  Language models (LMs) can solve tasks such as answering questions about
tables or images by writing programs. However, using primitive functions often
leads to verbose and error-prone programs, and higher-level functions require
expert design. To enable better solutions without human labor, we ask code LMs
to curate reusable high-level functions, and use them to write solutions. We
present TROVE, a training-free method of inducing a verifiable and efficient
toolbox of functions, by generating via using, growing, and periodically
trimming the toolbox. On 11 datasets from math, table question answering, and
image reasoning tasks, TROVE consistently yields simpler solutions with higher
accuracy than baselines using CODELLAMA and previous methods using GPT, while
using 79-98% smaller toolboxes. TROVE further enables 31% faster and 13% more
accurate human verification than baselines. With the same pipeline, it creates
diverse functions for varied tasks and datasets, providing insights into their
individual characteristics.
