# MI-Distillation: Selecting from Model-Interpolated Instruct-Reasoning Data Spectrum for Chain-of-Thought Distillation

arXiv: https://arxiv.org/abs/2608.29623 · HTML: https://mlsanity.com/paper/2608.29623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## 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, 22 of 22)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Stealing Part of a Production Language Model](https://mlsanity.com/paper/2403.06634/) (2024)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [What Happened in LLMs Layers when Trained for Fast vs. Slow Thinking: A Gradient Perspective](https://mlsanity.com/paper/2410.23743/) (2024)
- [Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment](https://mlsanity.com/paper/2601.14249/) (2026)
- [When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale](https://mlsanity.com/paper/2309.04564/) (2023)
- [Revisiting Model Interpolation for Efficient Reasoning](https://mlsanity.com/paper/2510.10977/) (2025)
- [The Signal is in the Steps: Local Scoring for Reasoning Data Selection](https://mlsanity.com/paper/2510.03988/) (2025)
- [In Their Own Words: Reasoning Traces Tailored for Small Models Make Them Better Reasoners](https://mlsanity.com/paper/2509.22230/) (2025)

## Abstract (arXiv)

Recent advances in large reasoning models (LRMs) have shown strong performance on complex problems through long chain-of-thought (Long CoT) reasoning. However, distilling such trajectories into smaller student models remains challenging: direct Long CoT supervision often provides limited gains and can be less effective than concise Short CoT rationales. In this work, we investigate this phenomenon from a gradient-centric perspective. Our analysis shows that Long CoT induces larger gradient magnitudes and more concentrated update directions than Short CoT, with this effect becoming more pronounced as student model capacity increases. These findings suggest that effective Long CoT distillation requires balancing the reasoning information density of reasoning trajectories with their distributional alignment to the student model. Motivated by this insight, we propose Model Interporlation Distillation (MI-Distillation), a framework that constructs a continuous Instruct-Reasoning data spectrum through model interpolation. To select suitable trajectories from this spectrum, we further introduce Sequential Learnable Surprisal Score (SeqLSS), which favors reasoning paths that are both informative and learnable for the student. Extensive experiments on reasoning benchmarks show that MI-Distillation consistently improves small model CoT distillation over strong Long CoT baselines.