Title: Variational Multi-Task Learning. Abstract: Multi-task learning aims to improve the overall performance of a set of tasks by leveraging their relatedness. When training data is limited using priors is pivotal, but currently this is done in ad-hoc ways. In this paper, we develop variational multi-task learning - VMTL, a general probabilistic inference framework for simultaneously learning multiple related tasks. We cast multi-task learning as a variational Bayesian inference problem, which enables task relatedness to be explored in a principled way by specifying priors. We introduce Gumbel-softmax priors to condition the prior of each task on related tasks. Each prior is represented as a mixture of variational posteriors of other related tasks and the mixing weights are learned in a data-driven manner for each individual task. The posteriors over representations and classifiers are inferred jointly for all tasks and individual tasks are able to improve their performance by using the shared inductive bias. Experimental results demonstrate that VMTL is able to tackle challenging multi-task learning with limited training data well, and it achieves state-of-the-art performance on four benchmarks, consistently surpassing previous methods.