A Weyl geometric approach to the gradient-flow equations in information geometry

TL;DR

This paper explores gradient-flow equations in information geometry through the lens of Weyl integrable geometry, offering a geometric reinterpretation of these equations and their associated pre-geodesic equations.

Contribution

It introduces a Weyl geometric framework to analyze gradient-flow equations in information geometry, providing a novel geometric perspective.

Findings

Reinterpretation of gradient-flow equations as pre-geodesic equations in Weyl geometry

Establishment of a geometric foundation for gradient flows in information geometry

Potential new methods for analyzing information geometric structures

Abstract

The gradient-flow equations with respect to the potential functions in information geometry are reconsidered from the perspective of the Weyl integrable geometry. The pre-geodesic equations associated with the gradient-flow equations are regarded as the general pre-geodesic equations in the Weyl integrable geometry.