Abstract: Given the increasing number of parameter-efficient adapters of large language models (LLMs), how can we reuse them to improve LLM performance on new tasks? We study how to best build a *library* of adapters given multi-task data and devise techniques for both *zero-shot* and *supervised* task generalization through *routing* in such library. We benchmark existing approaches to build this library and introduce model-based clustering, $\texttt{MBC}$, a method that groups tasks based on the similarity of their adapter parameters, indirectly optimizing for transfer across the multi-task dataset. In order to reuse the library, we present a novel zero-shot routing mechanism, $\texttt{Arrow}$, which enables dynamic selection of the most relevant adapters for new inputs without the need for retraining. We experiment with several LLMs, such as Phi-2 and Mistral, on a wide array of held-out tasks, verifying that MBC-based adapters and Arrow routing lead to superior generalization to new tasks. Thus, we make steps towards creating modular, adaptable LLMs that can match or outperform traditional joint training.