Symmetry Discovery Beyond Affine Transformations
This work addresses a limitation in symmetry detection for machine learning tasks, offering incremental improvements over existing methods.
The authors tackled the problem of detecting continuous symmetries in data beyond affine transformations, proposing a framework for both continuous and discrete symmetry discovery. Their method outperformed LieGAN in detecting affine symmetries for small sample sizes and was more computationally efficient.
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.