Symmetry meets AI

TL;DR

This paper investigates whether neural networks can autonomously discover symmetries in data by training on physics-based tasks and analyzing hidden layer representations, with applications to art style analysis.

Contribution

It demonstrates that neural networks can identify symmetries without explicit guidance and applies this method to analyze artistic paintings.

Findings

Neural networks encode symmetry information in hidden layers.

Symmetry detection is possible without explicit symmetry labels.

Application to art styles reveals underlying symmetries in paintings.

Abstract

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.