Latent Space Symmetry Discovery

Existing equivariant neural networks require explicit knowledge of the symmetry group before model implementation. Various symmetry discovery methods have been developed to learn invariance and equivariance from data, but their search spaces are limited to linear symmetries. We propose to discover arbitrary nonlinear symmetries by factorizing the group action into nonlinear transformations parameterized by an autoencoder network and linear symmetries generated by an existing symmetry discovery framework, LieGAN. Our method can capture the intrinsic symmetry in high-dimensional observations, which also results in a well-structured latent space that is useful for other downstream tasks, including long-term prediction and latent space equation discovery.