Interpretation of higher-order terms for Kolmogorov complexity in F-diagrams

Determine the precise meaning and interpretation of the higher-order interaction terms obtained by applying the generalized Hu theorem to Kolmogorov complexity within the F-diagram framework, clarifying how these terms relate to algorithmic information and whether they admit a coherent semantic characterization analogous to Shannon interaction information.

Background

The paper generalizes information diagrams from Shannon entropy to a broad class of functions F satisfying the chain rule, including Kullback-Leibler divergence, cross-entropy, Tsallis entropy, and Kolmogorov complexity. For entropy-based cases, higher-order terms (e.g., mutual and interaction information) have established interpretations, and the generalized diagrams preserve structural relationships.

However, when F is Kolmogorov complexity, the authors note that the semantic interpretation of higher-order terms is not established. Clarifying the meaning of these higher-order interactions derived from Kolmogorov complexity would strengthen the bridge between algorithmic and classical information theory in the generalized diagrammatic framework.