Research identifies near-zero error-injection rate threshold that separates beneficial from harmful iterative self-correction in LLMs, with verify-first prompting shown to make the threshold actionable

Researchers framed iterative self-correction as a cybernetic feedback loop and developed a two-state Markov diagnostic model to predict when repeated refinement helps versus hurts. Testing across 7 models and 3 datasets (GSM8K, MATH, StrategyQA), they found a sharp threshold at error-injection rate (EIR) ≤ 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) remained non-degrading; GPT-5 degraded by −1.8 pp. A verify-first prompt ablation reduced EIR on GPT-4o-mini from 2% to 0% and converted −6.2 pp degradation into +0.2 pp (paired McNemar p < 10^−4).

The authors argue self-correction should be treated as a control decision governed by measurable error dynamics rather than a default behavior. Adaptive self-correction (ASC) can halt harmful refinement but incurs a 3.8 pp confidence-elicitation cost.