# On Symmetries in Convolutional Weights

arXiv: https://arxiv.org/abs/2503.19215 · HTML: https://mlsanity.com/paper/2503.19215/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 24 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Synthesizing the preferred inputs for neurons in neural networks via deep generator networks](https://mlsanity.com/paper/1605.09304/) (2016)
- [Mind the Pad -- CNNs can Develop Blind Spots](https://mlsanity.com/paper/2010.02178/) (2020)
- [Partial Convolution based Padding](https://mlsanity.com/paper/1811.11718/) (2018)

## Built on by (most cited first, 1 of 1)

- [The Mechanics of CNN Filtering with Rectification](https://mlsanity.com/paper/2512.24338/) (2025)

## Abstract (arXiv)

We explore the symmetry of the mean k x k weight kernel in each layer of various convolutional neural networks. Unlike individual neurons, the mean kernels in internal layers tend to be symmetric about their centers instead of favoring specific directions. We investigate why this symmetry emerges in various datasets and models, and how it is impacted by certain architectural choices. We show how symmetry correlates with desirable properties such as shift and flip consistency, and might constitute an inherent inductive bias in convolutional neural networks.