper/2302.13926/) (2023)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal Distillation for 3D Shape Recognition](https://mlsanity.com/paper/2207.03128/) (2022)
- [Learning Canonical View Representation for 3D Shape Recognition with Arbitrary Views](https://mlsanity.com/paper/2108.07084/) (2021)
- [EqNIO: Subequivariant Neural Inertial Odometry](https://mlsanity.com/paper/2408.06321/) (2024)
- [MVTN: Learning Multi-View Transformations for 3D Understanding](https://mlsanity.com/paper/2212.13462/) (2022)
- [Equivariant Single View Pose Prediction Via Induced and Restricted Representations](https://mlsanity.com/paper/2307.03704/) (2023)
- [SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimation](https://mlsanity.com/paper/2411.07326/) (2024)
- [Explicit Discovery of Nonlinear Symmetries from Dynamic Data](https://mlsanity.com/paper/2510.01855/) (2025)
- [Learning Color Equivariant Representations](https://mlsanity.com/paper/2406.09588/) (2024)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [Describe, Adapt and Combine: Empowering CLIP Encoders for Open-set 3D Object Retrieval](https://mlsanity.com/paper/2507.21489/) (2025)
- [APP-Net: Auxiliary-point-based Push and Pull Operations for Efficient Point Cloud Classification](https://mlsanity.com/paper/2205.00847/) (2022)
- [Image to Icosahedral Projection for SO(3) Object Reasoning from Single-View Images](https://mlsanity.com/paper/2207.08925/) (2022)
- [PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNs](https://mlsanity.com/paper/2208.03720/) (2022)
- [Shifting Perspective to See Difference: A Novel Multi-View Method for Skeleton based Action Recognition](https://mlsanity.com/paper/2209.02986/) (2022)
- [MELON: NeRF with Unposed Images in SO(3)](https://mlsanity.com/paper/2303.08096/) (2023)
- [PICASO: Permutation-Invariant Cascaded Attentional Set Operator](https://mlsanity.com/paper/2107.08305/) (2021)
- [Equivariant Light Field Convolution and Transformer](https://mlsanity.com/paper/2212.14871/) (2022)
- [Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning](https://mlsanity.com/paper/2409.07327/) (2024)

## Abstract (arXiv)

Several popular approaches to 3D vision tasks process multiple views of the input independently with deep neural networks pre-trained on natural images, achieving view permutation invariance through a single round of pooling over all views. We argue that this operation discards important information and leads to subpar global descriptors. In this paper, we propose a group convolutional approach to multiple view aggregation where convolutions are performed over a discrete subgroup of the rotation group, enabling, thus, joint reasoning over all views in an equivariant (instead of invariant) fashion, up to the very last layer. We further develop this idea to operate on smaller discrete homogeneous spaces of the rotation group, where a polar view representation is used to maintain equivariance with only a fraction of the number of input views. We set the new state of the art in several large scale 3D shape retrieval tasks, and show additional applications to panoramic scene classification.