Learning Lie Group Symmetry Transformations with Neural Networks
Alex Gabel Victoria Klein Riccardo Valperga Jeroen S. W. Lamb Kevin Webster Rick Quax Efstratios Gavves
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.