# Toward Skill-Native LLMs: Skill Entropy for Benchmarking and Training Long-Horizon Reasoning

arXiv: https://arxiv.org/abs/2608.05139 · HTML: https://mlsanity.com/paper/2608.05139/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 64 of its 71 references that are in the map.
- First posted on arXiv 5 Aug 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 64)

- [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)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [AgentBench: Evaluating LLMs as Agents](https://mlsanity.com/paper/2308.03688/) (2023)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Compositional Semantic Parsing on Semi-Structured Tables](https://mlsanity.com/paper/1508.00305/) (2015)
- [PaperBench: Evaluating AI's Ability to Replicate AI Research](https://mlsanity.com/paper/2504.01848/) (2025)
- [SkillsBench: Benchmarking How Well Agent Skills Work Across Diverse Tasks](https://mlsanity.com/paper/2602.12670/) (2026)
- [Evaluating Memory in LLM Agents via Incremental Multi-Turn Interactions](https://mlsanity.com/paper/2507.05257/) (2025)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [NATURAL PLAN: Benchmarking LLMs on Natural Language Planning](https://mlsanity.com/paper/2406.04520/) (2024)
- [BIG-Bench Extra Hard](https://mlsanity.com/paper/2502.19187/) (2025)
- [Thinkless: LLM Learns When to Think](https://mlsanity.com/paper/2505.13379/) (2025)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [WebSRC: A Dataset for Web-Based Structural Reading Comprehension](https://mlsanity.com/paper/2101.09465/) (2021)
- [Reinforcement Learning for Self-Improving Agent with Skill Library](https://mlsanity.com/paper/2512.17102/) (2025)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [Self-Distillation Zero: Self-Revision Turns Binary Rewards into Dense Supervision](https://mlsanity.com/paper/2604.12002/) (2026)
- [Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models](https://mlsanity.com/paper/2310.17567/) (2023)
- [SkillRouter: Skill Routing for LLM Agents at Scale](https://mlsanity.com/paper/2603.22455/) (2026)
- [RLVMR: Reinforcement Learning with Verifiable Meta-Reasoning Rewards for Robust Long-Horizon Agents](https://mlsanity.com/paper/2507.22844/) (2025)
- [OdysseyBench: Evaluating LLM Agents on Long-Horizon Complex Office Application Workflows](https://mlsanity.com/paper/2508.09124/) (2025)
- [SkillLearnBench: Benchmarking Continual Learning Methods for Agent Skill Generation on Real-World Tasks](https://mlsanity.com/paper/2604.20087/) (2026)

## Abstract (arXiv)

Long-horizon reasoning in recent LLMs demands that the model switch between distinct skills inside a reasoning chain, such as first doing a math derivation, then using the result to plan a schedule. We call such problems cross-skill long-horizon tasks: multi-step tasks whose steps require different reasoning skills and depend on earlier outputs. Existing benchmarks often evaluate individual skills, lacking a principled way to measure how well a model switches between skills. We address this gap from both the evaluation and training sides. We introduce Skill Entropy, a measure of the difficulty of switching from one skill to another. We then propose Skill^2-Bench, a benchmark of cross-skill long-horizon tasks built over 558 skills across 9 verifiable and open-ended domains. Each task is assigned a task-level skill-entropy score and grouped into three difficulty levels. Evaluating 8 frontier and 4 open-source models on Skill^2-Bench reveals a skill-switching gap: accuracy decreases on higher-entropy tasks. We then turn skill entropy from a benchmark scale into a training signal. We propose Skill-Entropy RL, an RL framework where the model predicts not only the answer at each step but also the skill used to produce it. The reward combines step-level correctness with a skill-entropy reward that measures the alignment between the model-predicted skill sequence and the gold skill sequence. On Qwen3-4B-Instruct and Qwen3-1.7B, Skill-Entropy RL improves the Skill^2-Bench score from 34.4% to 68.4% and from 14.6% to 40.1%, respectively, outperforming competitive baselines. The same pipeline can be applied to off-the-shelf training data such as OpenR1-Math, indicating that skill entropy is a reusable training signal. Code available at: https://github.com/Gen-Verse/Skill-Entropy-RL