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This work introduces a new multi-task, parameter-efficient language model (LM) tuning method that learns to transfer knowledge across different tasks via a mixture of soft prompts-small prefix embedding vectors pre-trained for different tasks. Our method, called ATTEMPT (ATTEntional Mixtures of Prompt Tuning), obtains source prompts as encodings of large-scale source tasks into a small number of parameters and trains an attention module to interpolate the source prompts and a newly initialized target prompt for every instance in the target task. During training, only the target task prompt and the attention weights, which are shared between tasks in multi-task training, are updated, while the original LM and source prompts are intact. ATTEMPT is highly parameter-efficient (e.g., updates 2,300 times fewer parameters than full fine-tuning) while achieving high task performance using knowledge from high-resource tasks. Moreover, it is modular using pre-trained soft prompts, and can flexibly add or remove source prompts for effective knowledge transfer. Our experimental results across 21 diverse NLP datasets show that ATTEMPT significantly outperforms prompt tuning and outperforms or matches fully fine-tuned or other parameter-efficient tuning approaches that use over ten times more parameters. Finally, ATTEMPT outperforms previous work in few-shot learning settings.