AbstractPrompt tuning is an efficient method for adapting large language models, and Soft Prompt Transfer (SPoT) further narrows the gap between prompt tuning and full model tuning by transferring prompts learned from source tasks to target tasks. It is nevertheless difficult and expensive to identify the source task that provides optimal prompts. In this work, we propose to learn a shared latent space which captures a set of basis skills from a mixture of source tasks. Given an instance, its embedding queries the latent space, yielding a basis skill vector. This vector generates soft prompts, via a lightweight prompt generator, which modulates a frozen model. The latent space and prompt transformation are learned end-to-end by training on source tasks. Transfer learning from source tasks to a target task simply amounts to finetuning the prompt generator, accounting for roughly 0.3% parameters of the frozen backbone model, while the shared latent space is also frozen in finetuning. Our approach outperforms prior soft prompt methods by a significant margin on a variety of tasks such as NLI, sentence completion, QA, conference resolution, word sense disambiguation. We also find, on various model scales, our method achieves competitive performance compared to finetuning the full model.