  An effective approach in meta-learning is to utilize multiple "train tasks"
to learn a good initialization for model parameters that can help solve unseen
"test tasks" with very few samples by fine-tuning from this initialization.
Although successful in practice, theoretical understanding of such methods is
limited. This work studies an important aspect of these methods: splitting the
data from each task into train (support) and validation (query) sets during
meta-training. Inspired by recent work (Raghu et al., 2020), we view such
meta-learning methods through the lens of representation learning and argue
that the train-validation split encourages the learned representation to be
low-rank without compromising on expressivity, as opposed to the non-splitting
variant that encourages high-rank representations. Since sample efficiency
benefits from low-rankness, the splitting strategy will require very few
samples to solve unseen test tasks. We present theoretical results that
formalize this idea for linear representation learning on a subspace
meta-learning instance, and experimentally verify this practical benefit of
splitting in simulations and on standard meta-learning benchmarks.
