  There is a rapidly growing number of open-source Large Language Models (LLMs)
and benchmark datasets to compare them. While some models dominate these
benchmarks, no single model typically achieves the best accuracy in all tasks
and use cases. In this work, we address the challenge of selecting the best LLM
out of a collection of models for new tasks. We propose a new formulation for
the problem, in which benchmark datasets are repurposed to learn a "router"
model for this LLM selection, and we show that this problem can be reduced to a
collection of binary classification tasks. We demonstrate the utility and
limitations of learning model routers from various benchmark datasets, where we
consistently improve performance upon using any single model for all tasks.
