Latent Space Symmetry Discovery

Jianke Yang, Nima Dehmamy, Robin Walters, Rose Yu

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: symmetry discovery, equivariance, equivariant neural network, scientific machine learning, Lie theory, equation discovery

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TL;DR: A method for discovering symmetries of nonlinear group actions from data.

Abstract: 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.

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Submission Number: 952