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

• URL: http://arxiv.org/abs/2607.14185v1
• Date: Wed, 15 Jul 2026 15:06:15 GMT
• Title: Closed-Loop Knowledge Dynamics: An Operational Framework for Saturation and Escape
• Abstract summary: We study why closed-loop knowledge systems saturate and what external information can move them beyond their current attractors.<n>We introduce a three-level operational framework in which knowledge states $x_t$ evolve through transition kernels $K_$ indexed by a structural parameter $$.<n>We characterize escape through a metric condition on intervention-induced attractor displacement and a baseline-relative KL lower bound for increasing escape probability.
• Score: 10.96851791770302
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $x_t$ evolve through transition kernels $K_θ$ indexed by a structural parameter $θ$. The governing structure is defined as the observational equivalence class of $θ$ induced by these kernels, while attractors and basins are properties of the fixed-$θ$ dynamics. A structural intervention changes $θ$ 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.

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