Learning Lie Group Symmetry Transformations with Neural Networks

TL;DR

This paper introduces a neural network-based method to discover and characterize unknown Lie group symmetries in datasets, extending beyond traditional transformations like rotation, scaling, and translation.

Contribution

It presents a novel approach for identifying and analyzing unknown Lie group symmetry transformations in datasets without prior knowledge of the symmetries.

Findings

Effective in characterizing unknown symmetry groups

Successfully identifies transformation parameters in datasets

Extends symmetry detection beyond traditional transformations

Abstract

The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks require prior knowledge of the symmetries of the task at hand, this work focuses on discovering and characterizing unknown symmetries present in the dataset, namely, Lie group symmetry transformations beyond the traditional ones usually considered in the field (rotation, scaling, and translation). Specifically, we consider a scenario in which a dataset has been transformed by a one-parameter subgroup of transformations with different parameter values for each data point. Our goal is to characterize the transformation group and the distribution of the parameter values. The results showcase the effectiveness of the approach in both these settings.