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Instead, transfer\nlearning at a higher level of abstraction is needed. We propose Leap, a\nframework that achieves this by transferring knowledge across learning\nprocesses. We associate each task with a manifold on which the training process\ntravels from initialization to final parameters and construct a meta-learning\nobjective that minimizes the expected length of this path. Our framework\nleverages only information obtained during training and can be computed on the\nfly at negligible cost. We demonstrate that our framework outperforms competing\nmethods, both in meta-learning and transfer learning, on a set of computer\nvision tasks. 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