# Detecting symmetries with neural networks

@article{Krippendorf2021DetectingSW, title={Detecting symmetries with neural networks}, author={Sven Krippendorf and Marc Syvaeri}, journal={Machine Learning: Science and Technology}, year={2021}, volume={2} }

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…

## 31 Citations

### Symmetry discovery with deep learning

- PhysicsPhysical Review D
- 2022

What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data…

### Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators

- Computer ScienceArXiv
- 2021

It is demonstrated that the amount of symmetry in the initialization density affects the accuracy of networks trained on Fashion-MNIST, and that symmetry breaking helps only when it is in the direction of ground truth.

### Symmetry meets AI

- Computer ScienceSciPost Physics
- 2021

An interdisciplinary application of this procedure identifies the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.

### Human Symmetry Uncertainty Detected by a Self-Organizing Neural Network Map

- Computer ScienceSymmetry
- 2021

An artificial neural network is presented that detects symmetry uncertainty states in human observers and is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data.

### Symmetries, safety, and self-supervision

- PhysicsSciPost Physics
- 2022

Collider searches face the challenge of defining a representation of
high-dimensional data such that physical symmetries are manifest, the discriminating
features are retained, and the choice of…

### Learning Equivariant Representations

- Computer ScienceArXiv
- 2020

This thesis proposes equivariant models for different transformations defined by groups of symmetries, and extends equivariance to other kinds of transformations, such as rotation and scaling.

### Cluster Algebras: Network Science and Machine Learning

- Mathematics, Computer ScienceArXiv
- 2022

Network analysis methods are applied to the exchange graphs for cluster algebras of varying mutation types and indicates that when the graphs are represented without identifying by permutation equivalence between clusters an elegant symmetry emerges in the quiver exchange graph embedding.

### Inverse Problems, Deep Learning, and Symmetry Breaking

- MathematicsArXiv
- 2020

This work shows that careful symmetry breaking on the training data can help get rid of the difficulties and significantly improve the learning performance of the generalized phase retrieval problem.

### Machine-Learning Mathematical Structures

- Computer ScienceInternational Journal of Data Science in the Mathematical Sciences
- 2022

Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, a comparative study of the accuracies on different problems is presented.

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