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Weyl symmetry of the gradient-flow in information geometry

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arxiv 2502.03866 v2 pith:HHNR3SCS submitted 2025-02-06 gr-qc cs.ITmath-phmath.ITmath.MP

Tatsuaki Wada , Sousuke Noda This is my paper · ORCID
classification gr-qccs.ITmath-phmath.ITmath.MP
keywords weylgeometrygradient-flowinformationinvariantsymmetryactionalpha
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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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Cited by 1 Pith paper

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  1. Revisiting Coincident GR in Internal STEGR Formulation

    gr-qc 2025-06 conditional novelty 5.0 of 10

    The paper derives internal-STEGR field equations, recovers coincident GR as the coincident-gauge sector, and finds that massive test particles obey a norm-flow equation instead of geodesics.

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