  The in-context learning ability of large language models (LLMs) enables them
to generalize to novel downstream tasks with relatively few labeled examples.
However, they require enormous computational resources to be deployed.
Alternatively, smaller models can solve specific tasks if fine-tuned with
enough labeled examples. These examples, however, are expensive to obtain. In
pursuit of the best of both worlds, we study synthetic data generation of
fine-tuning training data via fine-tuned teacher LLMs to improve the downstream
performance of much smaller models. In four text classification and two text
generation tasks, we find that both data generation and annotation dramatically
improve the respective downstream model's performance, occasionally
necessitating only a minor fraction of the original training dataset.
