用数学训练启动大模型推理能力，再迁移到其他领域提升通用推理。
Reasoning Curriculum: Bootstrapping Broad LLM Reasoning from Math
- 分两阶段：先纯数学强化学习打基础，再跨领域联合优化
- 在多个模型上实现稳定推理提升，无需复杂奖励模型
- 适合想低成本提升模型推理能力的研究者和开发者
强化学习（RL）可激发大语言模型（LLMs）的强推理能力，但现有开源工作多集中于数学和代码。本文提出推理课程（Reasoning Curriculum），一种简单的两阶段课程：第一阶段通过简短冷启动和仅数学的强化学习，利用可验证奖励培养推理技能；第二阶段在混合领域数据上进行联合强化学习，实现技能迁移与巩固。该方法轻量且不依赖特定模型架构，仅需标准可验证性检查作为奖励。在Qwen3-4B和Llama-3.1-8B上对多领域任务评估显示，该方法带来持续性能提升。消融实验与认知技能分析表明，两个阶段均必要，且以数学为起点能显著增强解决复杂问题所需的认知行为。该方案提供了一种紧凑、易部署的通用推理增强路径。
原文摘要 · Abstract (English)
Reinforcement learning (RL) can elicit strong reasoning in large language models (LLMs), yet most open efforts focus on math and code. We propose Reasoning Curriculum, a simple two-stage curriculum that first elicits reasoning skills in pretraining-aligned domains such as math, then adapts and refines these skills across other domains via joint RL. Stage 1 performs a brief cold start and then math-only RL with verifiable rewards to develop reasoning skills. Stage 2 runs joint RL on mixed-domain data to transfer and consolidate these skills. The curriculum is minimal and backbone-agnostic, requiring no specialized reward models beyond standard verifiability checks. Evaluated on Qwen3-4B and Llama-3.1-8B over a multi-domain suite, reasoning curriculum yields consistent gains. Ablations and a cognitive-skill analysis indicate that both stages are necessary and that math-first elicitation increases cognitive behaviors important for solving complex problems. Reasoning Curriculum provides a compact, easy-to-adopt recipe for general reasoning.
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