arXiv:2512.20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries automatically is challenging. We propose LieFlow, a novel framework that reframes symmetry discovery as a distribution learning problem on Lie groups. Instead of searching for the symmetry generators, our approach operates directly in group space, modeling a symmetry distribution over a large hypothesis group $G$.
The continuous advancements in AI and machine learning, coupled with increasing computational power, make sophisticated approaches to fundamental problems like symmetry discovery more tractable.
Improved capabilities in symmetry discovery can lead to more efficient, robust, and interpretable AI models, particularly in domains like physics, robotics, and generative AI.
The proposed LieFlow framework changes the approach to symmetry discovery by reframing it as a distribution learning problem on Lie groups, potentially enabling automatic and more effective identification of hidden structures in data.
- · AI researchers and developers
- · Robotics industry
- · Physics-based modeling
- · Generative AI
More efficient and generalizable AI models emerge from automated symmetry discovery.
AI systems gain the ability to understand and leverage fundamental physical principles more effectively, accelerating scientific discovery and engineering innovation.
The development of 'scientific AI' agents that can autonomously formulate hypotheses and conduct experiments based on discovered symmetries could become feasible, fundamentally changing research paradigms.
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Read at arXiv cs.AI