Learning Lie Group Symmetry Transformations with Neural Networks
This enables automated symmetry detection for model selection and data analysis without prior knowledge, addressing a domain-specific need in machine learning.
The paper tackled the problem of discovering unknown Lie group symmetries in datasets, where each data point is transformed by a one-parameter subgroup with varying parameters, and successfully characterized both the transformation group and parameter distributions.
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.