# Beyond Scaling Law: A Data-Efficient Distillation Framework for Reasoning

arXiv: https://arxiv.org/abs/2508.09883 · HTML: https://mlsanity.com/paper/2508.09883/

## Key facts

- Cited by 11 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 38 of its 45 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## 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, 30 of 38)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding](https://mlsanity.com/paper/2503.02951/) (2025)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [SRFT: A Single-Stage Method with Supervised and Reinforcement Fine-Tuning for Reasoning](https://mlsanity.com/paper/2506.19767/) (2025)
- [AceReason-Nemotron 1.1: Advancing Math and Code Reasoning through SFT and RL Synergy](https://mlsanity.com/paper/2506.13284/) (2025)

## Built on by (most cited first, 11 of 11)

- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [Distribution-Aligned Sequence Distillation for Superior Long-CoT Reasoning](https://mlsanity.com/paper/2601.09088/) (2026)
- [Which Reasoning Trajectories Teach Students to Reason Better? A Simple Metric of Informative Alignment](https://mlsanity.com/paper/2601.14249/) (2026)
- [The Signal is in the Steps: Local Scoring for Reasoning Data Selection](https://mlsanity.com/paper/2510.03988/) (2025)
- [Backtracking When It Strays: Mitigating Dual Exposure Biases in LLM Reasoning Distillation](https://mlsanity.com/paper/2605.19433/) (2026)
- [Merge-of-Thought Distillation](https://mlsanity.com/paper/2509.08814/) (2025)
- [Detecting Distillation Data from Reasoning Models](https://mlsanity.com/paper/2510.04850/) (2025)
- [Training-Trajectory-Aware Token Selection](https://mlsanity.com/paper/2601.10348/) (2026)
- [Context-CoT: Enhancing Context Learning via High-Quality Reasoning Synthesis](https://mlsanity.com/paper/2605.25354/) (2026)
- [Revisiting Knowledge Distillation: The Hidden Role of Dataset Size](https://mlsanity.com/paper/2510.15516/) (2025)
- ["The Whole Is Greater Than the Sum of Its Parts": A Compatibility-Aware Multi-Teacher CoT Distillation Framework](https://mlsanity.com/paper/2601.13992/) (2026)

## Abstract (arXiv)

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.