Title: Mint: Matrix-Interleaving for Multi-Task Learning. Abstract: Deep learning enables training of large and flexible function approximators from scratch at the cost of large amounts of data. Applications of neural networks often consider learning in the context of a single task. However, in many scenarios what we hope to learn is not just a single task, but a model that can be used to solve multiple different tasks. Such multi-task learning settings have the potential to improve data efficiency and generalization by sharing data and representations across tasks. However, in some challenging multi-task learning settings, particularly in reinforcement learning, it is very difficult to learn a single model that can solve all the tasks while realizing data efficiency and performance benefits. Learning each of the tasks independently from scratch can actually perform better in such settings, but it does not benefit from the representation sharing that multi-task learning can potentially provide. In this work, we develop an approach that endows a single model with the ability to represent both extremes: joint training and independent training. To this end, we introduce matrix-interleaving (Mint), a modification to standard neural network models that projects the activations for each task into a different learned subspace, represented by a per-task and per-layer matrix. By learning these matrices jointly with the other model parameters, the optimizer itself can decide how much to share representations between tasks. On three challenging multi-task supervised learning and reinforcement learning problems with varying degrees of shared task structure, we find that this model consistently matches or outperforms joint training and independent training, combining the best elements of both.