Abstract: Multi-task learning shares information between related tasks, sometimes reducing the number of parameters required. State-of-the-art results across multiple natural language understanding tasks in the GLUE benchmark have previously used transfer from a single large task: unsupervised pre-training with BERT, where a separate BERT model was fine-tuned for each task. We explore multi-task approaches that share a \hbox{single} BERT model with a small number of additional task-specific parameters. Using new adaptation modules, PALs or `projected attention layers', we match the performance of separately fine-tuned models on the GLUE benchmark with $\approx$7 times fewer parameters, and obtain state-of-the-art results on the Recognizing Textual Entailment dataset.