# Unified Data Selection for LLM Reasoning

arXiv: https://arxiv.org/abs/2605.22389 · HTML: https://mlsanity.com/paper/2605.22389/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 31 of its 60 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 31)

- [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)
- [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)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [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)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching](https://mlsanity.com/paper/2503.05179/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Algorithm of Thoughts: Enhancing Exploration of Ideas in Large Language Models](https://mlsanity.com/paper/2308.10379/) (2023)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [Unlocking Multimodal Mathematical Reasoning via Process Reward Model](https://mlsanity.com/paper/2501.04686/) (2025)
- [Self-Reflection in LLM Agents: Effects on Problem-Solving Performance](https://mlsanity.com/paper/2405.06682/) (2024)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)
- [Data-Efficient Finetuning Using Cross-Task Nearest Neighbors](https://mlsanity.com/paper/2212.00196/) (2022)
- [In-Context Alignment: Chat with Vanilla Language Models Before Fine-Tuning](https://mlsanity.com/paper/2308.04275/) (2023)
- [When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale](https://mlsanity.com/paper/2309.04564/) (2023)

## Built on by (most cited first, 3 of 3)

- [CausalMix: Data Mixture as Causal Inference for Language Model Training](https://mlsanity.com/paper/2607.01104/) (2026)
- [Scalable, Transferable Meta-network for Data Selection Requires a Different Loss (and Why the Obvious Choice is Problematic)](https://mlsanity.com/paper/2610.02092/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)

## Abstract (arXiv)

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.