When Does LLM Self-Correction Help? A Control-Theoretic Markov Diagnostic and Verify-First Intervention

Computer Science > Artificial Intelligence [Submitted on 24 Apr 2026] When Does LLM Self-Correction Help? A Control-Theoretic Markov Diagnostic and Verify-First Intervention Aofan Liu, Jingxiang Meng Iterative self-correction is widely used in agentic LLM systems, but when repeated refinement helps versus hurts remains unclear. We frame self-correction as a cybernetic feedback loop in which the same language model serves as both controller and plant, and use a two-state Markov model over {Correct, Incorrect} to operationalize a simple deployment diagnostic: iterate only when ECR/EIR > Acc/(1 - Acc). In this view, EIR functions as a stability margin and prompting functions as lightweight controller design. Across 7 models and 3 datasets (GSM8K, MATH, StrategyQA), we find a sharp near-zero EIR threshold (<= 0.5%) separating beneficial from harmful self-correction. Only o3-mini (+3.4 pp, EIR = 0%), Claude Opus 4.6 (+0.6 pp, EIR ~ 0.2%), and o4-mini (+/-0 pp) remain non-degrading; GPT-5 degrades by -1.8 pp. A verify-first prompt ablation provides causal evidence that this threshold is actionable through prompting alone: on GPT-4o-mini it reduces EIR from 2% to 0% and turns -6.2 pp degradation into +0.2 pp (paired McNemar p < 10^-4), while producing little change on already-sub-threshold models. ASC further illustrates the stopping trade-off: it halts harmful refinement but incurs a 3.8 pp confidence-elicitation cost. Overall, the paper argues that self-correction should be treated not as a default behavior, but as a control decision governed by measurable error dynamics. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.22273 [cs.AI]   (or arXiv:2604.22273v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.22273 Focus to learn more Submission history From: Jingxiang Meng [view email] [v1] Fri, 24 Apr 2026 06:34:40 UTC (8,919 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)