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

arXiv: https://arxiv.org/abs/2607.22653 · HTML: https://mlsanity.com/paper/2607.22653/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 8 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)

## Built on by (most cited first, 3 of 3)

- [If It's Not Buggy, Don't Fix It: On the Dynamics of Iterative Bug-fixing with LLMs](https://mlsanity.com/paper/2609.10123/) (2026)
- [Exact Feedback Is Not Control: Evaluating Text-based Closed-Loop Revision in LLMs](https://mlsanity.com/paper/2609.28150/) (2026)
- [Towards Better Exploration in Sequential Test-Time Scaling](https://mlsanity.com/paper/2609.39632/) (2026)

## Abstract (arXiv)

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.