# Scaling Code-Assisted Chain-of-Thoughts and Instructions for Model Reasoning

arXiv: https://arxiv.org/abs/2510.04081 · HTML: https://mlsanity.com/paper/2510.04081/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 23 of 23)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B](https://mlsanity.com/paper/2406.07394/) (2024)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding](https://mlsanity.com/paper/2503.02951/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [MathGenie: Generating Synthetic Data with Question Back-translation for Enhancing Mathematical Reasoning of LLMs](https://mlsanity.com/paper/2402.16352/) (2024)
- [Key-Point-Driven Data Synthesis with its Enhancement on Mathematical Reasoning](https://mlsanity.com/paper/2403.02333/) (2024)
- [CodeI/O: Condensing Reasoning Patterns via Code Input-Output Prediction](https://mlsanity.com/paper/2502.07316/) (2025)
- [MegaMath: Pushing the Limits of Open Math Corpora](https://mlsanity.com/paper/2504.02807/) (2025)
- [MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code](https://mlsanity.com/paper/2410.08196/) (2024)
- [MathFusion: Enhancing Mathematical Problem-solving of LLM through Instruction Fusion](https://mlsanity.com/paper/2503.16212/) (2025)
- [Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratch](https://mlsanity.com/paper/2410.18693/) (2024)
- [DotaMath: Decomposition of Thought with Code Assistance and Self-correction for Mathematical Reasoning](https://mlsanity.com/paper/2407.04078/) (2024)
- [MetaLadder: Ascending Mathematical Solution Quality via Analogical-Problem Reasoning Transfer](https://mlsanity.com/paper/2503.14891/) (2025)
- [Abstract Syntax Tree for Programming Language Understanding and Representation: How Far Are We?](https://mlsanity.com/paper/2312.00413/) (2023)

## Built on by (most cited first, 10 of 10)

- [MMFineReason: Closing the Multimodal Reasoning Gap via Open Data-Centric Methods](https://mlsanity.com/paper/2601.21821/) (2026)
- [SWE-World: Building Software Engineering Agents in Docker-Free Environments](https://mlsanity.com/paper/2602.03419/) (2026)
- [SWE-Master: Unleashing the Potential of Software Engineering Agents via Post-Training](https://mlsanity.com/paper/2602.03411/) (2026)
- [OpenDataArena: A Fair and Open Arena for Benchmarking Post-Training Dataset Value](https://mlsanity.com/paper/2512.14051/) (2025)
- [ChartVerse: Scaling Chart Reasoning via Reliable Programmatic Synthesis from Scratch](https://mlsanity.com/paper/2601.13606/) (2026)
- [Reasoning Models Will Sometimes Lie About Their Reasoning](https://mlsanity.com/paper/2601.07663/) (2026)
- [Tracing the Roots: A Multi-Agent Framework for Uncovering Data Lineage in Post-Training LLMs](https://mlsanity.com/paper/2604.10480/) (2026)
- [Not All Code Is Equal: A Data-Centric Study of Code Complexity and LLM Reasoning](https://mlsanity.com/paper/2601.21894/) (2026)
- [DiagramBank: A Quality-Audited Dataset of Scientific Schematic Diagrams with Multi-Level Document Context](https://mlsanity.com/paper/2604.20857/) (2026)
- [How code helps different tasks? A decompositional lens on LLM post-training](https://mlsanity.com/paper/2609.33845/) (2026)

## Abstract (arXiv)

Reasoning capability is pivotal for Large Language Models (LLMs) to solve complex tasks, yet achieving reliable and scalable reasoning remains challenging. While Chain-of-Thought (CoT) prompting has become a mainstream approach, existing methods often suffer from uncontrolled generation, insufficient quality, and limited diversity in reasoning paths. Recent efforts leverage code to enhance CoT by grounding reasoning in executable steps, but such methods are typically constrained to predefined mathematical problems, hindering scalability and generalizability. In this work, we propose Caco (Code-Assisted Chain-of-ThOught), a novel framework that automates the synthesis of high-quality, verifiable, and diverse instruction-CoT reasoning data through code-driven augmentation. Unlike prior work, Caco first fine-tunes a code-based CoT generator on existing math and programming solutions in a unified code format, then scales the data generation to a large amount of diverse reasoning traces. Crucially, we introduce automated validation via code execution and rule-based filtering to ensure logical correctness and structural diversity, followed by reverse-engineering filtered outputs into natural language instructions and language CoTs to enrich task adaptability. This closed-loop process enables fully automated, scalable synthesis of reasoning data with guaranteed executability. Experiments on our created Caco-1.3M dataset demonstrate that Caco-trained models achieve strong competitive performance on mathematical reasoning benchmarks, outperforming existing strong baselines. Further analysis reveals that Caco's code-anchored verification and instruction diversity contribute to superior generalization across unseen tasks. Our work establishes a paradigm for building self-sustaining, trustworthy reasoning systems without human intervention.