大模型反复自我修改，最终会收敛到稳定文本形态。
Do Language Models Converge to Themselves? Recursive Self-Refinement as Textual Relaxation
- 通过多次迭代自修正，文本逐渐逼近模型偏好的稳定状态。
- 前几步修改最明显，之后变化微小，约10步内基本饱和。
- 适合关注模型输出稳定性与优化终止条件的研究者。
大型语言模型越来越多地用于递归修正工作流中，即初始草稿由同一模型反复修订。尽管应用广泛，但此类流程的长期动态仍不清晰。重复修正是否持续提升输出？还是趋于稳定？我们研究了递归自修正作为动力学过程，发现重复修订使文本趋近于模型偏好的软固定点区域。使用 GPT-5.5 对 50 篇 ICML 2025 摘要进行 10 步修正轨迹分析，涵盖默认温度与确定性解码两种方式，并额外评估 15 篇 ICML 2020 摘要。通过归一化编辑距离、精确与近似固定点、词数稳定性、指数衰减规律及外部 LLM 作为裁判评估等指标发现：所有设置下修正轨迹迅速饱和。多数修改集中在前几步，随后进入仅含微小表层变化的软固定点区域。确定性解码更早达到精确固定点，残差波动更小，但两者均实现普遍近似收敛。平均编辑幅度遵循一致的指数衰减模式，表明向模型偏好的文本平衡态收敛，而非无限优化。外部评估显示，收敛后摘要在清晰度、简洁性和科学风格上均有提升，且技术含义保持不变。这些结果支持将大模型自修正视为动力系统，并为基于编辑幅度饱和的实用停止准则提供依据。
原文摘要 · Abstract (English)
Large language models are increasingly used in recursive refinement workflows, where an initial draft is repeatedly revised by the same model. Despite their growing use, the long-term dynamics of such workflows remain poorly understood. Does repeated refinement continue to improve outputs indefinitely, or does it converge toward a stable textual form? We study recursive self-refinement as a dynamical process in which repeated LLM revision drives text toward a model-preferred soft fixed-point region. Using GPT-5.5, we generate 10-step refinement trajectories for 50 ICML 2025 abstracts under both default-temperature and deterministic decoding, and additionally evaluate 15 ICML 2020 abstracts. We analyze normalized edit distance, exact and approximate fixed points, word-count stability, exponential relaxation, and external LLM-as-a-judge evaluation. Across all settings, refinement trajectories rapidly saturate. Most edits occur within the first few iterations, after which trajectories enter a soft fixed-point region with only minor surface-level changes. Deterministic decoding reaches exact fixed points earlier and exhibits smaller residual fluctuations than default-temperature decoding, while both achieve universal approximate convergence. The average edit magnitude follows a consistent exponential relaxation pattern, suggesting convergence toward a model-preferred textual equilibrium rather than open-ended optimization. External evaluation indicates that converged abstracts improve clarity, conciseness, and scientific style while preserving technical meaning. These findings support a dynamical-systems view of LLM self-refinement and motivate practical stopping criteria based on edit-magnitude saturation.
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