# Long-Chain Reasoning Distillation via Adaptive Prefix Alignment

arXiv: https://arxiv.org/abs/2601.10064 · HTML: https://mlsanity.com/paper/2601.10064/

## Key facts

- Cited by 6 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 26 of its 43 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 26 of 26)

- [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)
- [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)
- [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)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [GLM-4.5: Agentic, Reasoning, and Coding (ARC) Foundation Models](https://mlsanity.com/paper/2508.06471/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [The False Promise of Imitating Proprietary LLMs](https://mlsanity.com/paper/2305.15717/) (2023)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [Small Models Struggle to Learn from Strong Reasoners](https://mlsanity.com/paper/2502.12143/) (2025)
- [Making Large Language Models Better Reasoners with Alignment](https://mlsanity.com/paper/2309.02144/) (2023)
- [Learning From Failure: Integrating Negative Examples when Fine-tuning Large Language Models as Agents](https://mlsanity.com/paper/2402.11651/) (2024)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)
- [Pruning the Unsurprising: Efficient LLM Reasoning via First-Token Surprisal](https://mlsanity.com/paper/2508.05988/) (2025)
- [ReCUT: Balancing Reasoning Length and Accuracy in LLMs via Stepwise Trails and Preference Optimization](https://mlsanity.com/paper/2506.10822/) (2025)
- [Marco-o1 v2: Towards Widening The Distillation Bottleneck for Reasoning Models](https://mlsanity.com/paper/2503.01461/) (2025)
- [From Data-Centric to Sample-Centric: Enhancing LLM Reasoning via Progressive Optimization](https://mlsanity.com/paper/2507.06573/) (2025)
- [Enhancing Long-Chain Reasoning Distillation through Error-Aware Self-Reflection](https://mlsanity.com/paper/2505.22131/) (2025)
- [Well Begun, Half Done: Reinforcement Learning with Prefix Optimization for LLM Reasoning](https://mlsanity.com/paper/2512.15274/) (2025)

## Built on by (most cited first, 6 of 6)

- [ADWIN: Adaptive Windows for Horizon-Aware On-Policy Distillation](https://mlsanity.com/paper/2605.28396/) (2026)
- [Learning from Partial Chain-of-Thought via Truncated-Reasoning Self-Distillation](https://mlsanity.com/paper/2603.13274/) (2026)
- [Self-Verified Distillation: Your Language Model Is Secretly Its Own Synthetic Data Pipeline](https://mlsanity.com/paper/2605.26132/) (2026)
- [Diagnosing Harmful Continuation in Answer-Correct Long-CoT Training Traces](https://mlsanity.com/paper/2605.29288/) (2026)
- [ACTD: Anchor-Based Cross-Tokenizer Distillation with Residual Regularization](https://mlsanity.com/paper/2608.29662/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities, particularly in solving complex mathematical problems. Recent studies show that distilling long reasoning trajectories can effectively enhance the reasoning performance of small-scale student models. However, teacher-generated reasoning trajectories are often excessively long and structurally complex, making them difficult for student models to learn. This mismatch leads to a gap between the provided supervision signal and the learning capacity of the student model. To address this challenge, we propose Prefix-ALIGNment distillation (P-ALIGN), a framework that fully exploits teacher CoTs for distillation through adaptive prefix alignment. Specifically, P-ALIGN adaptively truncates teacher-generated reasoning trajectories by determining whether the remaining suffix is concise and sufficient to guide the student model. Then, P-ALIGN leverages the teacher-generated prefix to supervise the student model, encouraging effective prefix alignment. Experiments on multiple mathematical reasoning benchmarks demonstrate that P-ALIGN outperforms all baselines by over 3%. Further analysis indicates that the prefixes constructed by P-ALIGN provide more effective supervision signals, while avoiding the negative impact of redundant and uncertain reasoning components. All code is available at https://github.com/NEUIR/P-ALIGN.