Title: Compositional Models: Multi-Task Learning and Knowledge Transfer with Modular Networks. Abstract: Conditional computation and modular networks have been recently proposed for multitask learning and other problems as a way to decompose problem solving into multiple reusable computational blocks. We propose a novel fully-differentiable approach for learning modular networks.In our method, the modules can be invoked repeatedly and allow knowledge transfer to novel tasks by adjusting the order of computation. This allows soft weight sharing between tasks with only a small increase in the number of parameters. We show that our method leads to interpretable self-organization of modules in case of multi-task learning, transfer learning and domain adaptation while achieving competitive results on those tasks. From practical perspective, our approach allows to: (a) reuse existing modules for learning new task by adjusting the computation order, (b) use it for unsupervised multi-source domain adaptation to illustrate that adaptation to unseen data can be achieved by only manipulating the order of pretrained modules, (c) show how our approach can be used to increase accuracy of existing architectures for image classification tasks such as ImageNet, without any parameter increase, by reusing the same block multiple times.