# CoRT: Code-integrated Reasoning within Thinking

arXiv: https://arxiv.org/abs/2506.09820 · HTML: https://mlsanity.com/paper/2506.09820/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 47 of its 55 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [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)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [R1-Searcher: Incentivizing the Search Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2503.05592/) (2025)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)

## Built on by (most cited first, 15 of 15)

- [A Survey of Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2509.08827/) (2025)
- [Agentic Reinforced Policy Optimization](https://mlsanity.com/paper/2507.19849/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [RECODE-H: A Benchmark for Research Code Development with Interactive Human Feedback](https://mlsanity.com/paper/2510.06186/) (2025)
- [A Survey on Agentic Multimodal Large Language Models](https://mlsanity.com/paper/2510.10991/) (2025)
- [Toward Effective Tool-Integrated Reasoning via Self-Evolved Preference Learning](https://mlsanity.com/paper/2509.23285/) (2025)
- [AgentMath: Empowering Mathematical Reasoning for Large Language Models via Tool-Augmented Agent](https://mlsanity.com/paper/2512.20745/) (2025)
- [NeuReasoner: Towards Explainable, Controllable, and Unified Reasoning via Mixture-of-Neurons](https://mlsanity.com/paper/2604.02972/) (2026)
- [Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification](https://mlsanity.com/paper/2601.22642/) (2026)
- [ET-Agent: Incentivizing Effective Tool-Integrated Reasoning Agent via Behavior Calibration](https://mlsanity.com/paper/2601.06860/) (2026)
- [Bridging Formal Language with Chain-of-Thought Reasoning to Geometry Problem Solving](https://mlsanity.com/paper/2508.09099/) (2025)
- [CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling](https://mlsanity.com/paper/2510.04204/) (2025)
- [Teaching Thinking Models to Reason with Tools: A Full-Pipeline Recipe for Tool-Integrated Reasoning](https://mlsanity.com/paper/2605.06326/) (2026)
- [Contrastive Reinforced Policy Optimization via Privileged Self-Distillation](https://mlsanity.com/paper/2607.28026/) (2026)
- [Customer-Agent: Overcoming Context Limitations in Ultra-Long Shopping Trajectories via Tool-Augmented Agents and RLVR](https://mlsanity.com/paper/2606.07995/) (2026)

## Abstract (arXiv)

Large Reasoning Models (LRMs) like o1 and DeepSeek-R1 have shown remarkable progress in natural language reasoning with long chain-of-thought (CoT), yet they remain inefficient or inaccurate when handling complex mathematical operations. Addressing these limitations through computational tools (e.g., computation libraries and symbolic solvers) is promising, but it introduces a technical challenge: Code Interpreter (CI) brings external knowledge beyond the model's internal text representations, thus the direct combination is not efficient. This paper introduces CoRT, a post-training framework for teaching LRMs to leverage CI effectively and efficiently. As a first step, we address the data scarcity issue by synthesizing code-integrated reasoning data through Hint-Engineering, which strategically inserts different hints at appropriate positions to optimize LRM-CI interaction. We manually create 30 high-quality samples, upon which we post-train models ranging from 1.5B to 32B parameters, with supervised fine-tuning, rejection fine-tuning and reinforcement learning. Our experimental results demonstrate that Hint-Engineering models achieve 4% and 8% absolute improvements on DeepSeek-R1-Distill-Qwen-32B and DeepSeek-R1-Distill-Qwen-1.5B respectively, across five challenging mathematical reasoning datasets. Furthermore, Hint-Engineering models use about 30% fewer tokens for the 32B model and 50% fewer tokens for the 1.5B model compared with the natural language models. The models and code are available at https://github.com/ChengpengLi1003/CoRT.