A Hamiltonian approach to the gradient-flow equations in information geometry

TL;DR

This paper introduces a Hamiltonian framework for understanding gradient-flow equations in information geometry by modeling them as the motion of a null particle in curved space, providing a new perspective on these equations.

Contribution

It presents a novel Hamiltonian approach to gradient-flows in information geometry, derived from a null particle perspective in curved space.

Findings

Rederived Hamiltonians for gradient-flows in information geometry

Established a null particle model in curved space for these equations

Provided a new geometric interpretation of gradient-flow dynamics

Abstract

We have studied the gradient-flow equations in information geometry from a point-particle perspective. Based on the motion of a null (or light-like) particle in a curved space, we have rederived the Hamiltonians which describe the gradient-flows in information geometry.