Symmetry Discovery Beyond Affine Transformations

TL;DR

This paper introduces a new framework for discovering continuous and discrete symmetries in data beyond affine transformations, demonstrating improved efficiency and detection capabilities over existing methods like LieGAN.

Contribution

The paper presents a novel framework for symmetry detection that extends beyond affine transformations and is more computationally efficient than LieGAN.

Findings

Our method is competitive with LieGAN for affine symmetries at large sample sizes.

Our method outperforms LieGAN in detecting symmetries with small sample sizes.

The framework can detect continuous symmetries beyond the affine group efficiently.

Abstract

Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline a framework for discovering continuous symmetry in data beyond the affine transformation group. We also provide a similar framework for discovering discrete symmetry. We experimentally compare our method to an existing method known as LieGAN and show that our method is competitive at detecting affine symmetries for large sample sizes and superior than LieGAN for small sample sizes. We also show our method is able to detect continuous symmetries beyond the affine group and is generally more computationally efficient than LieGAN.