Huygens' equations and the gradient-flow equations in information geometry

2021/04/16 by Tatsuaki Wada, Wada, Tatsuaki, A.M. Scarfone +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Statistical Mechanics (cond-mat.stat-mech) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2105.12824

openalex publication_date 2021/04/16 · openalex created_date 2021/06/07 · openalex updated_date 2026/07/28

Abstract

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 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.

Citations

• Information Geometry and Evolutionary Game Theory

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