What question did this study set out to answer?

The central aim is to develop a framework for understanding observer entropy through the lens of information geometry.

March 3, 2026Open Access

KL-Geometric Structure of Observer Entropy: A Minimal Information-Theoretic Framework

Puntos clave

The central aim is to develop a framework for understanding observer entropy through the lens of information geometry.
Defined observer entropy based on Kullback-Leibler divergence under coarse-graining.
Established a finite information-geometric framework for observer entropy.
Derived the Bridge Theorem demonstrating the local expansion of observer entropy.
The main result shows observer entropy is influenced by the Fisher information matrix at leading order.
Local expansion involves terms including Fisher information and higher-order corrections.
An example of softmax and a resolution–information trade-off were discussed.

Resumen

This paper establishes a finite information-geometric formulation of observer entropy defined via Kullback–Leibler divergence under coarse-graining. The main result (Bridge Theorem) proves the local expansion Sₒbs (pₜheta, eps) = (1/2) eps² vT I (theta*) v + O (eps³), showing that observer entropy is governed at leading order by the Fisher information matrix. All results are derived in a fully finite setting with explicit regularity assumptions. An exact softmax example and a resolution–information trade-off are provided.

Leer artículo completoexternamente

Me gusta

Guardar

Ver artículo completo