Structural Bayesian Inference through Entropy Geometry: An Information Dynamical System Approach

We introduce Information Dynamical Systems (IDS) as a geometric frame- work that reconstructs Bayesian inference through structural entropy. In IDS, uncer- tainty is modeled not by traditional probability distributions, but by an entropy surface H(K,D,σ), where K captures temporal structure, D represents data modulation, and σ encodes spectral uncertainty. Entropy minima on this surface serve as structural attractors, replacing posterior maxima in classical Bayes. These attractors are robust under perturbations, and their geometric arrangement gives rise to time as an emergent property. We present a nu- merical scheme for computing H(K,D,σ), and demonstrate how IDS unifies inference, robustness, and dynamical modeling across physical and AI systems.