# CodeI/O: Condensing Reasoning Patterns via Code Input-Output Prediction

arXiv: https://arxiv.org/abs/2502.07316 · HTML: https://mlsanity.com/paper/2502.07316/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 30 of 34)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence](https://mlsanity.com/paper/2406.11931/) (2024)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning](https://mlsanity.com/paper/2402.06332/) (2024)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)

## Built on by (most cited first, 30 of 55)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Dream-Coder 7B: An Open Diffusion Language Model for Code](https://mlsanity.com/paper/2509.01142/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [1.4 Million Open-Source Distilled Reasoning Dataset to Empower Large Language Model Training](https://mlsanity.com/paper/2503.19633/) (2025)
- [ARM: Adaptive Reasoning Model](https://mlsanity.com/paper/2505.20258/) (2025)
- [CodeRL+: Improving Code Generation via Reinforcement with Execution Semantics Alignment](https://mlsanity.com/paper/2510.18471/) (2025)
- [O2-Searcher: A Searching-based Agent Model for Open-Domain Open-Ended Question Answering](https://mlsanity.com/paper/2505.16582/) (2025)
- [Could Thinking Multilingually Empower LLM Reasoning?](https://mlsanity.com/paper/2504.11833/) (2025)
- [NeuReasoner: Towards Explainable, Controllable, and Unified Reasoning via Mixture-of-Neurons](https://mlsanity.com/paper/2604.02972/) (2026)
- [Breaking the Data Barrier -- Building GUI Agents Through Task Generalization](https://mlsanity.com/paper/2504.10127/) (2025)
- [Scaling Code-Assisted Chain-of-Thoughts and Instructions for Model Reasoning](https://mlsanity.com/paper/2510.04081/) (2025)
- [Youtu-LLM: Unlocking the Native Agentic Potential for Lightweight Large Language Models](https://mlsanity.com/paper/2512.24618/) (2025)
- [Can We Predict Before Executing Machine Learning Agents?](https://mlsanity.com/paper/2601.05930/) (2026)
- [Variational Reasoning for Language Models](https://mlsanity.com/paper/2509.22637/) (2025)
- [Reasoning Curriculum: Bootstrapping Broad LLM Reasoning from Math](https://mlsanity.com/paper/2510.26143/) (2025)
- [Evaluating the Generalization Capabilities of Large Language Models on Code Reasoning](https://mlsanity.com/paper/2504.05518/) (2025)
- [Which Data Attributes Stimulate Math and Code Reasoning? An Investigation via Influence Functions](https://mlsanity.com/paper/2505.19949/) (2025)
- [Think in Games: Learning to Reason in Games via Reinforcement Learning with Large Language Models](https://mlsanity.com/paper/2508.21365/) (2025)
- [LLMs Lean on Priors, Not Programming Language Semantics](https://mlsanity.com/paper/2510.03415/) (2025)
- [ExecVerify: White-Box RL with Verifiable Stepwise Rewards for Code Execution Reasoning](https://mlsanity.com/paper/2603.11226/) (2026)
- [Learning, Fast and Slow: Towards LLMs That Adapt Continually](https://mlsanity.com/paper/2605.12484/) (2026)
- [From Chatbot to Digital Colleague: The Paradigm Shift Toward Persistent Autonomous AI](https://mlsanity.com/paper/2606.14502/) (2026)
- [Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale](https://mlsanity.com/paper/2606.15079/) (2026)
- [Rethinking Reasoning Quality in Large Language Models through Enhanced Chain-of-Thought via RL](https://mlsanity.com/paper/2509.06024/) (2025)
- [RE-Searcher: Robust Agentic Search with Goal-oriented Planning and Self-reflection](https://mlsanity.com/paper/2509.26048/) (2025)
- [Your Language Model is Its Own Critic: Reinforcement Learning with Value Estimation from Actor's Internal States](https://mlsanity.com/paper/2605.07579/) (2026)
- [Transferability for General Reasoning: An Automated Curriculum for Multi-Domain RLVR](https://mlsanity.com/paper/2606.25178/) (2026)
- [Verify Before You Distill: Prompt-Level Teacher Gating for On-Policy Distillation](https://mlsanity.com/paper/2609.02998/) (2026)
- [The Hitchhiker's Guide to Program Analysis, Part II: Deep Thoughts by LLMs](https://mlsanity.com/paper/2504.11711/) (2025)

## Abstract (arXiv)

Reasoning is a fundamental capability of Large Language Models. While prior research predominantly focuses on enhancing narrow skills like math or code generation, improving performance on many other reasoning tasks remains challenging due to sparse and fragmented training data. To address this issue, we propose CodeI/O, a novel approach that systematically condenses diverse reasoning patterns inherently embedded in contextually-grounded codes, through transforming the original code into a code input-output prediction format. By training models to predict inputs/outputs given code and test cases entirely in natural language as Chain-of-Thought (CoT) rationales, we expose them to universal reasoning primitives -- like logic flow planning, state-space searching, decision tree traversal, and modular decomposition -- while decoupling structured reasoning from code-specific syntax and preserving procedural rigor. Experimental results demonstrate CodeI/O leads to consistent improvements across symbolic, scientific, logic, math & numerical, and commonsense reasoning tasks. By matching the existing ground-truth outputs or re-executing the code with predicted inputs, we can verify each prediction and further enhance the CoTs through multi-turn revision, resulting in CodeI/O++ and achieving higher performance. Our data and models are available at https://github.com/hkust-nlp/CodeIO.