


































We revisit the relation between the gradient-flow equations and Hamilton's equations in information geometry. By regarding the gradient-flow equations as Huygens' equations in geometric optics, we have related the gradient flows to the geodesic flows induced by the geodesic Hamiltonian in an appropriate Riemannian geometry. The original evolution parameter $\textit{t}$ in the gradient-flow equations is related to the arc-length parameter in the associated Riemannian manifold by Jacobi-Maupertuis transformation. As a by-product, it is found the relation between the gradient-flow equation and replicator equations.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。