用混合对称性提升动态学习效率,适合传感器数据少的系统。
Latent Mixture of Symmetries for Sample-Efficient Dynamic Learning
- 通过潜空间混合对称性建模复杂动态系统的多组对称关系。
- 在插值和外推任务中优于现有方法,且保持对称变换的严格保留。
- 适用于机器人、电力系统等需要可解释性的安全关键场景。
动态学习对基于模型的控制和强化学习至关重要,尤其在机器人、电力系统等工程系统中。然而,受限于低分辨率传感器等测量条件,需实现高效样本学习。对称性通过刻画系统状态间的等变关系,提供强大归纳偏置以提升样本效率。现有方法通常假设单一全局对称群,并将对称发现与动态学习分开处理,导致表达能力有限且误差累积。本文提出潜空间对称混合(Latent Mixture of Symmetries, Latent MoS),能从复杂动态测量中捕捉多个对称性驱动的潜因子。该模型聚焦动态学习,同时局部且可证明地保留底层对称变换。为进一步建模长期等变性,引入分层结构堆叠MoS模块。在多种物理系统上的数值实验表明,Latent MoS在插值与外推任务中均优于当前最优基线,且提供可解释的潜表示,适合后续几何与安全关键分析。
原文摘要 · Abstract (English)
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.
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