# Embedding Self-Correction as an Inherent Ability in Large Language Models for Enhanced Mathematical Reasoning

arXiv: https://arxiv.org/abs/2410.10735 · HTML: https://mlsanity.com/paper/2410.10735/

## Key facts

- Cited by 13 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 33 of its 49 references that are in the map.
- First posted on arXiv 14 Oct 2024.

## 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, 30 of 33)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [OpenMathInstruct-1: A 1.8 Million Math Instruction Tuning Dataset](https://mlsanity.com/paper/2402.10176/) (2024)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [TinyGSM: achieving >80% on GSM8k with small language models](https://mlsanity.com/paper/2312.09241/) (2023)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [Improving Large Language Model Fine-tuning for Solving Math Problems](https://mlsanity.com/paper/2310.10047/) (2023)
- [Efficient Tool Use with Chain-of-Abstraction Reasoning](https://mlsanity.com/paper/2401.17464/) (2024)

## Built on by (most cited first, 13 of 13)

- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [A Survey of Test-Time Compute: From Intuitive Inference to Deliberate Reasoning](https://mlsanity.com/paper/2501.02497/) (2025)
- [Benchmarking Open-ended Audio Dialogue Understanding for Large Audio-Language Models](https://mlsanity.com/paper/2412.05167/) (2024)
- [QueryAttack: Jailbreaking Aligned Large Language Models Using Structured Non-natural Query Language](https://mlsanity.com/paper/2502.09723/) (2025)
- [Reasoning Physical Video Generation with Diffusion Timestep Tokens via Reinforcement Learning](https://mlsanity.com/paper/2504.15932/) (2025)
- [System-2 Mathematical Reasoning via Enriched Instruction Tuning](https://mlsanity.com/paper/2412.16964/) (2024)
- [PARSE: LLM Driven Schema Optimization for Reliable Entity Extraction](https://mlsanity.com/paper/2510.08623/) (2025)
- [Protecting Your Video Content: Disrupting Automated Video-based LLM Annotations](https://mlsanity.com/paper/2503.21824/) (2025)
- [LingBench++: A Linguistically-Informed Benchmark and Reasoning Framework for Multi-Step and Cross-Cultural Inference with LLMs](https://mlsanity.com/paper/2507.16809/) (2025)
- [Boosting Accuracy and Efficiency of Budget Forcing in LLMs via Reinforcement Learning for Mathematical Reasoning](https://mlsanity.com/paper/2510.21398/) (2025)
- [AgentSpec: Understanding Embodied Agent Scaffolds Through Controlled Composition](https://mlsanity.com/paper/2606.14674/) (2026)
- [Audited Reasoning Refinement: Fine-Tuning Language Models via LLM-Guided Step-Wise Evaluation and Correction](https://mlsanity.com/paper/2509.12476/) (2025)
- [When to Vote, When to Rewrite: Disagreement-Guided Strategy Routing for Test-Time Scaling](https://mlsanity.com/paper/2604.26644/) (2026)

## Abstract (arXiv)

Accurate mathematical reasoning with Large Language Models (LLMs) is crucial in revolutionizing domains that heavily rely on such reasoning. However, LLMs often encounter difficulties in certain aspects of mathematical reasoning, leading to flawed reasoning and erroneous results. To mitigate these issues, we introduce a novel mechanism, the Chain of Self-Correction (CoSC), specifically designed to embed self-correction as an inherent ability in LLMs, enabling them to validate and rectify their own results. The CoSC mechanism operates through a sequence of self-correction stages. In each stage, the LLMs generate a program to address a given problem, execute this program using program-based tools to obtain an output, subsequently verify this output. Based on the verification, the LLMs either proceed to the next correction stage or finalize the answer. This iterative self-correction process allows the LLMs to refine its reasoning steps and improve the accuracy of its mathematical reasoning. We implement CoSC using a two-phase fine-tuning approach. First, LLMs are trained with a relatively small volume of seeding data generated from GPT-4. Then, we enhance CoSC by training with a larger volume of self-generated data, without relying on GPT-4. Experiments show that CoSC significantly boosts performance on standard mathematical datasets compared to existing open-source LLMs. Notably, our CoSC-Code-34B model achieved a 53.5% score on the challenging MATH dataset, outperforming models like ChatGPT, GPT-4, and multi-modal LLMs such as GPT-4V and Gemini-1.0. Importantly, CoSC operates in a zero-shot manner without requiring demonstrations.