Coherence as a Control Problem: Intervention Thresholds and Stability in Large Language Models

Recent advances in large language models (LLMs) have highlighted persistent challenges in maintaining coherence over extended interactions. While these issues are often attributed to memory limitations or context window constraints, this work proposes an alternative perspective: coherence emerges from the interaction between state persistence and regulatory intervention.Through controlled experiments, we observe a non-monotonic relationship between intervention frequency and coherence. Specifically, beyond a critical threshold, increasing corrective interventions leads to a degradation of coherence rather than improvement. We interpret this phenomenon as a form of control instability, where persistent intervention acts as a continuous forcing signal that disrupts the natural evolution of the system’s internal state.We introduce a dynamical framework in which LLM behavior is modeled as a state-dependent process governed by the balance between memory-induced state dimensionality and regulatory gain. Within this framework, coherence is not determined solely by representational capacity, but by the system’s ability to maintain stable trajectories under intervention.Our findings suggest that effective control in LLMs requires adaptive, state-aware regulation rather than static or frequent corrective mechanisms. This reframing has implications for the design of memory-augmented systems, alignment strategies, and long-horizon interaction stability.