Closed-Loop Knowledge Dynamics: An Operational Framework for Saturation and Escape
arXiv:2607.14185
The paper proposes a framework for understanding why feedback loops in AI systems like large language models and reinforcement learning eventually stop improving, and how external interventions can push them out of these stagnant states.
Abstract
Feedback-driven loops support iterative improvement in large language models, reinforcement learning, and autonomous discovery, yet their gains often diminish under repeated internal feedback. We study why closed-loop knowledge systems saturate and what external information can move them beyond their current attractors. We introduce a three-level operational framework in which knowledge states evolve through transition kernels indexed by a structural parameter . The governing structure is defined as the observational equivalence class of induced by these kernels, while attractors and basins are properties of the fixed- dynamics. A structural intervention changes and produces a detectable kernel discrepancy on pre-specified probe states, making structural change falsifiable. Using a Lyapunov drift condition, we show that stable internal dynamics approach bounded stability regions with exponentially attenuated transients and a noise-controlled residual floor. We characterize escape through a metric condition on intervention-induced attractor displacement and a baseline-relative KL lower bound for increasing escape probability. This analysis also explains why conditional mutual information alone cannot certify escape: it measures variation among intervention-conditioned updates rather than departure from the no-intervention law. Case studies in LLM code repair, sparse-reward reinforcement learning, and Bayesian optimization use matched continuation controls to illustrate how feedback strength and alignment affect quality-improving escape. Our contribution is an operational connection among stability tools, measurable intervention effects, and cross-domain diagnostics.