Reframing of Information Geometry via Symmetric Teleparallel Gravity

Tatsuaki Wada

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arXiv · 2607.00649

Reframing of Information Geometry via Symmetric Teleparallel Gravity

Tatsuaki Wada

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Abstract

Information geometry has traditionally been formulated within the framework of Riemannian geometry and dual affine connections. This work aims to reframe the foundational structure of information geometry by introducing the geometric machinery of symmetric teleparallel gravity. By requiring both curvature and torsion to vanish globally on the statistical manifold, it is demonstrated that the fundamental properties of the information space can be entirely encoded in the non-metricity tensor. This approach clarifies the distinction between the general $\xi $-parameterized case and the $\theta$- or $\eta $-parameterized cases, which correspond to general symmetric teleparallel gravity and its coincident gauge, respectively. Specifically, the $\theta$- or $\eta $-coordinates emerge as special coordinates in the coincident gauge, where the connection coefficients vanish.

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Tatsuaki Wada. 2026-07-01. Reframing of Information Geometry via Symmetric Teleparallel Gravity. https://arxiv.org/abs/2607.00649

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