Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning
The article presents a novel approach to neural dynamics using Lie group embedding through supervised projective manifold learning. The authors introduce LieEDNN, which utilizes Lie groups to achieve stable dynamics for various engineering applications. Key challenges include the incompatibility of general Lie groups with addition arithmetic and the nonlinear representation of dynamics, which the authors address through innovative algorithms.
- ▪The proposed method is called LieEDNN, which stands for Lie group embedded dynamical neural networks.
- ▪It leverages the representation capabilities of Lie groups like SO(3) and SE(3) for real-world engineering problems.
- ▪The authors tackle challenges related to the arithmetic operations on Lie groups and the nonlinear dynamics representation.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.26167 |
| Publication time | Wed, 27 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-27T04:07:56.398Z |
| Last seen | 2026-05-27T04:07:56.398Z |
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Computer Science > Machine Learning arXiv:2605.26167 (cs) [Submitted on 24 May 2026] Title:Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning Authors:Tianwei Wang, Bryan Chen, Qian Zuo, Qiyue Xia, Xin Li, Wei Pang View a PDF of the paper titled Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning, by Tianwei Wang and 5 other authors View PDF HTML (experimental) Abstract: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.
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