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

Long-horizon reasoning in recent LLMs increasingly demands that the model switch between distinct skills inside a reasoning chain, such as a task that requires the model to first do a math derivation, then use 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 Skill²-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 Skill²-Bench surfaces a structural skill-switching gap: accuracy decreases monotonically with task-level skill entropy and drops by 5–30% when the same skill is exercised inside a cross-skill task rather than a single-skill question. 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 Skill²-Bench score from 34.4% to 68.4% and from 14.6% to 40.1% respectively, outperforming SFT and vanilla GRPO. 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.