Closed-Loop Knowledge Dynamics: An Operational Framework for Saturation and Escape

Short summary

This paper formalizes why closed-loop knowledge systems saturate and what external information can break them out of attractors. It introduces a three-level framework where knowledge states evolve through transition kernels, with structural interventions that are falsifiable via probe-state discrepancies. Using Lyapunov analysis, it proves stable dynamics approach bounded regions and characterizes escape via attractor displacement and KL lower bounds. Case studies in LLM code repair, sparse-reward RL, and Bayesian optimization illustrate the framework.

• •Three-level framework connects stability tools, measurable interventions, and cross-domain diagnostics for feedback loops
• •Lyapunov drift conditions prove bounded stability with noise-controlled residual floor
• •Escape requires structural intervention changing the transition kernel, not just more internal feedback

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