Self-Correction as Feedback Control: Error Dynamics, Stability Thresholds, and Prompt Interventions in LLMs

Abstract

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.