Laying the Foundation First? Investigating the Generalization from Atomic Skills to Complex Reasoning Tasks

Abstract: Current LLMs 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.