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

TL;DR

This paper studies context drift in multi-turn interactions with LLMs, modeling it as a stochastic process, and shows that simple interventions can reliably maintain goal consistency, revealing stable equilibria rather than inevitable decay.

Contribution

It introduces a dynamical framework for understanding context drift as a controllable equilibrium, supported by experiments on synthetic and realistic tasks with open-weight LLMs.

Findings

Stable, noise-limited equilibria observed in experiments.

Reminder interventions effectively reduce divergence.

Drift can be controlled rather than being inevitable.

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 such as in $\tau$-Bench, 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. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.