# Symmetry meets AI

arXiv: https://arxiv.org/abs/2103.06115 · HTML: https://mlsanity.com/paper/2103.06115/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 14 references that are in the map.
- First posted on arXiv 10 Mar 2021.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [A disciplined approach to neural network hyper-parameters: Part 1 -- learning rate, batch size, momentum, and weight decay](https://mlsanity.com/paper/1803.09820/) (2018)
- [Detecting Symmetries with Neural Networks](https://mlsanity.com/paper/2003.13679/) (2020)

## Built on by (most cited first, 13 of 13)

- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Discovering Sparse Representations of Lie Groups with Machine Learning](https://mlsanity.com/paper/2302.05383/) (2023)
- [Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6](https://mlsanity.com/paper/2307.04891/) (2023)
- [Identifying the Group-Theoretic Structure of Machine-Learned Symmetries](https://mlsanity.com/paper/2309.07860/) (2023)
- [Oracle-Preserving Latent Flows](https://mlsanity.com/paper/2302.00806/) (2023)
- [Beyond permutation equivariance in graph networks](https://mlsanity.com/paper/2103.14066/) (2021)
- [Stable and Interpretable Jet Physics with IRC-Safe Equivariant Feature Extraction](https://mlsanity.com/paper/2509.22059/) (2025)
- [Symmetry-driven graph neural networks](https://mlsanity.com/paper/2105.14058/) (2021)
- [Encoding Involutory Invariances in Neural Networks](https://mlsanity.com/paper/2106.12891/) (2021)
- [Data-driven discovery of self-similarity using neural networks](https://mlsanity.com/paper/2406.03896/) (2024)
- [Learning symmetries in datasets](https://mlsanity.com/paper/2504.05174/) (2025)
- [Artificial Intelligence and Symmetries: Learning, Encoding, and Discovering Structure in Physical Data](https://mlsanity.com/paper/2602.02351/) (2026)

## Abstract (arXiv)

We explore whether Neural Networks (NNs) can it discover the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a it decoy task based on well-controlled Physics templates, where no information on symmetry is provided. We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance. As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.