Neural Symmetry Detection for Learning Neural Network Constraints

Neural symmetry detection can be defined as the deep learning-aided task of recovering both thenature of the transformation that relates points in a data set and the distribution with respect to themagnitude of the transformation. Applications range from automatic data augmentation to modelselection. In this work, we investigate how the matrix exponential can be leveraged to recover thecorrect symmetry transformation, encoded as a generator of a Lie group for various transformations,both affine and non-affine. In order to make the calculation of the matrix exponential tractable, thisoperation is performed in a low-dimensional latent space. Additionally, a loss term is introduced toenforce matching the generator in latent space to the one in pixel-space.