信息几何中梯度流的Weyl对称性
Weyl symmetry of the gradient-flow in information geometry
Tatsuaki Wada, Sousuke Noda
arXiv
2025年2月6日
我们从Weyl对称性的角度重新审视了信息几何中的梯度流。 梯度流方程来自Weyl的仪表变换下不变的拟动作。 在 Weyl 集成几何中,我们有相关的 Amari 的 α 连接 IG 与配备缩放度量的黎曼流形上的 Weyl 不变连接。
We have revisited the gradient-flow in information geometry from the perspective of Weyl symmetry. The gradient-flow equations are derived from the proposed action which is invariant under the Weyl's gauge transformations. In Weyl integrable geometry, we have related Amari's α-connections in IG to the Weyl invariant connection on the Riemannian manifold equipped with the scaled metric.