用控制理论分析大模型自修正，发现何时该改、何时该停。
Self-Correction as Feedback Control: Error Dynamics, Stability Thresholds, and Prompt Interventions in LLMs
- 把自修正看作闭环控制系统，用错误引入率和纠正率判断稳定性。
- 实测显示只有少数模型（如o3-mini）在错误率低于0.5%时能提升性能。
- 提示词干预可大幅降低错误率，让退化模型转为小幅提升，适合优化工具链。
迭代自修正在智能体大模型系统中日益普及，但其效果在不同模型间不一致。本文将其建模为闭环反馈控制问题，将同一模型同时视为控制器与被控对象，通过双状态马尔可夫模型分析误差动态，关键参数为错误引入率（EIR）与错误纠正率（ECR）。模型推导出可直接测量的稳定阈值：仅当ECR/EIR > Acc/(1-Acc)时才应迭代。实验覆盖7个模型和3个数据集（GSM8K、MATH、StrategyQA），发现近零的EIR边界（<0.5%）能清晰区分有益与有害自修正：仅o3-mini（+3.4 pp）、Claude Opus 4.6（+0.6 pp）和o4-mini（±0 pp）保持不退化，而GPT-5等四个模型准确率下降。验证先行提示干预证明因果关系：使GPT-4o-mini的EIR从2%降至0%，将-6.2 pp退化转为+0.2 pp（配对McNemar检验，p<10⁻⁴），对已低于阈值的模型无影响，完全符合预测。另对自适应自一致性（ASC）分析表明，其以3.8 pp置信度代价停止有害修正，揭示两层能力结构：提示级抑制EIR可防退化，而真正增益需提升ECR（可能需训练级优化）。因此，自修正不应作为默认行为，而应基于可量化的误差动态做出控制决策。
原文摘要 · Abstract (English)
Iterative self-correction is increasingly deployed in agentic LLM systems, yet whether repeated refinement improves or degrades performance remains inconsistent across models. We recast self-correction as a closed-loop feedback-control problem in which the same model is both controller and plant, and analyze its error dynamics via a two-state Markov model over {Correct, Incorrect}, parameterized by the Error Introduction Rate (EIR) and Error Correction Rate (ECR). The model yields a directly measurable stability threshold -- iterate only when ECR/EIR > Acc/(1-Acc) -- in which EIR acts as a stability margin and prompting becomes lightweight controller design. Empirically, across 7 models and 3 datasets (GSM8K, MATH, StrategyQA), a sharp near-zero EIR boundary (< 0.5%) cleanly separates beneficial from harmful self-correction: only o3-mini (+3.4 pp), Claude Opus 4.6 (+0.6 pp), and o4-mini (+/-0 pp) stay non-degrading, while GPT-5 and four others lose accuracy. A verify-first prompt intervention then provides causal evidence: it drives GPT-4o-mini's EIR from 2% to 0% and converts a -6.2 pp degradation into +0.2 pp (paired McNemar, p<10^{-4}), with negligible change on already-sub-threshold models -- exactly as the diagnostic predicts. A complementary analysis of adaptive self-consistency (ASC) shows it halts harmful refinement at a 3.8 pp confidence-elicitation cost, exposing a two-tier capability structure: prompt-level EIR suppression prevents degradation, whereas ECR enhancement -- plausibly training-level -- is required for genuine gains. Self-correction should thus be treated not as a default behavior but as a control decision governed by measurable error dynamics.
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