Discovering Lie Groups with Flow Matching
Published:Dec 24, 2025 05:00
•1 min read
•ArXiv AI
Analysis
This paper introduces a novel approach, \"lieflow,\" for learning symmetries directly from data using flow matching on Lie groups. The core idea is to learn a distribution over a hypothesis group that matches observed symmetries. The method demonstrates flexibility in discovering various group types with fewer assumptions compared to prior work. The paper addresses a key challenge of \"last-minute convergence\" in symmetric arrangements and proposes a novel interpolation scheme. The experimental results on 2D and 3D point clouds showcase successful discovery of discrete groups, including reflections. This research has the potential to improve performance and sample efficiency in machine learning by leveraging underlying data symmetries. The approach seems promising for applications where identifying and exploiting symmetries is crucial.
Key Takeaways
- •Introduces a new method, \"lieflow,\" for symmetry discovery using flow matching.
- •Addresses the challenge of \"last-minute convergence\" in symmetric data.
- •Demonstrates successful discovery of discrete groups in 2D and 3D point clouds.
Reference
“We propose learning symmetries directly from data via flow matching on Lie groups.”