  In question answering requiring common sense, language models (e.g., GPT-3)
have been used to generate text expressing background knowledge that helps
improve performance. Yet the cost of working with such models is very high; in
this work, we finetune smaller language models to generate useful intermediate
context, referred to here as elaborations. Our framework alternates between
updating two language models -- an elaboration generator and an answer
predictor -- allowing each to influence the other. Using less than 0.5% of the
parameters of GPT-3, our model outperforms alternatives with similar sizes and
closes the gap on GPT-3 on four commonsense question answering benchmarks.
Human evaluations show that the quality of the generated elaborations is high.
