Meta-learning models transfer the knowledge acquired from previous tasks to quickly learn new ones. They are trained on benchmarks with a fixed number of data points per task. This number is usually arbitrary and it is unknown how it affects performance at testing. Since labelling of data is expensive, finding the optimal allocation of labels across training tasks may reduce costs. Given a fixed budget of labels, should we use a small number of highly labelled tasks, or many tasks with few labels each? Should we allocate more labels to some tasks and less to others?
We show that: 1) If tasks are homogeneous, there is a uniform optimal allocation, whereby all tasks get the same amount of data; 2) At fixed budget, there is a trade-off between number of tasks and number of data points per task, with a unique solution for the optimum; 3) When trained separately, harder task should get more data, at the cost of a smaller number of tasks; 4) When training on a mixture of easy and hard tasks, more data should be allocated to easy tasks. Interestingly, Neuroscience experiments have shown that human visual skills also transfer better from easy tasks. We prove these results mathematically on mixed linear regression, and we show empirically that the same results hold for few-shot image classification on CIFAR-FS and mini-ImageNet. Our results provide guidance for allocating labels across tasks when collecting data for meta-learning.
We introduce CAFLOW, a new diverse image-to-image translation model that simultaneously leverages the power of auto-regressive modeling and the modeling efficiency of conditional normalizing flows. We transform the conditioning image into a sequence of latent encodings using a multi-scale normalizing flow and repeat the process for the conditioned image. We model the conditional distribution of the latent encodings by modeling the auto-regressive distributions with an efficient multi-scale normalizing flow, where each conditioning factor affects image synthesis at its respective resolution scale. Our proposed framework performs well on a range of image-to-image translation tasks. It outperforms former designs of conditional flows because of its expressive auto-regressive structure.Preprint. Under review.
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