Potential functions in information geometry via bi-forms
Preprint
- 17 June 2026
- preprint
- Published by Elsevier in SSRN Electronic Journal
Abstract
In this paper we develop a general framework for potentials on Lauritzen manifolds, namely smooth manifolds equipped with a pseudo-Riemannian metric and a pair of conjugate affine connections that may have non-vanishing torsion. We show how the theory of bi-forms accommodates torsion-full statistical structures and unifies contrast and pre-contrast functions in a cohomological framework. Within this formalism, we construct a canonical contrast bi-form on dually curvature-free Lauritzen manifolds and establish its principal structural properties. Several illustrative examples are analysed.Keywords
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