Fractal Information Dynamics – Part 2

Abstract

We propose Fractal Information AI (FIAI), a graph-based architecture for adaptive learning in which knowledge is represented as recursively organized information structures and learning actions are prioritized by validated information gain, uncertainty reduction, network propagation, and decision relevance. The framework originates from a fractal-tree interpretation in which branches carry information, knots encode rule families, and paths represent inferential relations. For artificial intelligence, the logical notion of formal provability is retained only where machine-checkable verification is available; in open-domain settings it is generalized to an evidence-validation or consistency gate. Each knowledge node carries an unresolved-state variable, provenance, verifier status, information-gain estimate, decision relevance, and propagation weights. A Learning Efficiency Metric (LEM) quantifies validated uncertainty reduction per available unresolved mass or, in cost-aware form, per unit acquisition/computation cost. Multiple agents exchange validated knowledge through bound coupling operators, allowing the study of knowledge hubs, bottlenecks, redundancy, and emergent collaborative structures. We derive deterministic and stochastic node dynamics, stability conditions for propagation, and bounds on cross-agent transfer. A reproducible numerical illustration with three interacting 20-node knowledge trees demonstrates LEM trajectories, decreasing unresolved mass, and node-level utility concentration. FIAI is presented as a testable architectural hypothesis rather than a demonstrated replacement for transformer, graph-neural, retrieval-augmented, or multi-agent systems. Its central empirical claim is that explicit knowledge-utility accounting can improve the allocation of learning and verification resources under fixed budgets.