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

arXiv: https://arxiv.org/abs/2607.14185 · HTML: https://mlsanity.com/paper/2607.14185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 4 of 4)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Self-Play Only Evolves When Self-Synthetic Pipeline Ensures Learnable Information Gain](https://mlsanity.com/paper/2603.02218/) (2026)
- [On the Convergence of Moral Self-Correction in Large Language Models](https://mlsanity.com/paper/2510.07290/) (2025)

## Abstract (arXiv)

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 xt evolve through transition kernels Kθ 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.