Do Language Models Converge to Themselves? Recursive Self-Refinement as Textual Relaxation

arXiv:2607.22653v1 Announce Type: new Abstract: 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.

Source: arXiv cs.AI | 2026-07-28

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