Weyl symmetry of the gradient-flow in information geometry

TL;DR

This paper explores the gradient-flow in information geometry through the lens of Weyl symmetry, deriving invariant equations and relating connections in Weyl integrable geometry to Amari's $ extstyle\alpha$-connections.

Contribution

It introduces a Weyl-invariant formulation of gradient-flow in information geometry and connects Amari's $ extstyle\alpha$-connections to Weyl invariant connections.

Findings

Derived Weyl-invariant gradient-flow equations.

Linked Amari's $ extstyle\alpha$-connections to Weyl geometry.

Provided a new geometric perspective on information flow.

Abstract

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 $\alpha$-connections in IG to the Weyl invariant connection on the Riemannian manifold equipped with the scaled metric.