Latent Space Symmetry Discovery
Jianke Yang Nima Dehmamy Robin Walters Rose Yu
Equivariant neural networks require explicit knowledge of the symmetry group.
Automatic symmetry discovery methods aim to relax this constraint and learn
invariance and equivariance from data. However, existing symmetry discovery
methods are limited to linear symmetries in their search space and cannot
handle the complexity of symmetries in real-world, often high-dimensional data.
We propose a novel generative model, Latent LieGAN (LaLiGAN), which can
discover nonlinear symmetries from data. It learns a mapping from data to a
latent space where the symmetries become linear and simultaneously discovers
symmetries in the latent space. Theoretically, we show that our method can
express any nonlinear symmetry under certain conditions. Experimentally, our
method can capture the intrinsic symmetry in high-dimensional observations,
which results in a well-structured latent space that is useful for other
downstream tasks. We demonstrate the use cases for LaLiGAN in improving
equation discovery and long-term forecasting for various dynamical systems.