Work

Non-Metricity in Information Geometry

Year: 2026

Type: article

Abstract: The importance of non-metricity in information geometry is described through studies on gradient flow from the perspective of Weyl geometry. The Amari-Centsov tensor Ckij is the non-metricity tensor with respect to the α connection ∇(α) and Fisher metric gij. We derive the explicit expression of the α connection based on the non-metricity ∇k(α)gij=αCkij. The scalar field obtained from a potential function in information geometry plays a key role and characterizes Weyl's gauge field, Weyl's non-metricity, and the rate of the potential function during the associated gradient flow.

Source: Entropy

DOI: 10.3390/e28040447

Authors: Tatsuaki Wada, Antonio Maria Scarfone

Institutions: Ibaraki University, Politecnico di Torino, Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Institute for Complex Systems, National Research Council

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Japan Society for the Promotion of Science