🤖 AI Summary
Closed knowledge systems often saturate in performance under internal feedback, hindering sustained improvement. This work proposes a three-layer operational framework that characterizes knowledge evolution through structural parameters θ, leveraging tools such as transition kernels, Lyapunov drift conditions, and lower bounds on KL divergence to analyze attractor dynamics within fixed structures and structural transitions induced by external interventions. The study innovatively constructs a falsifiable mechanism for structural intervention, establishing an operational link among system stability, measurable intervention effects, and cross-domain diagnostics, while revealing why conditional mutual information fundamentally fails to verify “escape” phenomena. Empirical validation across large language model code repair, sparse-reward reinforcement learning, and Bayesian optimization demonstrates that feedback intensity and alignment critically govern quality-enhancing escapes, clarifying their theoretical preconditions.
📝 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.