Closed-Loop Knowledge Dynamics: An Operational Framework for Saturation and Escape
This paper analyzes why closed-loop knowledge systems (e.g., LLMs, RL) saturate under repeated internal feedback and introduces a three-level operational framework to enable escape via structural interventions. Using Lyapunov drift, stability is characterized, and escape is quantified by attractor displacement and a KL lower bound. Case studies include LLM code repair, sparse-reward RL, and Bayesian optimization.
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[Submitted on 15 Jul 2026]
Title:Closed-Loop Knowledge Dynamics: An Operational Framework for Saturation and Escape
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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 $K_{\theta}$ indexed by a structural parameter $\theta$. The governing structure is defined as the observational equivalence class of $\theta$ induced by these kernels, while attractors and basins are properties of the fixed-$\theta$ dynamics. A structural intervention changes $\theta$ 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.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2607.14185 [cs.LG]
(or arXiv:2607.14185v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.14185
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Xuening Wu [view email] [v1] Wed, 15 Jul 2026 15:06:15 UTC (224 KB)
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