# The Imitation Game: When LLMs Learn to Reason Like Programs via Code-Centric Reasoning Data Synthesis

arXiv: https://arxiv.org/abs/2609.16076 · HTML: https://mlsanity.com/paper/2609.16076/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 33 of its 75 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- Synthetic data and self-improvement for LLMs / [Self-play RL for reasoning](https://mlsanity.com/synth/self-play-rl-for-reasoning/)

## Builds on (most cited first, 30 of 33)

- [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)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [Why Do Large Language Models (LLMs) Struggle to Count Letters?](https://mlsanity.com/paper/2412.18626/) (2024)
- [AlphaMaze: Enhancing Large Language Models' Spatial Intelligence via GRPO](https://mlsanity.com/paper/2502.14669/) (2025)
- [Counting Ability of Large Language Models and Impact of Tokenization](https://mlsanity.com/paper/2410.19730/) (2024)
- [Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratch](https://mlsanity.com/paper/2410.18693/) (2024)
- [Frontier LLMs Still Struggle with Simple Reasoning Tasks](https://mlsanity.com/paper/2507.07313/) (2025)
- [CodeACT: Code Adaptive Compute-efficient Tuning Framework for Code LLMs](https://mlsanity.com/paper/2408.02193/) (2024)
- [EvoRubrics: Dynamic Rubrics as Rewards via Adversarial Co-Evolution for LLM Reinforcement Learning](https://mlsanity.com/paper/2606.23038/) (2026)
- [Learning Beyond Pattern Matching? Assaying Mathematical Understanding in LLMs](https://mlsanity.com/paper/2405.15485/) (2024)
- [Do VLMs Perceive or Recall? Probing Visual Perception vs. Memory with Classic Visual Illusions](https://mlsanity.com/paper/2601.22150/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) excel at programming tasks but frequently fail at deterministic, fine-grained reasoning in natural language, relying heavily on semantic approximations rather than robust symbolic execution. To bridge this gap, we propose MIMIC, a framework that leverages executable code as a rigorous medium for reasoning data synthesis. MIMIC fundamentally transforms algorithms into verifiable reasoning trajectories through narrative fusion, code-guided test synthesis, and dynamic code instrumentation. Crucially, these explicit intermediate execution states naturally form a Code-Instrumented Reward (CIR), providing dense, high-fidelity process supervision for reinforcement learning without external reward models. Extensive evaluations reveal that models trained via SFT and GRPO on our synthesized dataset achieve substantial, consistent gains. Our method significantly elevates accuracy across general reasoning, complex mathematical benchmarks, and fine-grained deterministic tasks, demonstrating that the procedural rigor of executable code can effectively unlock and enhance the generalized reasoning capabilities of LLMs. Our code and data are available at https://github.com/zjy1298/MIMIC.