Drift No More? Context Equilibria in Multi-Turn LLM Interactions

Vardhan Dongre, Ryan A. Rossi, Viet Dac Lai, Seunghyun Yoon, Gokhan Tur, Dilek Hakkani-Tür, Trung Bui

Keywords: Personalization, Control Theory, Dynamical System, Mechanistic Interpretability

Abstract: Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model’s outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user–agent simulations, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions, indicating multi-turn drift as a controllable equilibrium phenomenon rather than inevitable decay.

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Submission Number: 6