mlsanityData to 14 Oct 2026

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

arXiv 2604.22273 ↗First posted 24 Apr 2026cs.AIcited by 3

On the map: LLM agents and tool use → General LLM agent frameworks and benchmarks

Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in General LLM agent frameworks and benchmarks, one of 16 directions in LLM agents and tool use. Builds on 18 of its 19 references that are in the map. First posted on arXiv 24 Apr 2026.

Builds on

18 of 19 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024MAgICoRe: Multi-Agent, Iterative, Coarse-to-Fine Refinement for Reasoning18 Sep

Other references · 17

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2020Measuring Massive Multitask Language Understandingcited by 7,963
  4. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  5. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  6. 2023Reflexion: Language Agents with Verbal Reinforcement Learningcited by 4,276
  7. 2023Toolformer: Language Models Can Teach Themselves to Use Toolscited by 4,182
  8. 2023Self-Refine: Iterative Refinement with Self-Feedbackcited by 3,442
  9. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,986
  10. 2023Large Language Models Cannot Self-Correct Reasoning Yetcited by 1,017
  11. 2023CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquingcited by 783
  12. 2022Self-critiquing models for assisting human evaluatorscited by 380
5 more
  1. 2022Generating Sequences by Learning to Self-Correctcited by 277
  2. 2024When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMscited by 240
  3. 2024On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Taskscited by 142
  4. 2022Learning Iterative Reasoning through Energy Minimizationcited by 32
  5. 2025A Probabilistic Inference Scaling Theory for LLM Self-Correctioncited by 9

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Delayed Verification Destabilizes Multi-Agent LLM Belief: Instability Thresholds and Optimal Corrector Placementcited by 4
  2. 2026Onnes: A Physics-Grounded Multi-Agent LLM Simulator for Cryogenic Fault Diagnosis in Quantum Computing Infrastructurecited by 0
  3. 2026Exact Feedback Is Not Control: Evaluating Text-based Closed-Loop Revision in LLMscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026CyberCorrect: A Cybernetic Framework for Closed-Loop Self-Correction in Large Language Models
  2. 2026Structured Feedback Improves Repair in an LLM Agent Loop
  3. 2026Memory Reward Inflation in Self-Improving LLM Agents
  4. 2026PID-Gated Continual Prompt Adaptation Under Noisy Feedback
  5. 2026Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
  6. 2026Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs
  7. 2026Rethinking Self-Evolving Agent Skills: Feedback Dynamics over Multiple Rounds
  8. 2026ANCHOR: An External LLM-Driven Supervisory Module Facilitating Healthy Evolution in Self-Evolving Systems