迭代自我修正越来越多地部署在代理 LLM 系统, 中，但重复细化是否提高或降低性能在模型之间仍然不一致。我们将自校正重新定义为闭环反馈控制问题，其中同一模型既是控制器又是被控对象,，并通过 {Correct, In Correct}, 上的两态马尔可夫模型分析其误差动态，该模型由误差引入率 (EIR) 和误差校正率 (ECR) 参数化。该模型产生一个可直接测量的稳定性阈值——仅在 ECR/EIR> Acc/(1-Acc) 时迭代——其中 EIR 充当稳定性裕度，提示成为轻量级控制器设计。根据经验，, 跨越 7 个模型和 3 个数据集 (GSM8K, MATH, StrategyQA), 一个尖锐的接近于零的 EIR 边界 (< 0.5%) 清楚地区分有益与有害的自我校正: 仅 o3-mini (+3.4 pp), Claude Opus 4.6 (+0.6 pp), 和 o4-mini (+/-0 pp) 保持非降级,，而 GPT-5 和其他四个则失去准确性。然后，验证优先的即时干预提供因果证据:，它将 GPT-4o-mini的 EIR 从 2% 驱动到 0%，并将 -6.2 pp 降级转换为 +0.2 pp (paired McNemar, p<10^{-4}),，对已经低于阈值的模型的变化可以忽略不计 - 完全相同诊断预测。对自适应自我一致性(ASC) 的补充分析表明，它以 3.8 pp 置信度诱导成本, 停止有害的细化，暴露了两层能力结构: 提示级 EIR 抑制可防止退化,，而 ECR 增强（貌似是训练级别）是真正收益所必需的。因此，自我纠正不应被视为默认行为，而应被视为由可测量的误差动态控制的控制决策。
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的 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.
科目:人工智能(cs.AI)
Subjects: Artificial Intelligence (cs.AI)