# What Affects Learned Equivariance in Deep Image Recognition Models?

arXiv: https://arxiv.org/abs/2304.02628 · HTML: https://mlsanity.com/paper/2304.02628/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 5 Apr 2023.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [ViTAE: Vision Transformer Advanced by Exploring Intrinsic Inductive Bias](https://mlsanity.com/paper/2106.03348/) (2021)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [On Translation Invariance in CNNs: Convolutional Layers can Exploit Absolute Spatial Location](https://mlsanity.com/paper/2003.07064/) (2020)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [3D G-CNNs for Pulmonary Nodule Detection](https://mlsanity.com/paper/1804.04656/) (2018)
- [LieGG: Studying Learned Lie Group Generators](https://mlsanity.com/paper/2210.04345/) (2022)
- [Quantifying Translation-Invariance in Convolutional Neural Networks](https://mlsanity.com/paper/1801.01450/) (2017)
- [Grounding inductive biases in natural images:invariance stems from variations in data](https://mlsanity.com/paper/2106.05121/) (2021)
- [Scale Equivariant U-Net](https://mlsanity.com/paper/2210.04508/) (2022)
- [Global Pooling, More than Meets the Eye: Position Information is Encoded Channel-Wise in CNNs](https://mlsanity.com/paper/2108.07884/) (2021)
- [Do Deep Networks Transfer Invariances Across Classes?](https://mlsanity.com/paper/2203.09739/) (2022)
- [Pooling is neither necessary nor sufficient for appropriate deformation stability in CNNs](https://mlsanity.com/paper/1804.04438/) (2018)
- [Learning Translation Invariance in CNNs](https://mlsanity.com/paper/2011.11757/) (2020)
- [Exploiting Learned Symmetries in Group Equivariant Convolutions](https://mlsanity.com/paper/2106.04914/) (2021)

## Built on by (most cited first, 15 of 15)

- [Steerers: A framework for rotation equivariant keypoint descriptors](https://mlsanity.com/paper/2312.02152/) (2023)
- [Investigating how ReLU-networks encode symmetries](https://mlsanity.com/paper/2305.17017/) (2023)
- [Flopping for FLOPs: Leveraging equivariance for computational efficiency](https://mlsanity.com/paper/2502.05169/) (2025)
- [Color Equivariant Convolutional Networks](https://mlsanity.com/paper/2310.19368/) (2023)
- [Affine steerers for structured keypoint description](https://mlsanity.com/paper/2408.14186/) (2024)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)
- [Don't Think It Twice: Exploit Shift Invariance for Efficient Online Streaming Inference of CNNs](https://mlsanity.com/paper/2408.03223/) (2024)
- [GEPC: Group-Equivariant Posterior Consistency for Out-of-Distribution Detection in Diffusion Models](https://mlsanity.com/paper/2602.00191/) (2026)
- [SEIS: Subspace-based Equivariance and Invariance Scores for Neural Representations](https://mlsanity.com/paper/2602.04054/) (2026)
- [Stimulus symmetries can confound representational similarity analyses](https://mlsanity.com/paper/2605.21324/) (2026)
- [Adapting Pretrained ViTs with Convolution Injector for Visuo-Motor Control](https://mlsanity.com/paper/2406.06072/) (2024)
- [MARs: Multi-view Attention Regularizations for Patch-based Feature Recognition of Space Terrain](https://mlsanity.com/paper/2410.05182/) (2024)
- [Scale-invariant Gaussian derivative residual networks](https://mlsanity.com/paper/2603.02843/) (2026)
- [Transformation Laws in Neural Representations: Structure, Realisability, and Construction](https://mlsanity.com/paper/2609.18190/) (2026)
- [Measuring Learned Equivariance: An Information Theoretic Approach](https://mlsanity.com/paper/2610.17269/) (2026)

## Abstract (arXiv)

Equivariance w.r.t. geometric transformations in neural networks improves data efficiency, parameter efficiency and robustness to out-of-domain perspective shifts. When equivariance is not designed into a neural network, the network can still learn equivariant functions from the data. We quantify this learned equivariance, by proposing an improved measure for equivariance. We find evidence for a correlation between learned translation equivariance and validation accuracy on ImageNet. We therefore investigate what can increase the learned equivariance in neural networks, and find that data augmentation, reduced model capacity and inductive bias in the form of convolutions induce higher learned equivariance in neural networks.