Neural Symmetry Detection for Learning Neural Network Constraints

Alex Gabel, Rick Quax, Stratis Gavves

Keywords: symmetry detection, Lie theory, weight constraints

TL;DR: We investigate how the matrix exponential can be leveraged to learn continuous symmetry transformations by performing it in latent space.

Abstract:

Neural symmetry detection can be defined as the deep learning-aided task of recovering both the
nature of the transformation that relates points in a data set and the distribution with respect to the
magnitude of the transformation. Applications range from automatic data augmentation to model
selection. In this work, we investigate how the matrix exponential can be leveraged to recover the
correct 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, this
operation is performed in a low-dimensional latent space. Additionally, a loss term is introduced to
enforce matching the generator in latent space to the one in pixel-space.

Student Paper: No

Submission Number: 68