# Deep Rotation Equivariant Network

arXiv: https://arxiv.org/abs/1705.08623 · HTML: https://mlsanity.com/paper/1705.08623/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2017.

## Built on by (most cited first, 16 of 16)

- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Network](https://mlsanity.com/paper/2211.11812/) (2022)
- [Equivariant Mesh Attention Networks](https://mlsanity.com/paper/2205.10662/) (2022)
- [Explicit Discovery of Nonlinear Symmetries from Dynamic Data](https://mlsanity.com/paper/2510.01855/) (2025)
- [Exploiting Learned Symmetries in Group Equivariant Convolutions](https://mlsanity.com/paper/2106.04914/) (2021)
- [R2Det: Exploring Relaxed Rotation Equivariance in 2D object detection](https://mlsanity.com/paper/2408.11760/) (2024)
- [DuEqNet: Dual-Equivariance Network in Outdoor 3D Object Detection for Autonomous Driving](https://mlsanity.com/paper/2302.13577/) (2023)
- [Towards glass-box CNNs](https://mlsanity.com/paper/2101.10443/) (2021)
- [Automated and Autonomous Experiment in Electron and Scanning Probe Microscopy](https://mlsanity.com/paper/2103.12165/) (2021)
- [RRL:Regional Rotation Layer in Convolutional Neural Networks](https://mlsanity.com/paper/2202.12509/) (2022)
- [Group Invariant Global Pooling](https://mlsanity.com/paper/2305.19207/) (2023)
- [Reinforcement Learning with Lie Group Orientations for Robotics](https://mlsanity.com/paper/2409.11935/) (2024)
- [PreCM: The Padding-based Rotation Equivariant Convolution Mode for Semantic Segmentation](https://mlsanity.com/paper/2411.01624/) (2024)
- [Normalize Filters! Classical Wisdom for Deep Vision](https://mlsanity.com/paper/2506.04401/) (2025)
- [SIM2E: Benchmarking the Group Equivariant Capability of Correspondence Matching Algorithms](https://mlsanity.com/paper/2208.09896/) (2022)
- [MARs: Multi-view Attention Regularizations for Patch-based Feature Recognition of Space Terrain](https://mlsanity.com/paper/2410.05182/) (2024)

## Abstract (arXiv)

Recently, learning equivariant representations has attracted considerable research attention. Dieleman et al. introduce four operations which can be inserted into convolutional neural network to learn deep representations equivariant to rotation. However, feature maps should be copied and rotated four times in each layer in their approach, which causes much running time and memory overhead. In order to address this problem, we propose Deep Rotation Equivariant Network consisting of cycle layers, isotonic layers and decycle layers. Our proposed layers apply rotation transformation on filters rather than feature maps, achieving a speed up of more than 2 times with even less memory overhead. We evaluate DRENs on Rotated MNIST and CIFAR-10 datasets and demonstrate that it can improve the performance of state-of-the-art architectures.