Latent Mixture of Symmetries for Sample-Efficient Dynamic Learning
Haoran Li, Chenhan Xiao, Muhao Guo, Yang Weng
TL;DR
This work tackles sample-efficient learning of dynamical systems under data scarcity by exploiting symmetries. It introduces Latent MoS, a symmetry-preserving framework that models dynamics as a mixture of latent Lie-group flows, with a hierarchical multi-scale extension to capture both short- and long-term equivariances. The approach provides theoretical guarantees on equivariance preservation and demonstrates strong empirical gains across diverse nonlinear and real-world datasets, along with interpretable latent representations. The results indicate meaningful improvements in interpolation, extrapolation, and control tasks, suggesting practical utility for engineering domains with limited measurements. Overall, Latent MoS offers a scalable, geometry-informed method for robust dynamic learning in complex systems.
Abstract
Learning dynamics is essential for model-based control and Reinforcement Learning in engineering systems, such as robotics and power systems. However, limited system measurements, such as those from low-resolution sensors, demand sample-efficient learning. Symmetry provides a powerful inductive bias by characterizing equivariant relations in system states to improve sample efficiency. While recent methods attempt to discover symmetries from data, they typically assume a single global symmetry group and treat symmetry discovery and dynamic learning as separate tasks, leading to limited expressiveness and error accumulation. In this paper, we propose the Latent Mixture of Symmetries (Latent MoS), an expressive model that captures a mixture of symmetry-governed latent factors from complex dynamical measurements. Latent MoS focuses on dynamic learning while locally and provably preserving the underlying symmetric transformations. To further capture long-term equivariance, we introduce a hierarchical architecture that stacks MoS blocks. Numerical experiments in diverse physical systems demonstrate that Latent MoS outperforms state-of-the-art baselines in interpolation and extrapolation tasks while offering interpretable latent representations suitable for future geometric and safety-critical analyses.