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arXiv · 2606.17990

Potential functions in information geometry via bi-forms

Florio M. Ciaglia·Giuseppe Marmo·Marco Pacelli·Luca Schiavone·Alessandro Zampini
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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.

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Florio M. Ciaglia, Giuseppe Marmo, Marco Pacelli, Luca Schiavone, Alessandro Zampini. 2026-06-16. Potential functions in information geometry via bi-forms. https://arxiv.org/abs/2606.17990

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