# DeepDistill: Enhancing LLM Reasoning Capabilities via Large-Scale Difficulty-Graded Data Training

arXiv: https://arxiv.org/abs/2504.17565 · HTML: https://mlsanity.com/paper/2504.17565/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 26 of its 61 references that are in the map.
- First posted on arXiv 24 Apr 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

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

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Free Process Rewards without Process Labels](https://mlsanity.com/paper/2412.01981/) (2024)
- [OpenCoder: The Open Cookbook for Top-Tier Code Large Language Models](https://mlsanity.com/paper/2411.04905/) (2024)
- [KodCode: A Diverse, Challenging, and Verifiable Synthetic Dataset for Coding](https://mlsanity.com/paper/2503.02951/) (2025)
- [Big-Math: A Large-Scale, High-Quality Math Dataset for Reinforcement Learning in Language Models](https://mlsanity.com/paper/2502.17387/) (2025)
- [NaturalReasoning: Reasoning in the Wild with 2.8M Challenging Questions](https://mlsanity.com/paper/2502.13124/) (2025)
- [1.4 Million Open-Source Distilled Reasoning Dataset to Empower Large Language Model Training](https://mlsanity.com/paper/2503.19633/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [D3: Diversity, Difficulty, and Dependability-Aware Data Selection for Sample-Efficient LLM Instruction Tuning](https://mlsanity.com/paper/2503.11441/) (2025)
- [InfinityMATH: A Scalable Instruction Tuning Dataset in Programmatic Mathematical Reasoning](https://mlsanity.com/paper/2408.07089/) (2024)
- [How Difficulty-Aware Staged Reinforcement Learning Enhances LLMs' Reasoning Capabilities: A Preliminary Experimental Study](https://mlsanity.com/paper/2504.00829/) (2025)
- [Beyond IID: Optimizing Instruction Learning from the Perspective of Instruction Interaction and Dependency](https://mlsanity.com/paper/2409.07045/) (2024)

## Built on by (most cited first, 18 of 18)

- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [Not All Correct Answers Are Equal: Why Your Distillation Source Matters](https://mlsanity.com/paper/2505.14464/) (2025)
- [HS-STaR: Hierarchical Sampling for Self-Taught Reasoners via Difficulty Estimation and Budget Reallocation](https://mlsanity.com/paper/2505.19866/) (2025)
- [Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey](https://mlsanity.com/paper/2507.09662/) (2025)
- [Hard Examples Are All You Need: Maximizing GRPO Post-Training Under Annotation Budgets](https://mlsanity.com/paper/2508.14094/) (2025)
- [MiroMind-M1: An Open-Source Advancement in Mathematical Reasoning via Context-Aware Multi-Stage Policy Optimization](https://mlsanity.com/paper/2507.14683/) (2025)
- [Tackling Length Inflation Without Trade-offs: Group Relative Reward Rescaling for Reinforcement Learning](https://mlsanity.com/paper/2603.10535/) (2026)
- [Unearthing Gems from Stones: Policy Optimization with Negative Sample Augmentation for LLM Reasoning](https://mlsanity.com/paper/2505.14403/) (2025)
- [SIGMA: Refining Large Language Model Reasoning via Sibling-Guided Monte Carlo Augmentation](https://mlsanity.com/paper/2506.06470/) (2025)
- [JT-Math: A Multi-Stage Framework for Advanced Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2507.19748/) (2025)
- [Rethinking Expert Trajectory Utilization in LLM Post-training for Mathematical Reasoning](https://mlsanity.com/paper/2512.11470/) (2025)
- [SFT Conflicts, RL Coexists: A Theoretical and Empirical Analysis of Multi-Task Learning for LLMs](https://mlsanity.com/paper/2608.03573/) (2026)
- [Exploring the Potential of Offline RL for Reasoning in LLMs: A Preliminary Study](https://mlsanity.com/paper/2505.02142/) (2025)
- [MathMixup: Boosting LLM Mathematical Reasoning with Difficulty-Controllable Data Synthesis and Curriculum Learning](https://mlsanity.com/paper/2601.17006/) (2026)
- [X-Intelligence 3.0: Training and Evaluating Reasoning LLM for Semiconductor Display](https://mlsanity.com/paper/2507.14430/) (2025)
- [Reasoning as State Transition: A Representational Analysis of Reasoning Evolution in Large Language Models](https://mlsanity.com/paper/2602.00770/) (2026)
- [Test-time RL alignment exposes task familiarity artifacts in LLM benchmarks](https://mlsanity.com/paper/2603.12875/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)

## Abstract (arXiv)

Although large language models (LLMs) have recently achieved remarkable performance on various complex reasoning benchmarks, the academic community still lacks an in-depth understanding of base model training processes and data quality. To address this, we construct a large-scale, difficulty-graded reasoning dataset containing approximately 3.34 million unique queries of varying difficulty levels and about 40 million distilled responses generated by multiple models over several passes. Leveraging pass rate and Coefficient of Variation (CV), we precisely select the most valuable training data to enhance reasoning capability. Notably, we observe a training pattern shift, indicating that reasoning-focused training based on base models requires higher learning rates for effective training. Using this carefully selected data, we significantly improve the reasoning capabilities of the base model, achieving a pass rate of 79.2% on the AIME2024 mathematical reasoning benchmark. This result surpasses most current distilled models and closely approaches state-of-the-art performance. We provide detailed descriptions of our data processing, difficulty assessment, and training methodology, and have publicly released all datasets and methods to promote rapid progress in open-source long-reasoning LLMs. The dataset is available at: hrefhttps://huggingface.co/datasets/a-m-team/AM-DeepSeek-Distilled-40Mhttps://huggingface.co/datasets/a-m-team/AM-DeepSeek-Distilled-40M