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Skill-Aware Data Selection and Fine-Tuning for Data-Efficient Reasoning Distillation

Lechen Zhang, Yunxiang Zhang, Wei Hu, Lu Wang

TL;DR

The paper tackles data efficiency in distilling reasoning from large LLMs by proposing a skill-centric framework that (1) attributes problems to a hierarchical skill tree, (2) samples data adaptively by per-skill weakness using an inverse-accuracy distribution P(skill) = clip(acc_skill^{-1}, 0, $w_{max}$) / sum_{skill'} clip(acc_skill'^{-1}, 0, $w_{max}$) with $w_{max}=10^4$, and (3) trains with explicit skill chains embedded in training instances. Using only 1K examples from a 100K pool, the approach yields consistent gains over random SFT on Qwen3-4B and Qwen3-8B across five math benchmarks, and the gains are amplified when combining skill-based sampling with skill-aware training. The method generalizes across skill taxonomies and model families (e.g., DeepSeek-R1-Distill-Llama-8B) and can outperform existing data-selection methods like LIMO and s1 in this data-constrained setting. These results demonstrate that structured, skill-centric training can dramatically improve data efficiency and interpretability in reasoning distillation, enabling smaller models to acquire robust, decomposed reasoning abilities with limited curated data.

Abstract

Large reasoning models such as DeepSeek-R1 and their distilled variants achieve strong performance on complex reasoning tasks. Yet, distilling these models often demands large-scale data for supervised fine-tuning (SFT), motivating the pursuit of data-efficient training methods. To address this, we propose a skill-centric distillation framework that efficiently transfers reasoning ability to weaker models with two components: (1) Skill-based data selection, which prioritizes examples targeting the student model's weaker skills, and (2) Skill-aware fine-tuning, which encourages explicit skill decomposition during problem solving. With only 1,000 training examples selected from a 100K teacher-generated corpus, our method surpasses random SFT baselines by +1.6% on Qwen3-4B and +1.4% on Qwen3-8B across five mathematical reasoning benchmarks. Further analysis confirms that these gains concentrate on skills emphasized during training, highlighting the effectiveness of skill-centric training for efficient reasoning distillation.

Skill-Aware Data Selection and Fine-Tuning for Data-Efficient Reasoning Distillation

TL;DR

The paper tackles data efficiency in distilling reasoning from large LLMs by proposing a skill-centric framework that (1) attributes problems to a hierarchical skill tree, (2) samples data adaptively by per-skill weakness using an inverse-accuracy distribution P(skill) = clip(acc_skill^{-1}, 0, ) / sum_{skill'} clip(acc_skill'^{-1}, 0, ) with , and (3) trains with explicit skill chains embedded in training instances. Using only 1K examples from a 100K pool, the approach yields consistent gains over random SFT on Qwen3-4B and Qwen3-8B across five math benchmarks, and the gains are amplified when combining skill-based sampling with skill-aware training. The method generalizes across skill taxonomies and model families (e.g., DeepSeek-R1-Distill-Llama-8B) and can outperform existing data-selection methods like LIMO and s1 in this data-constrained setting. These results demonstrate that structured, skill-centric training can dramatically improve data efficiency and interpretability in reasoning distillation, enabling smaller models to acquire robust, decomposed reasoning abilities with limited curated data.

Abstract

Large reasoning models such as DeepSeek-R1 and their distilled variants achieve strong performance on complex reasoning tasks. Yet, distilling these models often demands large-scale data for supervised fine-tuning (SFT), motivating the pursuit of data-efficient training methods. To address this, we propose a skill-centric distillation framework that efficiently transfers reasoning ability to weaker models with two components: (1) Skill-based data selection, which prioritizes examples targeting the student model's weaker skills, and (2) Skill-aware fine-tuning, which encourages explicit skill decomposition during problem solving. With only 1,000 training examples selected from a 100K teacher-generated corpus, our method surpasses random SFT baselines by +1.6% on Qwen3-4B and +1.4% on Qwen3-8B across five mathematical reasoning benchmarks. Further analysis confirms that these gains concentrate on skills emphasized during training, highlighting the effectiveness of skill-centric training for efficient reasoning distillation.
Paper Structure (34 sections, 3 figures, 6 tables)

This paper contains 34 sections, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Distillation of LLM Reasoning
  4. Data Selection for Efficient Training
  5. Skill Decomposition and Structured Reasoning
  6. Method
  7. Step 1: Skill tree attribution
  8. Step 2: Skill-based sampling
  9. Step 3: Skill-aware training
  10. Experiments
  11. Setup
  12. Main Results and Analysis
  13. Ablation Studies
  14. Effect of Sampling Aggressiveness
  15. Is the Full Chain of Skills Necessary?
  16. ...and 19 more sections

Figures (3)

  • Figure 1: Overview of our skill-centric distillation framework. (1) Skill Tree Attribution: Each problem is mapped to nodes on a hierarchical skill tree kaur2025instructskillmix via top-down LLM-based skill attribution (2) Skill-based Sampling: The student model’s per-skill accuracy guides sampling, with weaker skills emphasized. (3) Skill-aware Training: Selected examples are augmented with explicit skill chains (as shown in red) for skill-aware training.
  • Figure 2: Per-skill accuracy shift of skill-based selection on MATH-500. Skill-based sampling improves weaker skills while preserving strong ones, flattening the accuracy curve toward balanced mastery. Skill-aware augmentation further enhances robustness across skills. (Detailed version is in Appendix Figure \ref{['fig:per_skill_acc_full']})
  • Figure 3: Data proportion shift of skill-based selection and per-skill accuracy (%) on MATH-500. Skill-based sampling improves weaker skills while preserving strong ones, flattening the accuracy curve toward balanced mastery. Skill-aware augmentation further enhances robustness across skills.