# Detecting Symmetries with Neural Networks

arXiv: https://arxiv.org/abs/2003.13679 · HTML: https://mlsanity.com/paper/2003.13679/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 30 of 34)

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- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
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- [Regularizing Towards Soft Equivariance Under Mixed Symmetries](https://mlsanity.com/paper/2306.00356/) (2023)
- [Machine Learning Calabi-Yau Hypersurfaces](https://mlsanity.com/paper/2112.06350/) (2021)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
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- [Deep multi-task mining Calabi-Yau four-folds](https://mlsanity.com/paper/2108.02221/) (2021)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Discovering Sparse Representations of Lie Groups with Machine Learning](https://mlsanity.com/paper/2302.05383/) (2023)
- [Symmetry Discovery for Different Data Types](https://mlsanity.com/paper/2410.09841/) (2024)
- [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)
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- [Exploring how a Generative AI interprets music](https://mlsanity.com/paper/2308.00015/) (2023)
- [Rotationally Equivariant Super-Resolution of Velocity Fields in Two-Dimensional Fluids Using Convolutional Neural Networks](https://mlsanity.com/paper/2202.11099/) (2022)
- [Non-parametric Hypothesis Tests for Distributional Group Symmetry](https://mlsanity.com/paper/2307.15834/) (2023)
- [From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook](https://mlsanity.com/paper/2202.06086/) (2022)
- [Learning finite symmetry groups of dynamical systems via equivariance detection](https://mlsanity.com/paper/2503.03014/) (2025)
- [Machine-Learning the Classification of Spacetimes](https://mlsanity.com/paper/2201.01644/) (2022)
- [Learning quantum symmetries with interactive quantum-classical variational algorithms](https://mlsanity.com/paper/2206.11970/) (2022)
- [Deep learning complete intersection Calabi-Yau manifolds](https://mlsanity.com/paper/2311.11847/) (2023)
- [Data-driven discovery of self-similarity using neural networks](https://mlsanity.com/paper/2406.03896/) (2024)
- [SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservation](https://mlsanity.com/paper/2410.05232/) (2024)
- [Non-Gaussianities in Collider Metric Binning](https://mlsanity.com/paper/2503.03809/) (2025)

## Abstract (arXiv)

Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the structure in the embedding layer of the neural network which allows us to identify whether a symmetry is present and to identify orbits of the symmetry in the input. To determine which continuous or discrete symmetry group is present we analyse the invariant orbits in the input. We present examples based on rotation groups SO(n) and the unitary group SU(2). Further we find that this method is useful for the classification of complete intersection Calabi-Yau manifolds where it is crucial to identify discrete symmetries on the input space. For this example we present a novel data representation in terms of graphs.