Weyl symmetry of the gradient-flow in information geometry

Tatsuaki Wada; Sousuke Noda

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arXiv · 2502.03866

Weyl symmetry of the gradient-flow in information geometry

Tatsuaki Wada·Sousuke Noda

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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.

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gr-qc cs.IT math-ph math.IT math.MP

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Tatsuaki Wada, Sousuke Noda. 2025-02-06. Weyl symmetry of the gradient-flow in information geometry. https://arxiv.org/abs/2502.03866

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