Current language models have demonstrated their capability to develop basic
reasoning, but struggle in more complicated reasoning tasks that require a
combination of atomic skills, such as math word problem requiring skills like
arithmetic and unit conversion. Previous methods either do not improve the
inherent atomic skills of models or not attempt to generalize the atomic skills
to complex reasoning tasks. In this paper, we first propose a probing framework
to investigate whether the atomic skill can spontaneously generalize to complex
reasoning tasks. Then, we introduce a hierarchical curriculum learning training
strategy to achieve better skill generalization. In our experiments, we find
that atomic skills can not spontaneously generalize to compositional tasks. By
leveraging hierarchical curriculum learning, we successfully induce
generalization, significantly improve the performance of open-source LMs on
complex reasoning tasks. Promisingly, the skill generalization exhibit
effective in cross-dataset and cross-domain scenarios. Complex reasoning can
also help enhance atomic skills. Our findings offer valuable guidance for
designing better training strategies for complex reasoning tasks.

目前的语言模型在基本推理方面已经展示了它们的能力，但在需要结合原子技能的更复杂的推理任务上却存在困难，比如需要算术和单位转换等技能的数学问题。本文首先提出了一个探测框架，以研究原子技能是否能自主泛化到复杂推理任务。然后，引入了分层课程学习训练策略来实现更好的技能泛化。在我们的实验中，我们发现原子技能无法自主泛化到组合任务。通过利用分层课程学习，我们成功诱导了泛化，在复杂推理任务上显著提高了开源语言模型的性能。有希望的是，这种技能的泛化在跨数据集和跨领域的场景中也是有效的。复杂推理也有助于增强原子技能。我们的研究结果为设计更好的复杂推理任务训练策略提供了有价值的指导。