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The computer vision community is witnessing an unprecedented rate of new tasks being proposed and addressed, thanks to the deep convolutional networks' capability to find complex mappings from X to Y. The advent of each task often accompanies the release of a large-scale annotated dataset, for supervised training of deep network. However, it is expensive and time-consuming to manually label sufficient amount of training data. Therefore, it is important to develop algorithms that can leverage off-the-shelf labeled dataset to learn useful knowledge for the target task. While previous works mostly focus on transfer learning from a single source, we study multi-source transfer across domains and tasks (MS-DTT), in a semi-supervised setting. We propose GradMix, a model-agnostic method applicable to any model trained with gradient-based learning rule, to transfer knowledge via gradient descent by weighting and mixing the gradients from all sources during training. GradMix follows a meta-learning objective, which assigns layer-wise weights to the source gradients, such that the combined gradient follows the direction that minimize the loss for a small set of samples from the target dataset. In addition, we propose to adaptively adjust the learning rate for each mini-batch based on its importance to the target task, and a pseudo-labeling method to leverage the unlabeled samples in the target domain. We conduct MS-DTT experiments on two tasks: digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method against multiple baselines.