Symmetry Discovery Beyond Affine Transformations

2024/06/05 by Ben Shaw, Shaw, Ben, Abram Magner +3 · 5 citations
Biochemistry, Genetics and Molecular Biology · #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Gene expression and cancer classification #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Protein Structure and Dynamics

paper · pdf · doi:10.48550/arxiv.2406.03619

openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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