  Recent methods have demonstrated that Large Language Models (LLMs) can solve
reasoning tasks better when they are encouraged to solve subtasks of the main
task first. In this paper we devise a similar strategy that breaks down
reasoning tasks into a problem decomposition phase and a problem solving phase
and show that the strategy is able to outperform a single stage solution.
Further, we hypothesize that the decomposition should be easier to distill into
a smaller model compared to the problem solving because the latter requires
large amounts of domain knowledge while the former only requires learning
general problem solving strategies. We propose methods to distill these two
capabilities and evaluate their impact on reasoning outcomes and inference
cost. We find that we can distill the problem decomposition phase and at the
same time achieve good generalization across tasks, datasets, and models.
However, it is harder to distill the problem solving capability without losing
performance and the resulting distilled model struggles with generalization.
These results indicate that by using smaller, distilled problem decomposition
models in combination with problem solving LLMs we can achieve reasoning with
cost-efficient inference and local adaptation.
