# Why Distillation can Outperform Zero-RL: The Role of Flexible Reasoning

arXiv: https://arxiv.org/abs/2505.21067 · HTML: https://mlsanity.com/paper/2505.21067/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 27 May 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [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)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (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)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [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)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [A Sober Look at Progress in Language Model Reasoning: Pitfalls and Paths to Reproducibility](https://mlsanity.com/paper/2504.07086/) (2025)
- [RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?](https://mlsanity.com/paper/2501.11284/) (2025)
- [Understanding Aha Moments: from External Observations to Internal Mechanisms](https://mlsanity.com/paper/2504.02956/) (2025)

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

- [On-Policy RL Meets Off-Policy Experts: Harmonizing Supervised Fine-Tuning and Reinforcement Learning via Dynamic Weighting](https://mlsanity.com/paper/2508.11408/) (2025)
- [rStar2-Agent: Agentic Reasoning Technical Report](https://mlsanity.com/paper/2508.20722/) (2025)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)
- [On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation](https://mlsanity.com/paper/2603.22117/) (2026)
- [Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning](https://mlsanity.com/paper/2508.09883/) (2025)
- [Debunk the Myth of SFT Generalization](https://mlsanity.com/paper/2510.00237/) (2025)
- [Training Large Language Models To Reason In Parallel With Global Forking Tokens](https://mlsanity.com/paper/2510.05132/) (2025)
- [CoT-Evo: Evolutionary Distillation of Chain-of-Thought for Scientific Reasoning](https://mlsanity.com/paper/2510.13166/) (2025)
- [AIR: Post-training Data Selection for Reasoning via Attention Head Influence](https://mlsanity.com/paper/2512.13279/) (2025)
- [HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation](https://mlsanity.com/paper/2603.10359/) (2026)
- [AGPO: Asymmetric Group Policy Optimization for Verifiable Reasoning and Search Ads Relevance at JD](https://mlsanity.com/paper/2605.05826/) (2026)
- [D-CORE: Incentivizing Task Decomposition in Large Reasoning Models for Complex Tool Use](https://mlsanity.com/paper/2602.02160/) (2026)
- [Distilling Long-CoT Reasoning through Collaborative Step-wise Multi-Teacher Decoding](https://mlsanity.com/paper/2605.02290/) (2026)
- [When Does Reasoning Help in Machine Translation? A Hierarchical Analysis of LRM Reasoning Traces](https://mlsanity.com/paper/2609.21247/) (2026)
- [Distillation Defenses Easily Break After Reinforcement Learning](https://mlsanity.com/paper/2609.35699/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has played an important role in improving the reasoning ability of large language models (LLMs). Some studies apply RL directly to textitsmaller base models (known as zero-RL) and also achieve notable progress. However, in this paper, we show that using only 920 examples, a simple distillation method based on the base model can clearly outperform zero-RL, which typically requires much more data and computational cost. By analyzing the token frequency in model outputs, we find that the distilled model shows more flexible reasoning. It uses anthropomorphic tokens and logical connectors much more often than the zero-RL model. Further analysis reveals that distillation enhances the presence of two advanced cognitive behaviors: Multi-Perspective Thinking or Attempting and Metacognitive Awareness. Frequent occurrences of these two advanced cognitive behaviors give rise to flexible reasoning, which is essential for solving complex reasoning problems, while zero-RL fails to significantly boost the frequency of these behaviors.