# Exploiting Cyclic Symmetry in Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1602.02660 · HTML: https://mlsanity.com/paper/1602.02660/

## Key facts

- Cited by 91 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2016.

## Built on by (most cited first, 30 of 91)

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- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
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- [Maximum Class Separation as Inductive Bias in One Matrix](https://mlsanity.com/paper/2206.08704/) (2022)
- [RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Network](https://mlsanity.com/paper/2211.11812/) (2022)
- [Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolution](https://mlsanity.com/paper/2310.02299/) (2023)
- [A PAC-Bayesian Generalization Bound for Equivariant Networks](https://mlsanity.com/paper/2210.13150/) (2022)
- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Revisiting Data Augmentation for Rotational Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/2310.08429/) (2023)
- [Group Equivariant Subsampling](https://mlsanity.com/paper/2106.05886/) (2021)
- [What Affects Learned Equivariance in Deep Image Recognition Models?](https://mlsanity.com/paper/2304.02628/) (2023)
- [Relative stability toward diffeomorphisms indicates performance in deep nets](https://mlsanity.com/paper/2105.02468/) (2021)
- [Symmetry reduction for deep reinforcement learning active control of chaotic spatiotemporal dynamics](https://mlsanity.com/paper/2104.05437/) (2021)
- [Rotation Invariant Transformer for Recognizing Object in UAVs](https://mlsanity.com/paper/2311.02559/) (2023)
- [Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent](https://mlsanity.com/paper/2106.07832/) (2021)

## Abstract (arXiv)

Many classes of images exhibit rotational symmetry. Convolutional neural networks are sometimes trained using data augmentation to exploit this, but they are still required to learn the rotation equivariance properties from the data. Encoding these properties into the network architecture, as we are already used to doing for translation equivariance by using convolutional layers, could result in a more efficient use of the parameter budget by relieving the model from learning them. We introduce four operations which can be inserted into neural network models as layers, and which can be combined to make these models partially equivariant to rotations. They also enable parameter sharing across different orientations. We evaluate the effect of these architectural modifications on three datasets which exhibit rotational symmetry and demonstrate improved performance with smaller models.