# ProgCo: Program Helps Self-Correction of Large Language Models

arXiv: https://arxiv.org/abs/2501.01264 · HTML: https://mlsanity.com/paper/2501.01264/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 19 of 19)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Language Models can Solve Computer Tasks](https://mlsanity.com/paper/2303.17491/) (2023)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Making Language Models Better Tool Learners with Execution Feedback](https://mlsanity.com/paper/2305.13068/) (2023)
- [TICKing All the Boxes: Generated Checklists Improve LLM Evaluation and Generation](https://mlsanity.com/paper/2410.03608/) (2024)
- [Large Language Models Can Self-Correct with Key Condition Verification](https://mlsanity.com/paper/2405.14092/) (2024)
- [Progressive Multimodal Reasoning via Active Retrieval](https://mlsanity.com/paper/2412.14835/) (2024)
- [Small Language Model Can Self-correct](https://mlsanity.com/paper/2401.07301/) (2024)
- [HDFlow: Enhancing LLM Complex Problem-Solving with Hybrid Thinking and Dynamic Workflows](https://mlsanity.com/paper/2409.17433/) (2024)
- [Large Language Models as Code Executors: An Exploratory Study](https://mlsanity.com/paper/2410.06667/) (2024)

## Built on by (most cited first, 14 of 14)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Vibe Coding vs. Agentic Coding: Fundamentals and Practical Implications of Agentic AI](https://mlsanity.com/paper/2505.19443/) (2025)
- [CodeCriticBench: A Holistic Code Critique Benchmark for Large Language Models](https://mlsanity.com/paper/2502.16614/) (2025)
- [Process or Result? Manipulated Ending Tokens Can Mislead Reasoning LLMs to Ignore the Correct Reasoning Steps](https://mlsanity.com/paper/2503.19326/) (2025)
- [Diagnosing Visual Reasoning: Challenges, Insights, and a Path Forward](https://mlsanity.com/paper/2510.20696/) (2025)
- [Introspection of Thought Helps AI Agents](https://mlsanity.com/paper/2507.08664/) (2025)
- [RefineRL: Advancing Competitive Programming with Self-Refinement Reinforcement Learning](https://mlsanity.com/paper/2604.00790/) (2026)
- [RETuning: Upgrading Inference-Time Scaling for Stock Movement Prediction with Large Language Models](https://mlsanity.com/paper/2510.21604/) (2025)
- [From Atoms to Chains: Divergence-Guided Reasoning Curriculum for Unlabeled LLM Domain Adaptation](https://mlsanity.com/paper/2601.19588/) (2026)
- [Beyond Output Critique: Self-Correction via Task Distillation](https://mlsanity.com/paper/2602.00871/) (2026)
- [Counterexample Guided Learning in the Large using Reasoning Agents](https://mlsanity.com/paper/2606.11521/) (2026)
- [A Taxonomy of Cognitive Capability Gaps in Generative and Agentic AI](https://mlsanity.com/paper/2608.02553/) (2026)
- [Factorized Hypothesis Search for Evidence-to-Taxonomy Retrieval](https://mlsanity.com/paper/2608.06614/) (2026)

## Abstract (arXiv)

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further misleading refinement and leading to the failure of self-correction, especially in complex reasoning tasks. In this paper, we propose Program-driven Self-Correction (ProgCo). First, program-driven verification (ProgVe) achieves complex verification logic and extensive validation through self-generated, self-executing verification pseudo-programs. Then, program-driven refinement (ProgRe) receives feedback from ProgVe, conducts dual reflection and refinement on both responses and verification programs to mitigate misleading of incorrect feedback in complex reasoning tasks. Experiments on three instruction-following and mathematical benchmarks indicate that ProgCo achieves effective self-correction, and can be further enhance performance when combined with real program tools. We release our code at https://github.com/songxiaoshuai/progco.