Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning
We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for continuous symmetry of manifold geometry. Thereby we achieve learnable and stable dynamics on the underlying manifold for general Lie group, and we are able to utilize the powerful representation capability of Lie group such as SO(3) and SE(3) to solve real world engineering problems in areas such as robotics, graphics, and control. Two core challenges are: (i) General Lie groups are incompatible with addition arithmetic, which is necessary for neural netwo...
| Authors | Tianwei Wang, Bryan Chen, Qian Zuo et al. |
|---|---|
| Primary category | cs.LG |
| Published | 24 May 2026 |
| Last updated at source | 24 May 2026 |
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