# E(2) Equivariant Neural Networks for Robust Galaxy Morphology Classification

arXiv: https://arxiv.org/abs/2311.01500 · HTML: https://mlsanity.com/paper/2311.01500/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 2 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Adversarial Examples: Attacks and Defenses for Deep Learning](https://mlsanity.com/paper/1712.07107/) (2017)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Rotation-invariant convolutional neural networks for galaxy morphology prediction](https://mlsanity.com/paper/1503.07077/) (2015)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Galaxy Zoo DECaLS: Detailed Visual Morphology Measurements from Volunteers and Deep Learning for 314,000 Galaxies](https://mlsanity.com/paper/2102.08414/) (2021)
- [DeepAdversaries: Examining the Robustness of Deep Learning Models for Galaxy Morphology Classification](https://mlsanity.com/paper/2112.14299/) (2021)
- [Can we have it all? On the Trade-off between Spatial and Adversarial Robustness of Neural Networks](https://mlsanity.com/paper/2002.11318/) (2020)
- [Robustness of Rotation-Equivariant Networks to Adversarial Perturbations](https://mlsanity.com/paper/1802.06627/) (2018)
- [Robustness of deep learning algorithms in astronomy -- galaxy morphology studies](https://mlsanity.com/paper/2111.00961/) (2021)
- [Nonlinearities in Steerable SO(2)-Equivariant CNNs](https://mlsanity.com/paper/2109.06861/) (2021)

## Built on by (most cited first, 7 of 7)

- [SIDDA: SInkhorn Dynamic Domain Adaptation for Image Classification with Equivariant Neural Networks](https://mlsanity.com/paper/2501.14048/) (2025)
- [Interpreting "Interpretability" and Explaining "Explainability" in Machine Learning in Physics](https://mlsanity.com/paper/2606.26228/) (2026)
- [Galaxy Morphology Classification with Counterfactual Explanation](https://mlsanity.com/paper/2510.14655/) (2025)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [From Simulations to Surveys: Domain Adaptation for Galaxy Observations](https://mlsanity.com/paper/2511.18590/) (2025)
- [Deep learning from the crowd Fundamentals of morphological galaxy classification](https://mlsanity.com/paper/2609.06316/) (2026)
- [On Making SE(2)-Invariant Networks Optimal](https://mlsanity.com/paper/2610.17424/) (2026)

## Abstract (arXiv)

We propose the use of group convolutional neural network architectures (GCNNs) equivariant to the 2D Euclidean group, E(2), for the task of galaxy morphology classification by utilizing symmetries of the data present in galaxy images as an inductive bias in the architecture. We conduct robustness studies by introducing artificial perturbations via Poisson noise insertion and one-pixel adversarial attacks to simulate the effects of limited observational capabilities. We train, validate, and test GCNNs equivariant to discrete subgroups of E(2) - the cyclic and dihedral groups of order N - on the Galaxy10 DECals dataset and find that GCNNs achieve higher classification accuracy and are consistently more robust than their non-equivariant counterparts, with an architecture equivariant to the group D16 achieving a 95.52 ± 0.18% test-set accuracy. We also find that the model loses <6% accuracy on a 50%-noise dataset and all GCNNs are less susceptible to one-pixel perturbations than an identically constructed CNN. Our code is publicly available at https://github.com/snehjp2/GCNNMorphology.