# Use of symmetric kernels for convolutional neural networks

arXiv: https://arxiv.org/abs/1805.09421 · HTML: https://mlsanity.com/paper/1805.09421/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 6 of 6)

- [Symmetry Structured Convolutional Neural Networks](https://mlsanity.com/paper/2203.02056/) (2022)
- [SRE-Conv: Symmetric Rotation Equivariant Convolution for Biomedical Image Classification](https://mlsanity.com/paper/2501.09753/) (2025)
- [Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net](https://mlsanity.com/paper/2501.14592/) (2025)
- [GMR-Conv: An Efficient Rotation and Reflection Equivariant Convolution Kernel Using Gaussian Mixture Rings](https://mlsanity.com/paper/2504.02819/) (2025)
- [Equivariant Imaging Biomarkers for Robust Unsupervised Segmentation of Histopathology](https://mlsanity.com/paper/2505.05689/) (2025)
- [Equi-ViT: Rotational Equivariant Vision Transformer for Robust Histopathology Analysis](https://mlsanity.com/paper/2601.09130/) (2026)

## Abstract (arXiv)

At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance, and approximate rotational invariance. We show that usage of such kernels acts as regularizer, and improves generalization of the convolutional neural networks at the cost of more complicated training process.